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Sample records for two-dimensional lattice boltzmann

  1. Two-dimensional lattice Boltzmann model for magnetohydrodynamics.

    Science.gov (United States)

    Schaffenberger, Werner; Hanslmeier, Arnold

    2002-10-01

    We present a lattice Boltzmann model for the simulation of two-dimensional magnetohydro dynamic (MHD) flows. The model is an extension of a hydrodynamic lattice Boltzman model with 9 velocities on a square lattice resulting in a model with 17 velocities. Earlier lattice Boltzmann models for two-dimensional MHD used a bidirectional streaming rule. However, the use of such a bidirectional streaming rule is not necessary. In our model, the standard streaming rule is used, allowing smaller viscosities. To control the viscosity and the resistivity independently, a matrix collision operator is used. The model is then applied to the Hartmann flow, giving reasonable results.

  2. Two Dimensional Lattice Boltzmann Method for Cavity Flow Simulation

    Directory of Open Access Journals (Sweden)

    Panjit MUSIK

    2004-01-01

    Full Text Available This paper presents a simulation of incompressible viscous flow within a two-dimensional square cavity. The objective is to develop a method originated from Lattice Gas (cellular Automata (LGA, which utilises discrete lattice as well as discrete time and can be parallelised easily. Lattice Boltzmann Method (LBM, known as discrete Lattice kinetics which provide an alternative for solving the Navier–Stokes equations and are generally used for fluid simulation, is chosen for the study. A specific two-dimensional nine-velocity square Lattice model (D2Q9 Model is used in the simulation with the velocity at the top of the cavity kept fixed. LBM is an efficient method for reproducing the dynamics of cavity flow and the results which are comparable to those of previous work.

  3. Two-dimensional lattice Boltzmann model for compressible flows with high Mach number

    Science.gov (United States)

    Gan, Yanbiao; Xu, Aiguo; Zhang, Guangcai; Yu, Xijun; Li, Yingjun

    2008-03-01

    In this paper we present an improved lattice Boltzmann model for compressible Navier-Stokes system with high Mach number. The model is composed of three components: (i) the discrete-velocity-model by M. Watari and M. Tsutahara [Phys. Rev. E 67 (2003) 036306], (ii) a modified Lax-Wendroff finite difference scheme where reasonable dissipation and dispersion are naturally included, (iii) artificial viscosity. The improved model is convenient to compromise the high accuracy and stability. The included dispersion term can effectively reduce the numerical oscillation at discontinuity. The added artificial viscosity helps the scheme to satisfy the von Neumann stability condition. Shock tubes and shock reflections are used to validate the new scheme. In our numerical tests the Mach numbers are successfully increased up to 20 or higher. The flexibility of the new model makes it suitable for tracking shock waves with high accuracy and for investigating nonlinear nonequilibrium complex systems.

  4. Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow: Two-Dimensional Case

    Science.gov (United States)

    Gan, Yan-Biao; Xu, Ai-Guo; Zhang, Guang-Cai; Zhang, Ping; Zhang, Lei; Li, Ying-Jun

    2008-07-01

    Lattice Boltzmann (LB) modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 (2007) 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests: shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.

  5. Deformation of Two-Dimensional Nonuniform-Membrane Red Blood Cells Simulated by a Lattice Boltzmann Model

    Institute of Scientific and Technical Information of China (English)

    LI Hua-Bing; JIN Li; QIU Bing

    2008-01-01

    To study two-dimensional red blood cells deforming in a shear flow with the membrane nonuniform on the rigidity and mass, the membrane is discretized into equilength segments. The fluid inside and outside the red blood cell is simulated by the D2Q9 lattice Boltzmann model and the hydrodynamic forces exerted on the membrane from the inner and outer of the red blood cell are calculated by a stress-integration method. Through the global deviation from the curvature of uniform-membrane, we find that when the membrane is nonuniform on the rigidity, the deviation first decreases with the time increases and implies that the terminal profile of the red blood cell is static. To a red blood cell with the mass nonuniform on the membrane, the deviation becomes more large, and the mass distribution affects the profile of the two sides of the flattened red blood cell in a shear flow.

  6. Shear viscosity of a two-dimensional emulsion of drops using a multiple-relaxation-time-step lattice Boltzmann method.

    Science.gov (United States)

    Halliday, I; Xu, X; Burgin, K

    2017-02-01

    An extended Benzi-Dellar lattice Boltzmann equation scheme [R. Benzi, S. Succi, and M. Vergassola, Europhys. Lett. 13, 727 (1990)EULEEJ0295-507510.1209/0295-5075/13/8/010; R. Benzi, S. Succi, and M. Vergassola, Phys. Rep. 222, 145 (1992)PRPLCM0370-157310.1016/0370-1573(92)90090-M; P. J. Dellar, Phys. Rev. E 65, 036309 (2002)1063-651X10.1103/PhysRevE.65.036309] is developed and applied to the problem of confirming, at low Re and drop fluid concentration, c, the variation of effective shear viscosity, η_{eff}=η_{1}[1+f(η_{1},η_{2})c], with respect to c for a sheared, two-dimensional, initially crystalline emulsion [here η_{1} (η_{2}) is the fluid (drop fluid) shear viscosity]. Data obtained with our enhanced multicomponent lattice Boltzmann method, using average shear stress and hydrodynamic dissipation, agree well once appropriate corrections to Landau's volume average shear stress [L. Landau and E. M. Lifshitz, Fluid Mechanics, 6th ed. (Pergamon, London, 1966)] are applied. Simulation results also confirm the expected form for f(η_{i},η_{2}), and they provide a reasonable estimate of its parameters. Most significantly, perhaps, the generality of our data supports the validity of Taylor's disputed simplification [G. I. Taylor, Proc. R. Soc. London, Ser. A 138, 133 (1932)1364-502110.1098/rspa.1932.0175] to reduce the effect of one hydrodynamic boundary condition (on the continuity of the normal contraction of stress) to an assumption that interfacial tension is sufficiently strong to maintain a spherical drop shape.

  7. Shear viscosity of a two-dimensional emulsion of drops using a multiple-relaxation-time-step lattice Boltzmann method

    Science.gov (United States)

    Halliday, I.; Xu, X.; Burgin, K.

    2017-02-01

    An extended Benzi-Dellar lattice Boltzmann equation scheme [R. Benzi, S. Succi, and M. Vergassola, Europhys. Lett. 13, 727 (1990), 10.1209/0295-5075/13/8/010; R. Benzi, S. Succi, and M. Vergassola, Phys. Rep. 222, 145 (1992), 10.1016/0370-1573(92)90090-M; P. J. Dellar, Phys. Rev. E 65, 036309 (2002), 10.1103/PhysRevE.65.036309] is developed and applied to the problem of confirming, at low Re and drop fluid concentration, c , the variation of effective shear viscosity, ηeff=η1[1 +f (η1,η2) c ] , with respect to c for a sheared, two-dimensional, initially crystalline emulsion [here η1 (η2) is the fluid (drop fluid) shear viscosity]. Data obtained with our enhanced multicomponent lattice Boltzmann method, using average shear stress and hydrodynamic dissipation, agree well once appropriate corrections to Landau's volume average shear stress [L. Landau and E. M. Lifshitz, Fluid Mechanics, 6th ed. (Pergamon, London, 1966)] are applied. Simulation results also confirm the expected form for f (ηi,η2) , and they provide a reasonable estimate of its parameters. Most significantly, perhaps, the generality of our data supports the validity of Taylor's disputed simplification [G. I. Taylor, Proc. R. Soc. London, Ser. A 138, 133 (1932), 10.1098/rspa.1932.0175] to reduce the effect of one hydrodynamic boundary condition (on the continuity of the normal contraction of stress) to an assumption that interfacial tension is sufficiently strong to maintain a spherical drop shape.

  8. Local membrane length conservation in two-dimensional vesicle simulation using a multicomponent lattice Boltzmann equation method.

    Science.gov (United States)

    Halliday, I; Lishchuk, S V; Spencer, T J; Pontrelli, G; Evans, P C

    2016-08-01

    We present a method for applying a class of velocity-dependent forces within a multicomponent lattice Boltzmann equation simulation that is designed to recover continuum regime incompressible hydrodynamics. This method is applied to the problem, in two dimensions, of constraining to uniformity the tangential velocity of a vesicle membrane implemented within a recent multicomponent lattice Boltzmann simulation method, which avoids the use of Lagrangian boundary tracers. The constraint of uniform tangential velocity is carried by an additional contribution to an immersed boundary force, which we derive here from physical arguments. The result of this enhanced immersed boundary force is to apply a physically appropriate boundary condition at the interface between separated lattice fluids, defined as that region over which the phase-field varies most rapidly. Data from this enhanced vesicle boundary method are in agreement with other data obtained using related methods [e.g., T. Krüger, S. Frijters, F. Günther, B. Kaoui, and J. Harting, Eur. Phys. J. 222, 177 (2013)10.1140/epjst/e2013-01834-y] and underscore the importance of a correct vesicle membrane condition.

  9. General velocity, pressure, and initial condition for two-dimensional and three-dimensional lattice Boltzmann simulations

    Science.gov (United States)

    Mohammadipour, Omid Reza; Niazmand, Hamid; Succi, Sauro

    2017-03-01

    In this paper, an alternative approach to implement initial and boundary conditions in the lattice Boltzmann method is presented. The main idea is to approximate the nonequilibrium component of distribution functions as a third-order power series in the lattice velocities and formulate a procedure to determine boundary node distributions by using fluid variables, consistent with such an expansion. The velocity shift associated with the body force effects is included in this scheme, along with an approximation to determine the mass density in complex geometries. Different strategies based on the present scheme are developed to implement velocity and pressure conditions for arbitrarily shaped boundaries, using the D2Q9, D3Q15, D3Q19 and D3Q27 lattices, in two and three space dimensions, respectively. The proposed treatment is tested against several well-established problems, showing second-order spatial accuracy and often improved behavior as compared to various existing methods, with no appreciable computational overhead.

  10. Parametric lattice Boltzmann method

    Science.gov (United States)

    Shim, Jae Wan

    2017-06-01

    The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the Maxwell-Boltzmann distribution. The ranges of flow velocity and temperature providing positive valued distributions vary with regulating discrete velocities as parameters. New isothermal and thermal compressible models are proposed for flows of the level of the isothermal and thermal compressible Navier-Stokes equations. Thermal compressible shock tube flows are simulated by only five on-lattice discrete velocities. Two-dimensional isothermal and thermal vortices provoked by the Kelvin-Helmholtz instability are simulated by the parametric models.

  11. Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

    Institute of Scientific and Technical Information of China (English)

    Chai Zhen-Hua; Shi Bao-Chang; Zheng Lin

    2006-01-01

    By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number (Re) flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.

  12. Lattice Boltzmann Stokesian dynamics.

    Science.gov (United States)

    Ding, E J

    2015-11-01

    Lattice Boltzmann Stokesian dynamics (LBSD) is presented for simulation of particle suspension in Stokes flows. This method is developed from Stokesian dynamics (SD) with resistance and mobility matrices calculated using the time-independent lattice Boltzmann algorithm (TILBA). TILBA is distinguished from the traditional lattice Boltzmann method (LBM) in that a background matrix is generated prior to the calculation. The background matrix, once generated, can be reused for calculations for different scenarios, thus the computational cost for each such subsequent calculation is significantly reduced. The LBSD inherits the merits of the SD where both near- and far-field interactions are considered. It also inherits the merits of the LBM that the computational cost is almost independent of the particle shape.

  13. A hybrid wavelet-based adaptive immersed boundary finite-difference lattice Boltzmann method for two-dimensional fluid-structure interaction

    Science.gov (United States)

    Cui, Xiongwei; Yao, Xiongliang; Wang, Zhikai; Liu, Minghao

    2017-03-01

    A second generation wavelet-based adaptive finite-difference Lattice Boltzmann method (FD-LBM) is developed in this paper. In this approach, the adaptive wavelet collocation method (AWCM) is firstly, to the best of our knowledge, incorporated into the FD-LBM. According to the grid refinement criterion based on the wavelet amplitudes of density distribution functions, an adaptive sparse grid is generated by the omission and addition of collocation points. On the sparse grid, the finite differences are used to approximate the derivatives. To eliminate the special treatments in using the FD-based derivative approximation near boundaries, the immersed boundary method (IBM) is also introduced into FD-LBM. By using the adaptive technique, the adaptive code requires much less grid points as compared to the uniform-mesh code. As a consequence, the computational efficiency can be improved. To justify the proposed method, a series of test cases, including fixed boundary cases and moving boundary cases, are invested. A good agreement between the present results and the data in previous literatures is obtained, which demonstrates the accuracy and effectiveness of the present AWCM-IB-LBM.

  14. Two-Dimensional Toda-Heisenberg Lattice

    Directory of Open Access Journals (Sweden)

    Vadim E. Vekslerchik

    2013-06-01

    Full Text Available We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy, and derive its N-soliton solutions.

  15. Two-dimensional subwavelength plasmonic lattice solitons

    CERN Document Server

    Ye, F; Hu, B; Panoiu, N C

    2010-01-01

    We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two classes of 2D PLSs families, namely, fundamental and vortical PLSs in both focusing and defocusing media. Their existence, stability, and subwavelength spatial confinement are studied in detai

  16. Lattice Boltzmann Model for Compressible Fluid on a Square Lattice

    Institute of Scientific and Technical Information of China (English)

    SUN Cheng-Hai

    2000-01-01

    A two-level four-direction lattice Boltzmann model is formulated on a square lattice to simulate compressible flows with a high Mach number. The particle velocities are adaptive to the mean velocity and internal energy. Therefore, the mean flow can have a high Mach number. Due to the simple form of the equilibrium distribution, the 4th order velocity tensors are not involved in the calculations. Unlike the standard lattice Boltzmann model, o special treatment is need for the homogeneity of 4th order velocity tensors on square lattices. The Navier-Stokes equations were derived by the Chapman-Enskog method from the BGK Boltzmann equation. The model can be easily extended to three-dimensional cubic lattices. Two-dimensional shock-wave propagation was simulated

  17. Crystallographic Lattice Boltzmann Method

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    Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh

    2016-01-01

    Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098

  18. Lattice Boltzmann model for nanofluids

    Energy Technology Data Exchange (ETDEWEB)

    Xuan Yimin; Yao Zhengping [Nanjing University of Science and Technology, School of Power Engineering, Nanjing (China)

    2005-01-01

    A nanofluid is a particle suspension that consists of base liquids and nanoparticles and has great potential for heat transfer enhancement. By accounting for the external and internal forces acting on the suspended nanoparticles and interactions among the nanoparticles and fluid particles, a lattice Boltzmann model is proposed for simulating flow and energy transport processes inside the nanofluids. First, we briefly introduce the conventional lattice Boltzmann model for multicomponent systems. Then, we discuss the irregular motion of the nanoparticles and inherent dynamic behavior of nanofluids and describe a lattice Boltzmann model for simulating nanofluids. Finally, we conduct some calculations for the distribution of the suspended nanoparticles. (orig.)

  19. Fluctuating multicomponent lattice Boltzmann model.

    Science.gov (United States)

    Belardinelli, D; Sbragaglia, M; Biferale, L; Gross, M; Varnik, F

    2015-02-01

    Current implementations of fluctuating lattice Boltzmann equations (FLBEs) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the orthonormal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and nonideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.

  20. Spatiotemporal surface solitons in two-dimensional photonic lattices.

    Science.gov (United States)

    Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S

    2007-11-01

    We analyze spatiotemporal light localization in truncated two-dimensional photonic lattices and demonstrate the existence of two-dimensional surface light bullets localized in the lattice corners or the edges. We study the families of the spatiotemporal surface solitons and their properties such as bistability and compare them with the modes located deep inside the photonic lattice.

  1. Hybrid lattice Boltzmann method on overlapping grids.

    Science.gov (United States)

    Di Ilio, G; Chiappini, D; Ubertini, S; Bella, G; Succi, S

    2017-01-01

    In this work, a hybrid lattice Boltzmann method (HLBM) is proposed, where the standard lattice Boltzmann implementation based on the Bhatnagar-Gross-Krook (LBGK) approximation is combined together with an unstructured finite-volume lattice Boltzmann model. The method is constructed on an overlapping grid system, which allows the coexistence of a uniform lattice nodes spacing and a coordinate-free lattice structure. The natural adaptivity of the hybrid grid system makes the method particularly suitable to handle problems involving complex geometries. Moreover, the provided scheme ensures a high-accuracy solution near walls, given the capability of the unstructured submodel of achieving the desired level of refinement in a very flexible way. For these reasons, the HLBM represents a prospective tool for solving multiscale problems. The proposed method is here applied to the benchmark problem of a two-dimensional flow past a circular cylinder for a wide range of Reynolds numbers and its numerical performances are measured and compared with the standard LBGK ones.

  2. Lattice Boltzmann solver of Rossler equation

    Institute of Scientific and Technical Information of China (English)

    GuangwuYAN; LiRUAN

    2000-01-01

    We proposed a lattice Boltzmann model for the Rossler equation. Using a method of multiscales in the lattice Boltzmann model, we get the diffusion reaction as a special case. If the diffusion effect disappeared, we can obtain the lattice Boltzmann solution of the Rossler equation on the mesescopic scale. The numerical results show the method can be used to simulate Rossler equation.

  3. Spatiotemporal dissipative solitons in two-dimensional photonic lattices.

    Science.gov (United States)

    Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S

    2008-11-01

    We analyze spatiotemporal dissipative solitons in two-dimensional photonic lattices in the presence of gain and loss. In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, we demonstrate the existence of novel classes of two-dimensional spatiotemporal dissipative lattice solitons, which also include surface solitons located in the corners or at the edges of the truncated two-dimensional photonic lattice. We find the domains of existence and stability of such spatiotemporal dissipative solitons in the relevant parameter space, for both on-site and intersite lattice solitons. We show that the on-site solitons are stable in the whole domain of their existence, whereas most of the intersite solitons are unstable. We describe the scenarios of the instability-induced dynamics of dissipative solitons in two-dimensional lattices.

  4. Noise source identification with the lattice Boltzmann method.

    Science.gov (United States)

    Vergnault, Etienne; Malaspinas, Orestis; Sagaut, Pierre

    2013-03-01

    In this paper the sound source identification problem is addressed with the use of the lattice Boltzmann method. To this aim, a time-reversed problem coupled to a complex differentiation method is used. In order to circumvent the inherent instability of the time-reversed lattice Boltzmann scheme, a method based on a split of the lattice Boltzmann equation into a mean and a perturbation component is used. Lattice Boltzmann method formulation around an arbitrary base flow is recalled and specific applications to acoustics are presented. The implementation of the noise source detection method for two-dimensional weakly compressible (low Mach number) flows is discussed, and the applicability of the method is demonstrated.

  5. Two dimensional axisymmetric smooth lattice Ricci flow

    CERN Document Server

    Brewin, Leo

    2015-01-01

    A lattice based method will be presented for numerical investigations of Ricci flow. The method will be applied to the particular case of 2-dimensional axially symmetric initial data on manifolds with S^2 topology. Results will be presented that show that the method works well and agrees with results obtained using contemporary finite difference methods.

  6. Analytical solutions of the lattice Boltzmann BGK model

    CERN Document Server

    Zou, Q; Doolen, G D; Zou, Qisu; Hou, Shuling; Doolen, Gary D.

    1995-01-01

    Abstract: Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time representation of these two flows without any approximation.

  7. Pseudo-two-dimensional random dimer lattices

    Energy Technology Data Exchange (ETDEWEB)

    Naether, U., E-mail: naether@unizar.es [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC – Universidad de Zaragoza, 50009 Zaragoza (Spain); Mejía-Cortés, C.; Vicencio, R.A. [Departamento de Física and MSI – Nucleus for Advanced Optics, Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago (Chile)

    2015-06-05

    We study the long-time wave transport in correlated and uncorrelated disordered 2D arrays. When a separation of dimensions is applied to the model, we find that the previously predicted 1D random dimer phenomenology also appears in so-called pseudo-2D arrays. Therefore, a threshold behavior is observed in terms of the effective size for eigenmodes, as well as in long-time dynamics. A minimum system size is required to observe this threshold, which is very important when considering a possible experimental realization. For the long-time evolution, we find that for correlated lattices a super-diffusive long-range transport is observed. For completely uncorrelated disorder 2D transport becomes sub-diffusive within the localization length and for random binary pseudo-2D arrays localization is observed.

  8. Existence and Stability of Two-Dimensional Compact-Like Discrete Breathers in Discrete Two-Dimensional Monatomic Square Lattices

    Institute of Scientific and Technical Information of China (English)

    XU Quan; TIAN Qiang

    2007-01-01

    Two-dimensional compact-like discrete breathers in discrete two-dimensional monatomic square lattices are investigated by discussing a generafized discrete two-dimensional monatomic model.It is proven that the twodimensional compact-like discrete breathers exist not only in two-dimensional soft Ф4 potentials but also in hard two-dimensional Ф4 potentials and pure two-dimensional K4 lattices.The measurements of the two-dimensional compact-like discrete breather cores in soft and hard two-dimensional Ф4 potential are determined by coupling parameter K4,while those in pure two-dimensional K4 lattices have no coupling with parameter K4.The stabilities of the two-dimensional compact-like discrete breathers correlate closely to the coupling parameter K4 and the boundary condition of lattices.

  9. Explicit finite-difference lattice Boltzmann method for curvilinear coordinates.

    Science.gov (United States)

    Guo, Zhaoli; Zhao, T S

    2003-06-01

    In this paper a finite-difference-based lattice Boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method [R. Mei and W. Shyy, J. Comput. Phys. 143, 426 (1998)] in which the collision term of the Boltzmann Bhatnagar-Gross-Krook equation for discrete velocities is treated implicitly. In the present method, the implicitness of the numerical scheme is removed by introducing a distribution function different from that being used currently. As a result, an explicit finite-difference lattice Boltzmann method for curvilinear coordinates is obtained. The scheme is applied to a two-dimensional Poiseuille flow, an unsteady Couette flow, a lid-driven cavity flow, and a steady flow around a circular cylinder. The numerical results are in good agreement with the results of previous studies. Extensions to other lattice Boltzmann models based on nonuniform meshes are also discussed.

  10. Logarithmic divergent thermal conductivity in two-dimensional nonlinear lattices.

    Science.gov (United States)

    Wang, Lei; Hu, Bambi; Li, Baowen

    2012-10-01

    Heat conduction in three two-dimensional (2D) momentum-conserving nonlinear lattices are numerically calculated via both nonequilibrium heat-bath and equilibrium Green-Kubo algorithms. It is expected by mainstream theories that heat conduction in such 2D lattices is divergent and the thermal conductivity κ increases with lattice length N logarithmically. Our simulations for the purely quartic lattice firmly confirm it. However, very robust finite-size effects are observed in the calculations for the other two lattices, which well explain some existing studies and imply the extreme difficulties in observing their true asymptotic behaviors with affordable computation resources.

  11. SIMPLE LATTICE BOLTZMANN MODEL FOR TRAFFIC FLOWS

    Institute of Scientific and Technical Information of China (English)

    Yan Guangwu; Hu Shouxin

    2000-01-01

    A lattice Boltzmann model with 5-bit lattice for traffic flows is proposed.Using the Chapman-Enskog expansion and multi-scale technique,we obtain the higher-order moments of equilibrium distribution function.A simple traffic light problem is simulated by using the present lattice Boltzmann model,and the result agrees well with analytical solution.

  12. Numerical simulation for the Gross-Pitaevskii equation based on the lattice Boltzmann method

    Science.gov (United States)

    Wang, Huimin

    2017-09-01

    A lattice Boltzmann model for the Gross-Pitaevskii equation is proposed in this paper. Some numerical tests for one- and two-dimensional Gross-Pitaevskii equation have been conducted. The waves of the Gross-Pitaevskii equation are simulated. Numerical results show that the lattice Boltzmann method is an effective method for the wave of the Gross-Pitaevskii equation.

  13. Lattice Boltzmann model with nearly constant density.

    Science.gov (United States)

    Fang, Hai-ping; Wan, Rong-zheng; Lin, Zhi-fang

    2002-09-01

    An improved lattice Boltzmann model is developed to simulate fluid flow with nearly constant fluid density. The ingredient is to incorporate an extra relaxation for fluid density, which is realized by introducing a feedback equation in the equilibrium distribution functions. The pressure is dominated by the moving particles at a node, while the fluid density is kept nearly constant and explicit mass conservation is retained as well. Numerical simulation based on the present model for the (steady) plane Poiseuille flow and the (unsteady) two-dimensional Womersley flow shows a great improvement in simulation results over the previous models. In particular, the density fluctuation has been reduced effectively while achieving a relatively large pressure gradient.

  14. Lattice Boltzmann model for resistive relativistic magnetohydrodynamics

    CERN Document Server

    Mohseni, F; Succi, S; Herrmann, H J

    2015-01-01

    In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfv\\'en waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to $\\sigma^{-\\frac{1}{2}}$, $\\sigma$ being the conductivity, w...

  15. Lattice Boltzmann modeling of water entry problems

    Science.gov (United States)

    Zarghami, A.; Falcucci, G.; Jannelli, E.; Succi, S.; Porfiri, M.; Ubertini, S.

    2014-12-01

    This paper deals with the simulation of water entry problems using the lattice Boltzmann method (LBM). The dynamics of the free surface is treated through the mass and momentum fluxes across the interface cells. A bounce-back boundary condition is utilized to model the contact between the fluid and the moving object. The method is implemented for the analysis of a two-dimensional flow physics produced by a symmetric wedge entering vertically a weakly-compressible fluid at a constant velocity. The method is used to predict the wetted length, the height of water pile-up, the pressure distribution and the overall force on the wedge. The accuracy of the numerical results is demonstrated through comparisons with data reported in the literature.

  16. Lattice Boltzmann Large Eddy Simulation Model of MHD

    CERN Document Server

    Flint, Christopher

    2016-01-01

    The work of Ansumali \\textit{et al.}\\cite{Ansumali} is extended to Two Dimensional Magnetohydrodynamic (MHD) turbulence in which energy is cascaded to small spatial scales and thus requires subgrid modeling. Applying large eddy simulation (LES) modeling of the macroscopic fluid equations results in the need to apply ad-hoc closure schemes. LES is applied to a suitable mesoscopic lattice Boltzmann representation from which one can recover the MHD equations in the long wavelength, long time scale Chapman-Enskog limit (i.e., the Knudsen limit). Thus on first performing filter width expansions on the lattice Boltzmann equations followed by the standard small Knudsen expansion on the filtered lattice Boltzmann system results in a closed set of MHD turbulence equations provided we enforce the physical constraint that the subgrid effects first enter the dynamics at the transport time scales. In particular, a multi-time relaxation collision operator is considered for the density distribution function and a single rel...

  17. Lattice Boltzmann equation for relativistic quantum mechanics.

    Science.gov (United States)

    Succi, Sauro

    2002-03-15

    Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation.

  18. Dielectric-barrier discharges in two-dimensional lattice potentials

    CERN Document Server

    Sinclair, Josiah

    2011-01-01

    We use a pin-grid electrode to introduce a corrugated electrical potential into a planar dielectric-barrier discharge (DBD) system, so that the amplitude of the applied electric field has the profile of a two-dimensional square lattice. The lattice potential provides a template for the spatial distribution of plasma filaments in the system and has pronounced effects on the patterns that can form. The positions at which filaments become localized within the lattice unit cell vary with the width of the discharge gap. The patterns that appear when filaments either overfill or under-fill the lattice are reminiscent of those observed in other physical systems involving 2d lattices. We suggest that the connection between lattice-driven DBDs and other areas of physics may benefit from the further development of models that treat plasma filaments as interacting particles.

  19. Two-Dimensional Breather Lattice Solutions and Compact-Like Discrete Breathers and Their Stability in Discrete Two-Dimensional Monatomic β-FPU Lattice

    Institute of Scientific and Technical Information of China (English)

    XU Quan; TIAN Qiang

    2009-01-01

    We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for twodimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry's linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete twodimensional monatomic β-FPU lattice.

  20. Thermal cascaded lattice Boltzmann method

    CERN Document Server

    Fei, Linlin

    2016-01-01

    In this paper, a thermal cascaded lattice Boltzmann method (TCLBM) is developed in combination with the double-distribution-function (DDF) approach. A density distribution function relaxed by the cascaded scheme is employed to solve the flow field, and a total energy distribution function relaxed by the BGK scheme is used to solve temperature field, where two distribution functions are coupled naturally. The forcing terms are incorporated by means of central moments, which is consistent with the previous force scheme [Premnath \\emph{et al.}, Phys. Rev. E \\textbf{80}, 036702 (2009)] but the derivation is more intelligible and the evolution process is simpler. In the method, the viscous heat dissipation and compression work are taken into account, the Prandtl number and specific-heat ratio are adjustable, the external force is considered directly without the Boussinesq assumption, and the low-Mach number compressible flows can also be simulated. The forcing scheme is tested by simulating a steady Taylor-Green f...

  1. Stress Wave Propagation in Two-dimensional Buckyball Lattice

    Science.gov (United States)

    Xu, Jun; Zheng, Bowen

    2016-11-01

    Orderly arrayed granular crystals exhibit extraordinary capability to tune stress wave propagation. Granular system of higher dimension renders many more stress wave patterns, showing its great potential for physical and engineering applications. At nanoscale, one-dimensionally arranged buckyball (C60) system has shown the ability to support solitary wave. In this paper, stress wave behaviors of two-dimensional buckyball (C60) lattice are investigated based on square close packing and hexagonal close packing. We show that the square close packed system supports highly directional Nesterenko solitary waves along initially excited chains and hexagonal close packed system tends to distribute the impulse and dissipates impact exponentially. Results of numerical calculations based on a two-dimensional nonlinear spring model are in a good agreement with the results of molecular dynamics simulations. This work enhances the understanding of wave properties and allows manipulations of nanoscale lattice and novel design of shock mitigation and nanoscale energy harvesting devices.

  2. Topological states in two-dimensional hexagon lattice bilayers

    Science.gov (United States)

    Zhang, Ming-Ming; Xu, Lei; Zhang, Jun

    2016-10-01

    We investigate the topological states of the two-dimensional hexagon lattice bilayer. The system exhibits a quantum valley Hall (QVH) state when the interlayer interaction t⊥ is smaller than the nearest neighbor hopping energy t, and then translates to a trivial band insulator state when t⊥ / t > 1. Interestingly, the system is found to be a single-edge QVH state with t⊥ / t = 1. The topological phase transition also can be presented via changing bias voltage and sublattice potential in the system. The QVH states have different edge modes carrying valley current but no net charge current. The bias voltage and external electric field can be tuned easily in experiments, so the present results will provide potential application in valleytronics based on the two-dimensional hexagon lattice.

  3. Vibrational Properties of a Two-Dimensional Silica Kagome Lattice.

    Science.gov (United States)

    Björkman, Torbjörn; Skakalova, Viera; Kurasch, Simon; Kaiser, Ute; Meyer, Jannik C; Smet, Jurgen H; Krasheninnikov, Arkady V

    2016-12-27

    Kagome lattices are structures possessing fascinating magnetic and vibrational properties, but in spite of a large body of theoretical work, experimental realizations and investigations of their dynamics are scarce. Using a combination of Raman spectroscopy and density functional theory calculations, we study the vibrational properties of two-dimensional silica (2D-SiO2), which has a kagome lattice structure. We identify the signatures of crystalline and amorphous 2D-SiO2 structures in Raman spectra and show that, at finite temperatures, the stability of 2D-SiO2 lattice is strongly influenced by phonon-phonon interaction. Our results not only provide insights into the vibrational properties of 2D-SiO2 and kagome lattices in general but also suggest a quick nondestructive method to detect 2D-SiO2.

  4. Electronic Transmission Properties of Two-Dimensional Quasi-Lattice

    Institute of Scientific and Technical Information of China (English)

    侯志林; 傅秀军; 刘有延

    2002-01-01

    In the framework of the tight binding model, the electronic transmission properties of two-dimensional Penrose lattices with free boundary conditions are studied using the generalized eigenfunction method (Phys. Rev. B 60(1999)13444). The electronic transmission coefficients for Penrose lattices with different sizes and widths are calculated, and the result shows strong energy dependence because of the quasiperiodic structure and quantum coherent effect. Around the Fermi level E = 0, there is an energy region with zero transmission amplitudes,which suggests that the studied systems are insulating. The spatial distributions of several typical electronic states with different transmission coefficients are plotted to display the propagation process.

  5. Multiphase lattice Boltzmann methods theory and application

    CERN Document Server

    Huang, Haibo; Lu, Xiyun

    2015-01-01

    Theory and Application of Multiphase Lattice Boltzmann Methods presents a comprehensive review of all popular multiphase Lattice Boltzmann Methods developed thus far and is aimed at researchers and practitioners within relevant Earth Science disciplines as well as Petroleum, Chemical, Mechanical and Geological Engineering. Clearly structured throughout, this book will be an invaluable reference  on the current state of all popular multiphase Lattice Boltzmann Methods (LBMs). The advantages and disadvantages of each model are presented in an accessible manner to enable the reader to choose the

  6. Lattice Boltzmann approach for complex nonequilibrium flows.

    Science.gov (United States)

    Montessori, A; Prestininzi, P; La Rocca, M; Succi, S

    2015-10-01

    We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequilibrium flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with analytical and numerical solutions of the Boltzmann equation across the full range of Knudsen numbers, from the hydrodynamic regime to ballistic motion.

  7. Two-dimensional chiral topological superconductivity in Shiba lattices

    Science.gov (United States)

    Li, Jian; Neupert, Titus; Wang, Zhijun; MacDonald, A. H.; Yazdani, A.; Bernevig, B. Andrei

    2016-07-01

    The chiral p-wave superconductor is the archetypal example of a state of matter that supports non-Abelian anyons, a highly desired type of exotic quasiparticle. With this, it is foundational for the distant goal of building a topological quantum computer. While some candidate materials for bulk chiral superconductors exist, they are subject of an ongoing debate about their actual paring state. Here we propose an alternative route to chiral superconductivity, consisting of the surface of an ordinary superconductor decorated with a two-dimensional lattice of magnetic impurities. We furthermore identify a promising experimental platform to realize this proposal.

  8. Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.

    Science.gov (United States)

    Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J

    2015-08-01

    In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.

  9. The characters of nonlinear vibration in the two-dimensional discrete monoatomic lattice

    Institute of Scientific and Technical Information of China (English)

    XU Quan; TIAN Qiang

    2005-01-01

    The two-dimensional discrete monoatomic lattice is analyzed. Taking nearest-neighbor interaction into account, the characters of the nonlinear vibration in two-dimensional discrete monoatomic lattice are described by the two-dimensional cubic nonlinear Schrodinger equation. Considering the quartic nonlinear potential, the two-dimensional discrete-soliton trains and the solutions perturbed by the neck mode are presented.

  10. The Simulation of High Reynolds Number Cavity Flow Based on Fractional Volumetric Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    HAN Shan-ling; ZHU Ping; LIN Zhong-qin

    2005-01-01

    The fractional volumetric lattice Boltzmann method with much better stability was used to simulate two dimensional cavity flows. Because the effective viscosity was reduced by the fraction factor, it is very effective forsimulating high Reynolds number flows. Simulations were carried out on a uniform grids system. The stream lines and the velocity profiles obtained from the simulations agree well with the standard lattice Boltzmann method simulations. Comparisons of detailed flow patterns with other studies via location of vortex centers are also satisfactory.

  11. Conjugate heat transfer with the entropic lattice Boltzmann method.

    Science.gov (United States)

    Pareschi, G; Frapolli, N; Chikatamarla, S S; Karlin, I V

    2016-07-01

    A conjugate heat-transfer model is presented based on the two-population entropic lattice Boltzmann method. The present approach relies on the extension of Grad's boundary conditions to the two-population model for thermal flows, as well as on the appropriate exact conjugate heat-transfer condition imposed at the fluid-solid interface. The simplicity and efficiency of the lattice Boltzmann method (LBM), and in particular of the entropic multirelaxation LBM, are retained in the present approach, thus enabling simulations of turbulent high Reynolds number flows and complex wall boundaries. The model is validated by means of two-dimensional parametric studies of various setups, including pure solid conduction, conjugate heat transfer with a backward-facing step flow, and conjugate heat transfer with the flow past a circular heated cylinder. Further validations are performed in three dimensions for the case of a turbulent flow around a heated mounted cube.

  12. Lattice Boltzmann model for incompressible flows through porous media.

    Science.gov (United States)

    Guo, Zhaoli; Zhao, T S

    2002-09-01

    In this paper a lattice Boltzmann model is proposed for isothermal incompressible flow in porous media. The key point is to include the porosity into the equilibrium distribution, and add a force term to the evolution equation to account for the linear and nonlinear drag forces of the medium (the Darcy's term and the Forcheimer's term). Through the Chapman-Enskog procedure, the generalized Navier-Stokes equations for incompressible flow in porous media are derived from the present lattice Boltzmann model. The generalized two-dimensional Poiseuille flow, Couette flow, and lid-driven cavity flow are simulated using the present model. It is found the numerical results agree well with the analytical and/or the finite-difference solutions.

  13. The effect of surface roughness on rarefied gas flows by lattice Boltzmann method

    Institute of Scientific and Technical Information of China (English)

    Liu Chao-Feng; Ni Yu-Shan

    2008-01-01

    This paper studies the roughness effect combining with effects of rarefaction and compressibility by a lattice Boltzmann model for rarefied gas flows at high Knudsen numbers. By discussing the effect of the tangential momentum accommodation coefficient on the rough boundary condition, the lattice Boltzmann simulations of nitrogen and helium flows are performed in a two-dimensional microchannel with rough boundaries. The surface roughness effects in the microchannel on the velocity field, the mass flow rate and the friction coefficient are studied and analysed. Numerical results for the two gases in micro scale show different characteristics from macroscopic flows and demonstrate the feasibility of the lattice Boltzmann model in rarefied gas dynamics.

  14. Matrix-valued Quantum Lattice Boltzmann Method

    CERN Document Server

    Mendl, Christian B

    2013-01-01

    We develop a numerical framework for the quantum analogue of the "classical" lattice Boltzmann method (LBM), with the Maxwell-Boltzmann distribution replaced by the Fermi-Dirac function. To accommodate the spin density matrix, the distribution functions become 2x2-matrix valued. We show that the efficient, commonly used BGK approximation of the collision operator is valid in the present setting. The framework could leverage the principles of LBM for simulating complex spin systems, with applications to spintronics.

  15. How good is the Lattice Boltzmann method?

    Science.gov (United States)

    Kocheemoolayil, Joseph; Barad, Michael; Kiris, Cetin

    2016-11-01

    Conflicting opinions exist in literature regarding how efficient the lattice Boltzmann method is relative to high-order finite difference approximations of the Navier-Stokes equations on Cartesian meshes, especially at high Mach numbers. We address the question from the pragmatic viewpoint of a practitioner. Dispersion, dissipation and aliasing errors of various lattice Boltzmann models are systematically quantified. The number of floating point operations and memory required for a desired accuracy level are carefully compared for the two numerical methods. Turbulent kinetic energy budgets for several standard test cases such as the decaying Taylor-Green vortex problem are used to evaluate how effective the stabilization mechanisms necessary for lattice Boltzmann method at high Reynolds numbers are. Detailed comments regarding the cyclomatic complexity of the underlying software, scalability of the underlying algorithm on state-of-the-art high-performance computing platforms and wall clock times and relative accuracy for selected simulations conducted using the two approaches are also made.

  16. Adaptive Lattice Boltzmann Model for Compressible Flows

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    A new lattice Boltzmann model for compressible flows is presented. The main difference from the standard lattice Boltzmann model is that the particle velocities are no longer constant, but vary with the mean velocity and internal energy. The adaptive nature of the particle velocities permits the mean flow to have a high Mach number. The introduction of a particle potential energy makes the model suitable for a perfect gas with arbitrary specific heat ratio. The Navier-Stokes (N-S) equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation. Two kinds of simulations have been carried out on the hexagonal lattice to test the proposed model. One is the Sod shock-tube simulation. The other is a strong shock of Mach number 5.09 diffracting around a corner.

  17. Many body localization in two dimensional square and triangular lattices

    CERN Document Server

    Gonzalez-Garcia, L; Paredes, R

    2016-01-01

    Ultracold interacting Bose atoms placed in disordered two dimensional optical lattices with square and triangular symmetries are found to be localized above a certain disorder strength amplitude. From a Gross-Pitaevskii mean analysis we determine the localization length as a function of the disorder strength and investigate the energy spectrum in terms of the disorder magnitude. We found that the localization length is observed to decrease faster in triangular geometries than in square ones. In the presence of a harmonic confinement localization is observed at the center of the trap. The analysis of the energy spectrum reveals that discrete energy levels acquire a finite width that is always smaller than the distance among energy levels.

  18. Compact triplexer in two-dimensional hexagonal lattice photonic crystals

    Institute of Scientific and Technical Information of China (English)

    Hongliang Ren; Jianping Ma; Hao Wen; Yali Qin; Zhefu Wu; Weisheng Hu; Chun Jiang; Yaohui Jin

    2011-01-01

    We design a contpact triplexer based on two-dimensional (2D) hexagonal lattice photonic crystals (PCs). A folded directional coupler (FDC) is introduced in the triplexer beside the point-defect micro-cavities and line-defect waveguides. Because of the reflection feedback of the FDC, high channel drop efficiency can be realized and a compact size with the order of micrometers can be maintained. The proposed device is analyzed using the plane wave expansion method, and its transmission characteristics are calculated using the finites-difference time-domain method. The footprint of the triplexer is about 12× 9 μm, and its extinction ratios are less than -20 dB for 1310 nm, approximately -20 dB for 1490 nm, and under -4O dB for 1550 nm, making it a potentially essential device ii future fiber-to-the-home networks.%@@ We design a compact triplexer based on two-dimensional (2D) hexagonal lattice photonic crystals (PCs).A folded directional coupler (FDC) is introduced in the triplexer beside the point-defect micro-cavities and line-defect waveguides.Because of the reflection feedback of the FDC, high channel drop efficiency can be realized and a compact size with the order of micrometers can be maintained.The proposed device is analyzed using the plane wave expansion method, and its transmission characteristics are calculated using the finite-difference time-domain method.The footprint of the triplexer is about 12×9 μm, and its extinction ratios are less than -20 dB for 1310 nm, approximately -20 dB for 1490 nm, and under -40 dB for 1550 nm, making it a potentially essential device in future fiber-to-the-home networks.

  19. Grid refinement for entropic lattice Boltzmann models.

    Science.gov (United States)

    Dorschner, B; Frapolli, N; Chikatamarla, S S; Karlin, I V

    2016-11-01

    We propose a multidomain grid refinement technique with extensions to entropic incompressible, thermal, and compressible lattice Boltzmann models. Its validity and accuracy are assessed by comparison to available direct numerical simulation and experiment for the simulation of isothermal, thermal, and viscous supersonic flow. In particular, we investigate the advantages of grid refinement for the setups of turbulent channel flow, flow past a sphere, Rayleigh-Bénard convection, as well as the supersonic flow around an airfoil. Special attention is paid to analyzing the adaptive features of entropic lattice Boltzmann models for multigrid simulations.

  20. Grid refinement for entropic lattice Boltzmann models

    CERN Document Server

    Dorschner, B; Chikatamarla, S S; Karlin, I V

    2016-01-01

    We propose a novel multi-domain grid refinement technique with extensions to entropic incompressible, thermal and compressible lattice Boltzmann models. Its validity and accuracy are accessed by comparison to available direct numerical simulation and experiment for the simulation of isothermal, thermal and viscous supersonic flow. In particular, we investigate the advantages of grid refinement for the set-ups of turbulent channel flow, flow past a sphere, Rayleigh-Benard convection as well as the supersonic flow around an airfoil. Special attention is payed to analyzing the adaptive features of entropic lattice Boltzmann models for multi-grid simulations.

  1. Fast lattice Boltzmann solver for relativistic hydrodynamics.

    Science.gov (United States)

    Mendoza, M; Boghosian, B M; Herrmann, H J; Succi, S

    2010-07-01

    A lattice Boltzmann formulation for relativistic fluids is presented and numerically validated through quantitative comparison with recent hydrodynamic simulations of relativistic fluids. In order to illustrate its capability to handle complex geometries, the scheme is also applied to the case of a three-dimensional relativistic shock wave, generated by a supernova explosion, impacting on a massive interstellar cloud. This formulation opens up the possibility of exporting the proven advantages of lattice Boltzmann methods, namely, computational efficiency and easy handling of complex geometries, to the context of (mildly) relativistic fluid dynamics at large, from quark-gluon plasmas up to supernovae with relativistic outflows.

  2. A new scheme based on the Hermite expansion to construct lattice Boltzmann models associated with arbitrary specific heat ratio

    CERN Document Server

    Hu, Kainan; Geng, Shaojuan

    2016-01-01

    A new lattice Boltzmann scheme associated with flexible specific heat ratio is proposed. The new free degree is introduced via the internal energy associated with the internal structure. The evolution equation of the distribution function is reduced to two evolution equations. One is connected to the density and velocity, the other is of the energy. A two-dimensional lattice Boltzmann model and a three-dimensional lattice Boltzmann model are derived via the Hermite expansion. The two lattice Boltzmann models are applied to simulating the shock tube of one dimension. Good agreement between the numerical results and the analytical solutions are obtained.

  3. Two-dimensional discrete gap breathers in a two-dimensional discrete diatomic Klein-Gordon lattice

    Institute of Scientific and Technical Information of China (English)

    XU Quan; QIANG Tian

    2009-01-01

    We study the existence and stability of two-dimensional discrete breathers in a two-dimensional discrete diatomic Klein-Gordon lattice consisting of alternating light and heavy atoms, with nearest-neighbor harmonic coupling.Localized solutions to the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum, i.e. two-dimensional gap breathers, are investigated numerically. The numerical results of the corresponding algebraic equations demonstrate the possibility of the existence of two-dimensional gap breathers with three types of symmetries, i.e., symmetric, twin-antisymmetric and single-antisymmetric. Their stability depends on the nonlinear on-site potential (soft or hard), the interaction potential (attractive or repulsive)and the center of the two-dimensional gap breather (on a light or a heavy atom).

  4. Least-squares finite-element lattice Boltzmann method.

    Science.gov (United States)

    Li, Yusong; LeBoeuf, Eugene J; Basu, P K

    2004-06-01

    A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented. The new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite-element method's geometric flexibility and numerical stability, while employing efficient and accurate least-squares optimization. For the pure advection equation on a uniform mesh, the proposed method provides for fourth-order accuracy in space and second-order accuracy in time, with unconditional stability in the time domain. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow and Couette flow.

  5. Fluctuating lattice Boltzmann method for the diffusion equation.

    Science.gov (United States)

    Wagner, Alexander J; Strand, Kyle

    2016-09-01

    We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.

  6. Multispeed models in off-lattice Boltzmann simulations

    NARCIS (Netherlands)

    Bardow, A.; Karlin, I.V.; Gusev, A.A.

    2008-01-01

    The lattice Boltzmann method is a highly promising approach to the simulation of complex flows. Here, we realize recently proposed multispeed lattice Boltzmann models [S. Chikatamarla et al., Phys. Rev. Lett. 97 190601 (2006)] by exploiting the flexibility offered by off-lattice Boltzmann methods.

  7. A Fluctuating Lattice Boltzmann Method for the Diffusion Equation

    CERN Document Server

    Wagner, Alexander J

    2016-01-01

    We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.

  8. Entropic lattice Boltzmann model for Burgers's equation.

    Science.gov (United States)

    Boghosian, Bruce M; Love, Peter; Yepez, Jeffrey

    2004-08-15

    Entropic lattice Boltzmann models are discrete-velocity models of hydrodynamics that possess a Lyapunov function. This feature makes them useful as nonlinearly stable numerical methods for integrating hydrodynamic equations. Over the last few years, such models have been successfully developed for the Navier-Stokes equations in two and three dimensions, and have been proposed as a new category of subgrid model of turbulence. In the present work we develop an entropic lattice Boltzmann model for Burgers's equation in one spatial dimension. In addition to its pedagogical value as a simple example of such a model, our result is actually a very effective way to simulate Burgers's equation in one dimension. At moderate to high values of viscosity, we confirm that it exhibits no trace of instability. At very small values of viscosity, however, we report the existence of oscillations of bounded amplitude in the vicinity of the shock, where gradient scale lengths become comparable with the grid size. As the viscosity decreases, the amplitude at which these oscillations saturate tends to increase. This indicates that, in spite of their nonlinear stability, entropic lattice Boltzmann models may become inaccurate when the ratio of gradient scale length to grid spacing becomes too small. Similar inaccuracies may limit the utility of the entropic lattice Boltzmann paradigm as a subgrid model of Navier-Stokes turbulence.

  9. On some classes of two-dimensional local models in discrete two-dimensional monatomic FPU lattice with cubic and quartic potential

    Institute of Scientific and Technical Information of China (English)

    Xu Quan; Tian Qiang

    2009-01-01

    This paper discusses the two-dimensional discrete monatomic Fermi-Pasta-Ulam lattice, by using the method of multiple-scale and the quasi-discreteness approach. By taking into account the interaction between the atoms in the lattice and their nearest neighbours, it obtains some classes of two-dimensional local models as follows: two-dimensional bright and dark discrete soliton trains, two-dimensional bright and dark line discrete breathers, and two-dimensional bright and dark discrete breather.

  10. A Novel Lattice Boltzmann Model For Reactive Flows with Fast Chemistry

    Institute of Scientific and Technical Information of China (English)

    CHEN Sheng; LIU Zhao-Hui; HE Zhu; ZHANG Chao; TIAN Zhi-Wei; SHI Bao-Chang; ZHENG Chu-Guang

    2006-01-01

    @@ A novel lattice Boltzmann model, in which we take the ratio of temperature difference in the temperature field to the environment one to be more than one order of magnitude than before, is developed to simulate two dimensional reactive flows with fast chemistry. Different from the hybrid scheme for reactive flows [Comput.Phys. Commun. 129 (2000)267], this scheme is strictly in a pure lattice Boltzmann style (i.e., we solve the flow, temperature, and concentration fields using the lattice Boltzmann method only). Different from the recent non-coupled lattice Boltzmann scheme [Int. J. Mod. Phys. B 17(2003) 197], the fluid density in our model is coupled directly with the temperature. Excellent agreement between the present results and other numerical data shows that this scheme is an efficient numerical method for practical reactive flows with fast chemistry.

  11. Lattice-Boltzmann simulations of droplet evaporation

    KAUST Repository

    Ledesma-Aguilar, Rodrigo

    2014-09-04

    © the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is

  12. Consistent lattice Boltzmann equations for phase transitions.

    Science.gov (United States)

    Siebert, D N; Philippi, P C; Mattila, K K

    2014-11-01

    Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling.

  13. Lattice Boltzmann Model for Numerical Relativity

    CERN Document Server

    Ilseven, E

    2015-01-01

    In the Bona-Masso formulation, Einstein equations are written as a set of flux conservative first order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for Numerical Relativity. Our model is validated with well-established tests, showing good agreement with analytical solutions. Furthermore, we show that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improves. Finally, in order to show the potential of our approach a linear scaling law for parallelisation with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

  14. Lattice Boltzmann model for numerical relativity.

    Science.gov (United States)

    Ilseven, E; Mendoza, M

    2016-02-01

    In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

  15. Critical phenomena in the majority voter model on two-dimensional regular lattices.

    Science.gov (United States)

    Acuña-Lara, Ana L; Sastre, Francisco; Vargas-Arriola, José Raúl

    2014-05-01

    In this work we studied the critical behavior of the critical point as a function of the number of nearest neighbors on two-dimensional regular lattices. We performed numerical simulations on triangular, hexagonal, and bilayer square lattices. Using standard finite-size scaling theory we found that all cases fall in the two-dimensional Ising model universality class, but that the critical point value for the bilayer lattice does not follow the regular tendency that the Ising model shows.

  16. Multireflection boundary conditions for lattice Boltzmann models.

    Science.gov (United States)

    Ginzburg, Irina; d'Humières, Dominique

    2003-12-01

    We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder.

  17. Entropic Lattice Boltzmann Methods for Fluid Mechanics

    Science.gov (United States)

    Chikatamarla, Shyam; Boesch, Fabian; Sichau, David; Karlin, Ilya

    2013-11-01

    With its roots in statistical mechanics and kinetic theory, the lattice Boltzmann method (LBM) is a paradigm-changing innovation, offering for the first time an intrinsically parallel CFD algorithm. Over the past two decades, LBM has achieved numerous results in the field of CFD and is now in a position to challenge state-of-the art CFD techniques. Our major restyling of LBM resulted in an unconditionally stable entropic LBM which restored Second Law (Boltzmann H theorem) in the LBM kinetics and thus enabled affordable direct simulations of fluid turbulence. We review here recent advances in ELBM as a practical, modeling-free tool for simulation of turbulent flows in complex geometries. We shall present recent simulations including turbulent channel flow, flow past a circular cylinder, knotted vortex tubes, and flow past a surface mounted cube. ELBM listed all admissible lattices supporting a discrete entropy function and has classified them in hierarchically increasing order of accuracy. Applications of these higher-order lattices to simulations of turbulence and thermal flows shall also be presented. This work was supported CSCS grant s437.

  18. One-dimensional lattices topologically equivalent to two-dimensional lattices within the context of the lattice gas model

    Science.gov (United States)

    Costanza, E. F.; Costanza, G.

    2016-10-01

    Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to two-dimensional lattices is described in detail in the case of a rectangular lattice. This example shows the general features that possess the procedure and extensions are also suggested in order to provide a wider insight in the present approach.

  19. Two-Dimensional Lattice Gravity as a Spin System

    CERN Document Server

    Beirl, W; Riedler, J

    1994-01-01

    Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin system with higher couplings on a Kagome lattice. Various measures acting as external field are considered. Extensions to matter fields and higher dimensions are discussed.

  20. Semi-Lagrangian off-lattice Boltzmann method for weakly compressible flows.

    Science.gov (United States)

    Krämer, Andreas; Küllmer, Knut; Reith, Dirk; Joppich, Wolfgang; Foysi, Holger

    2017-02-01

    The lattice Boltzmann method is a simulation technique in computational fluid dynamics. In its standard formulation, it is restricted to regular computation grids, second-order spatial accuracy, and a unity Courant-Friedrichs-Lewy (CFL) number. This paper advances the standard lattice Boltzmann method by introducing a semi-Lagrangian streaming step. The proposed method allows significantly larger time steps, unstructured grids, and higher-order accurate representations of the solution to be used. The appealing properties of the approach are demonstrated in simulations of a two-dimensional Taylor-Green vortex, doubly periodic shear layers, and a three-dimensional Taylor-Green vortex.

  1. Effects of Atomistic Domain Size on Hybrid Lattice Boltzmann-Molecular Dynamics Simulations of Dense Fluids

    Science.gov (United States)

    Dupuis, A.; Koumoutsakos, P.

    We present a convergence study for a hybrid Lattice Boltzmann-Molecular Dynamics model for the simulation of dense liquids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The velocity field from the atomistic domain is introduced as forcing terms to the Lattice Boltzmann model of the continuum while the mean field of the continuum imposes mean field conditions for the atomistic domain. In the present paper we investigate the effect of varying the size of the atomistic subdomain in simulations of two dimensional flows of liquid argon past carbon nanotubes and assess the efficiency of the method.

  2. Application of lattice Boltzmann scheme to nanofluids

    Institute of Scientific and Technical Information of China (English)

    XUAN Yimin; LI Qiang; YAO Zhengping

    2004-01-01

    A nanofluid is a particle suspension that consists of base liquids and nanoparticles. Nanofluid has greater potential for heat transfer enhancement than traditional solid-liquid mixture. By accounting for the external and internal forces acting on the suspended nanoparticles and interactions among the nanoparticles and fluid particles,a lattice Boltzmann model for simulating flow and energy transport processes inside the nanofluids is proposed. The irregular motion of the nanoparticles and inherent dynamic behavior of nanofluids are discussed. The distributions of suspended nanoparticles inside nanofluids are calculated.

  3. Lattice-Boltzmann-based Simulations of Diffusiophoresis

    Science.gov (United States)

    Castigliego, Joshua; Kreft Pearce, Jennifer

    We present results from a lattice-Boltzmann-base Brownian Dynamics simulation on diffusiophoresis and the separation of particles within the system. A gradient in viscosity that simulates a concentration gradient in a dissolved polymer allows us to separate various types of particles by their deformability. As seen in previous experiments, simulated particles that have a higher deformability react differently to the polymer matrix than those with a lower deformability. Therefore, the particles can be separated from each other. This simulation, in particular, was intended to model an oceanic system where the particles of interest were zooplankton, phytoplankton and microplastics. The separation of plankton from the microplastics was achieved.

  4. SIMULATION OF MIXED CONVECTIVE HEAT TRANSFER USING LATTICE BOLTZMANN METHOD

    Directory of Open Access Journals (Sweden)

    A. R. M. Rosdzimin

    2010-12-01

    Full Text Available In this paper, mixed (forced–natural convective heat transfer around a heated square cylinder located inside a lid driven cavity has been studied numerically using the lattice Boltzmann method in the range of 100≤ Re ≤ 1000 with the corresponding Richardson number 0.01≤Ri≤10. The double-population lattice Boltzmann formulation is used as the governing equation. Two dimensional nine-velocity models are used for the computation of the velocity field while a four-velocity model is used for the computation of the temperature field. We found that the combination of nine- and four-velocity models can be applied to the calculation without losing its accuracy. The results are presented in the form of streamline and isotherm plots as well as the variation of local Nusselt number at the top surface of the heated square. The computational results demonstrate that the flow pattern, formation of vortex and also the Nusselt number are influence by the Reynolds number and Richardson number.

  5. Hydrodynamic behaviour of Lattice Boltzmann and Lattice BGK models

    CERN Document Server

    Behrend, O; Warren, P

    1993-01-01

    Abstract: We present a numerical analysis of the validity of classical and generalized hydrodynamics for Lattice Boltzmann Equation (LBE) and Lattice BGK methods in two and three dimensions, as a function of the collision parameters of these models. Our analysis is based on the wave-number dependence of the evolution operator. Good ranges of validity are found for BGK models as long as the relaxation time is chosen smaller than or equal to unity. The additional freedom in the choice of collision parameters for LBE models does not seem to give significant improvement.

  6. Thermal diode from two-dimensional asymmetrical Ising lattices.

    Science.gov (United States)

    Wang, Lei; Li, Baowen

    2011-06-01

    Two-dimensional asymmetrical Ising models consisting of two weakly coupled dissimilar segments, coupled to heat baths with different temperatures at the two ends, are studied by Monte Carlo simulations. The heat rectifying effect, namely asymmetric heat conduction, is clearly observed. The underlying mechanisms are the different temperature dependencies of thermal conductivity κ at two dissimilar segments and the match (mismatch) of flipping frequencies of the interface spins.

  7. Simulating High Reynolds Number Flow by Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    KANG Xiu-Ying; LIU Da-He; ZHOU Jing; JIN Yong-Juan

    2005-01-01

    @@ A two-dimensional channel flow with different Reynolds numbers is tested by using the lattice Boltzmann method under different pressure and velocity boundary conditions. The results show that the simulation error increases,and the pressure and the flow rate become unstable under a high Reynolds number. To improve the simulation precision under a high Reynolds number, the number of fluid nodes should be enlarged. For a higher Reynoldsnumber flow, the velocity boundary with an approximately parabolic velocity profile is found to be more adaptive.Blood flow in an artery with cosine shape symmetrical narrowing is then simulated under a velocity boundary condition. Its velocity, pressure and wall shear stress distributions are consistent with previous studies.

  8. Modeling of metal foaming with lattice Boltzmann automata

    Energy Technology Data Exchange (ETDEWEB)

    Koerner, C.; Thies, M.; Singer, R.F. [WTM Institute, Department of Materials Science, University of Erlangen, Martensstrasse 5, D-91058 Erlangen (Germany)

    2002-10-01

    The formation and decay of foams produced by gas bubble expansion in a molten metal is numerically simulated with the Lattice Boltzmann Method (LBM) which belongs to the cellular automaton techniques. The present state of the two dimensional model allows the investigation of the foam evolution process comprising bubble expansion, bubble coalescence, drainage, and eventually foam collapse. Examples demonstrate the influence of the surface tension, viscosity and gravity on the foaming process and the resulting cell structure. In addition, the potential of the LBM to solve problems with complex boundary conditions is illustrated by means of a foam developing within the constraints of a mould as well as a foaming droplet exposed to gravity. (Abstract Copyright [2002], Wiley Periodicals, Inc.)

  9. Double MRT thermal lattice Boltzmann method for simulating convective flows

    Energy Technology Data Exchange (ETDEWEB)

    Mezrhab, Ahmed, E-mail: mezrhab@fso.ump.m [Laboratoire de Mecanique and Energetique, Departement de Physique, Faculte des Sciences, Universite Mohammed 1er, 60000 Oujda (Morocco); Amine Moussaoui, Mohammed; Jami, Mohammed [Laboratoire de Mecanique and Energetique, Departement de Physique, Faculte des Sciences, Universite Mohammed 1er, 60000 Oujda (Morocco); Naji, Hassan [Universite Lille Nord de France, F-59000 Lille, and LML UMR CNRS 8107, F-59655 Villeneuve d' Ascq cedex (France); Bouzidi, M' hamed [Universite Clermont 2, LaMI EA 3867, IUT de Montlucon, Av. A. Briand, BP 2235, F-03101 Montlucon cedex (France)

    2010-07-26

    A two-dimensional double Multiple Relaxation Time-Thermal Lattice Boltzmann Equation (2-MRT-TLBE) method is developed for predicting convective flows in a square differentially heated cavity filled with air (Pr=0.71). In this Letter, we propose a numerical scheme to solve the flow and the temperature fields using the MRT-D2Q9 model and the MRT-D2Q5 model, respectively. Thus, the main objective of this study is to show the effectiveness of such model to predict thermodynamics for heat transfer. This model is validated by the numerical simulations of the 2-D convective square cavity flow. Excellent agreements are obtained between numerical predictions. These results demonstrate the accuracy and the effectiveness of the proposed methodology.

  10. Evaluation of a lattice Boltzmann method in a complex nanoflow.

    Science.gov (United States)

    Suga, K; Takenaka, S; Ito, T; Kaneda, M; Kinjo, T; Hyodo, S

    2010-07-01

    In order to establish a cost-effective strategy to simulate complex flows in continuum to slip and transitional regimes, the present study assesses the performance of a lattice Boltzmann method (LBM) formerly discussed by the present authors' group [Niu, Phys. Rev. E 76, 036711 (2007)]. This LBM is based on a diffuse scattering wall boundary condition, a regularization procedure, and an effective relaxation time associated with the Knudsen number. The present assessment is on its regularization procedure and third-order truncated system based on the two-dimensional twenty-one discrete velocity (D2Q21) model for the Cartesian lattices. The test flow cases are force-driven Poiseuille flows, the Couette flows and a flow around a square cylinder situated in a nanochannel. For producing the reference data of the square cylinder flow, the molecular dynamics simulation using Lennard-Jones potential is also performed. Although the flow profiles and the slip velocities of the Poiseuille flows and the Couette flows are more accurately predicted by the third-order truncated system, the general velocity profiles around the square cylinder are also well predicted by the second-order truncated system based on the two-dimensional nine discrete velocity (D2Q9) model. It is also confirmed that without the regularization process, the entire flow field prediction suffers unphysical momentum oscillations around the square cylinder.

  11. A lattice Boltzmann model for adsorption breakthrough

    Energy Technology Data Exchange (ETDEWEB)

    Agarwal, Saurabh; Verma, Nishith [Indian Institute of Technology Kanpur, Department of Chemical Engineering, Kanpur (India); Mewes, Dieter [Universitat Hannover, Institut fur Verfahrenstechnik, Hannover (Germany)

    2005-07-01

    A lattice Boltzmann model is developed to simulate the one-dimensional (1D) unsteady state concentration profiles, including breakthrough curves, in a fixed tubular bed of non-porous adsorbent particles. The lattice model solves the 1D time dependent convection-diffusion-reaction equation for an ideal binary gaseous mixture, with solute concentrations at parts per million levels. The model developed in this study is also able to explain the experimental adsorption/desorption data of organic vapours (toluene) on silica gel under varying conditions of temperature, concentrations and flowrates. Additionally, the programming code written for simulating the adsorption breakthrough is modified with minimum changes to successfully simulate a few flow problems, such as Poiseuille flow, Couette flow, and axial dispersion in a tube. The present study provides an alternative numerical approach to solving such types of mass transfer related problems. (orig.)

  12. Axisymmetric multiphase lattice Boltzmann method for generic equations of state

    NARCIS (Netherlands)

    Reijers, Sten Arjen; Gelderblom, Hanneke; Toschi, F.

    2016-01-01

    We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation

  13. Thermal equation of state for lattice Boltzmann gases

    Institute of Scientific and Technical Information of China (English)

    Ran Zheng

    2009-01-01

    The Galilean invaxiance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar-Gross-Krook model axe proposed together with their rigorous theoretical background. From the viewpoint of group invariance,recovering the Galilean invariance for the isothermal lattice Boltzmann Bhatnagar-Gross-Krook equation (LBGKE) induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics.

  14. Axisymmetric multiphase lattice Boltzmann method for generic equations of state

    NARCIS (Netherlands)

    Reijers, S.A.; Gelderblom, H.; Toschi, F.

    2016-01-01

    We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid–gas density ratios up to 103. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation

  15. Optical properties of two-dimensional magnetoelectric point scattering lattices

    DEFF Research Database (Denmark)

    Hansen, Per Lunnemann; Sersic, Ivana; Koenderink, A. Femius

    2013-01-01

    of split ring resonators and provide a quantitative comparison of measured and calculated transmission spectra at normal incidence as a function of lattice density, showing excellent agreement. We further show angle-dependent transmission calculations for circularly polarized light and compare...

  16. Immersed boundary lattice Boltzmann model based on multiple relaxation times.

    Science.gov (United States)

    Lu, Jianhua; Han, Haifeng; Shi, Baochang; Guo, Zhaoli

    2012-01-01

    As an alterative version of the lattice Boltzmann models, the multiple relaxation time (MRT) lattice Boltzmann model introduces much less numerical boundary slip than the single relaxation time (SRT) lattice Boltzmann model if some special relationship between the relaxation time parameters is chosen. On the other hand, most current versions of the immersed boundary lattice Boltzmann method, which was first introduced by Feng and improved by many other authors, suffer from numerical boundary slip as has been investigated by Le and Zhang. To reduce such a numerical boundary slip, an immerse boundary lattice Boltzmann model based on multiple relaxation times is proposed in this paper. A special formula is given between two relaxation time parameters in the model. A rigorous analysis and the numerical experiments carried out show that the numerical boundary slip reduces dramatically by using the present model compared to the single-relaxation-time-based model.

  17. Two-dimensional Chern semimetals on the Lieb lattice

    Science.gov (United States)

    Palumbo, Giandomenico; Meichanetzidis, Konstantinos

    2015-12-01

    In this work we propose a simple model that supports Chern semimetals. These gapless topological phases share several properties with the Chern insulators like a well-defined Chern number associated with each band, topologically protected edge states and topological phase transitions that occur when the bands touch each, with linear dispersion around the contact points. The tight-binding model, defined on the Lieb lattice with intra-unit-cell and suitable nearest-neighbor hopping terms between three different species of spinless fermions, supports a single Dirac-like point. The dispersion relation around this point is fully relativistic and the 3 ×3 matrices in the corresponding effective Hamiltonian satisfy the Duffin-Kemmer-Petiau algebra. We show the robustness of the topologically protected edge states by employing the entanglement spectrum. Moreover, we prove that the Chern number of the lowest band is robust with respect to weak disorder. For its simplicity, our model can be naturally implemented in real physical systems like cold atoms in optical lattices.

  18. Two-dimensional lattice gauge theories with superconducting quantum circuits

    Energy Technology Data Exchange (ETDEWEB)

    Marcos, D., E-mail: david.marcos@me.com [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Widmer, P. [Albert Einstein Center, Institute for Theoretical Physics, Bern University, CH-3012, Bern (Switzerland); Rico, E. [IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg (France); Hafezi, M. [Joint Quantum Institute, NIST/University of Maryland, College Park 20742 (United States); Department of Electrical Engineering and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742 (United States); Rabl, P. [Institute of Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020 Wien (Austria); Wiese, U.-J. [Albert Einstein Center, Institute for Theoretical Physics, Bern University, CH-3012, Bern (Switzerland); Zoller, P. [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria)

    2014-12-15

    A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

  19. Lattice Boltzmann modelling of intrinsic permeability

    CERN Document Server

    Li, Jun; Wu, Lei; Zhang, Yonghao

    2016-01-01

    Lattice Boltzmann method (LBM) has been applied to predict flow properties of porous media including intrinsic permeability, where it is implicitly assumed that the LBM is equivalent to the incompressible (or near incompressible) Navier-Stokes equation. However, in LBM simulations, high-order moments, which are completely neglected in the Navier-Stokes equation, are still available through particle distribution functions. To ensure that the LBM simulation is correctly working at the Navier-Stokes hydrodynamic level, the high-order moments have to be negligible. This requires that the Knudsen number (Kn) is small so that rarefaction effect can be ignored. In this technical note, we elaborate this issue in LBM modelling of porous media flows, which is particularly important for gas flows in ultra-tight media.

  20. The Lattice Boltzmann method principles and practice

    CERN Document Server

    Krüger, Timm; Kuzmin, Alexandr; Shardt, Orest; Silva, Goncalo; Viggen, Erlend Magnus

    2017-01-01

    This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a va...

  1. Flux Limiter Lattice Boltzmann for Compressible Flows

    Institute of Scientific and Technical Information of China (English)

    陈峰; 许爱国; 张广财; 李英骏

    2011-01-01

    In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann (LB) model for shacked compressible flows. The proposed flux limiter scheme is efficient in decreasing the artificial oscillations and numerical diffusion around the interface. Due to the kinetic nature, some interface problems being difficult to handle at the macroscopic level can be modeled more naturally through the LB method. Numerical simulations for the Richtmyer-Meshkov instability show that with the new model the computed interfaces are smoother and more consistent with physical analysis. The growth rates of bubble and spike present a satisfying agreement with the theoretical predictions and other numerical simulations.

  2. Larkin-Ovchinnikov phases in two-dimensional square lattices

    Science.gov (United States)

    Baarsma, J. E.; Törmä, P.

    2016-10-01

    We consider a two-component gas of fermions in optical lattices in the presence of a population imbalance within a mean-field theory. We study phase transitions from a normal gas of unpaired fermions to a superfluid phase of Bose-condensed Cooper pairs. The possibility of Cooper pairs with a nonzero centre-of-mass momentum is included, which corresponds to a so-called Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state. We find that for population-imbalanced systems such states can form the ground state. The FF and LO state are compared and it is shown that actually the LO state is energetically more favourable. We complete the mean-field phase diagram for the LO phase and show that it is qualitatively in excellent agreement with recent diagrammatic Monte Carlo calculations. Subsequently, we calculate the atomic density modulations in the LO phase.

  3. Negative Dispersion of Lattice Waves in a Two-Dimensional Yukawa System

    Institute of Scientific and Technical Information of China (English)

    刘艳红; 刘斌; 杨思泽; 王龙

    2002-01-01

    Collective motion modes existing in a two-dimensional Yukawa system are investigated by molecular dynamics simulation. The dispersion relations of transverse and longitudinal lattice waves obtained for hexagonal lattice are in agreement with the theoretical results. The negative dispersion of the parallel longitudinal wave is demonstrated by the simulation, and is explained by a physical model.

  4. Two-dimensional ion trap lattice on a microchip for quantum simulation

    CERN Document Server

    Sterling, R C; Weidt, S; Lake, K; Srinivasan, P; Webster, S C; Kraft, M; Hensinger, W K

    2013-01-01

    Using a controllable quantum system it is possible to simulate other highly complex quantum systems efficiently overcoming an in-principle limitation of classical computing. Trapped ions constitute such a highly controllable quantum system. So far, no dedicated architectures for the simulation of two-dimensional spin lattices using trapped ions in radio-frequency ion traps have been produced, limiting the possibility of carrying out such quantum simulations on a large scale. We report the operation of a two-dimensional ion trap lattice integrated in a microchip capable of implementing quantum simulations of two-dimensional spin lattices. Our device provides a scalable microfabricated architecture for trapping such ion lattices with coupling strengths between neighbouring ions sufficient to provide a powerful platform for the implementation of quantum simulations. In order to realize this device we developed a specialist fabrication process that allows for the application of very large voltages. We fabricated ...

  5. Immersed Boundary-Lattice Boltzmann Method Using Two Relaxation Times

    Directory of Open Access Journals (Sweden)

    Kosuke Hayashi

    2012-06-01

    Full Text Available An immersed boundary-lattice Boltzmann method (IB-LBM using a two-relaxation time model (TRT is proposed. The collision operator in the lattice Boltzmann equation is modeled using two relaxation times. One of them is used to set the fluid viscosity and the other is for numerical stability and accuracy. A direct-forcing method is utilized for treatment of immersed boundary. A multi-direct forcing method is also implemented to precisely satisfy the boundary conditions at the immersed boundary. Circular Couette flows between a stationary cylinder and a rotating cylinder are simulated for validation of the proposed method. The method is also validated through simulations of circular and spherical falling particles. Effects of the functional forms of the direct-forcing term and the smoothed-delta function, which interpolates the fluid velocity to the immersed boundary and distributes the forcing term to fixed Eulerian grid points, are also examined. As a result, the following conclusions are obtained: (1 the proposed method does not cause non-physical velocity distribution in circular Couette flows even at high relaxation times, whereas the single-relaxation time (SRT model causes a large non-physical velocity distortion at a high relaxation time, (2 the multi-direct forcing reduces the errors in the velocity profile of a circular Couette flow at a high relaxation time, (3 the two-point delta function is better than the four-point delta function at low relaxation times, but worse at high relaxation times, (4 the functional form of the direct-forcing term does not affect predictions, and (5 circular and spherical particles falling in liquids are well predicted by using the proposed method both for two-dimensional and three-dimensional cases.

  6. Quantum search on the two-dimensional lattice using the staggered model with Hamiltonians

    Science.gov (United States)

    Portugal, R.; Fernandes, T. D.

    2017-04-01

    Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk models to provide efficient algorithms from the theoretical side and means to implement quantum walks in laboratories from the practical side. In this paper, we rigorously prove that the recent-proposed staggered quantum walk model provides an efficient quantum search on the two-dimensional lattice, if the reflection operators associated with the graph tessellations are used as Hamiltonians, which is an important theoretical result for validating the staggered model with Hamiltonians. Numerical results show that on the two-dimensional lattice staggered models without Hamiltonians are not as efficient as the one described in this paper and are, in fact, as slow as classical random-walk-based algorithms.

  7. Lattice Boltzmann method fundamentals and engineering applications with computer codes

    CERN Document Server

    Mohamad, A A

    2014-01-01

    Introducing the Lattice Boltzmann Method in a readable manner, this book provides detailed examples with complete computer codes. It avoids the most complicated mathematics and physics without scarifying the basic fundamentals of the method.

  8. Lattice Boltzmann modeling of directional wetting: Comparing simulations to experiments

    NARCIS (Netherlands)

    Jansen, H.P.; Sotthewes, K.; Swigchem, van J.; Zandvliet, H.J.W.; Kooij, E.S.

    2013-01-01

    Lattice Boltzmann Modeling (LBM) simulations were performed on the dynamic behavior of liquid droplets on chemically striped patterned surfaces, ultimately with the aim to develop a predictive tool enabling reliable design of future experiments. The simulations accurately mimic experimental results,

  9. Computational Aeroacoustics Using the Generalized Lattice Boltzmann Equation Project

    Data.gov (United States)

    National Aeronautics and Space Administration — The overall objective of the proposed project is to develop a generalized lattice Boltzmann (GLB) approach as a potential computational aeroacoustics (CAA) tool for...

  10. Maxwell iteration for the lattice Boltzmann method with diffusive scaling.

    Science.gov (United States)

    Zhao, Weifeng; Yong, Wen-An

    2017-03-01

    In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.

  11. A new lattice Boltzmann model for incompressible magnetohydrodynamics

    Institute of Scientific and Technical Information of China (English)

    Chen Xing-Wang; Shi Bao-Chang

    2005-01-01

    Most of the existing lattice Boltzmann magnetohydrodynamics (MHD) models can be viewed as compressible schemes to simulate incompressible MHD flows. The compressible effect might lead to some undesired errors in numerical simulations. In this paper a new incompressible lattice Boltzmann MHD model without compressible effect is presented for simulating incompressible MHD flows. Numerical simulations of the Hartmann flow are performed. We do numerous tests and make comparison with Dellar's model in detail. The numerical results are in good agreement with the analytical error.

  12. Extended lattice Boltzmann scheme for droplet combustion

    Science.gov (United States)

    Ashna, Mostafa; Rahimian, Mohammad Hassan; Fakhari, Abbas

    2017-05-01

    The available lattice Boltzmann (LB) models for combustion or phase change are focused on either single-phase flow combustion or two-phase flow with evaporation assuming a constant density for both liquid and gas phases. To pave the way towards simulation of spray combustion, we propose a two-phase LB method for modeling combustion of liquid fuel droplets. We develop an LB scheme to model phase change and combustion by taking into account the density variation in the gas phase and accounting for the chemical reaction based on the Cahn-Hilliard free-energy approach. Evaporation of liquid fuel is modeled by adding a source term, which is due to the divergence of the velocity field being nontrivial, in the continuity equation. The low-Mach-number approximation in the governing Navier-Stokes and energy equations is used to incorporate source terms due to heat release from chemical reactions, density variation, and nonluminous radiative heat loss. Additionally, the conservation equation for chemical species is formulated by including a source term due to chemical reaction. To validate the model, we consider the combustion of n-heptane and n -butanol droplets in stagnant air using overall single-step reactions. The diameter history and flame standoff ratio obtained from the proposed LB method are found to be in good agreement with available numerical and experimental data. The present LB scheme is believed to be a promising approach for modeling spray combustion.

  13. Extended lattice Boltzmann scheme for droplet combustion.

    Science.gov (United States)

    Ashna, Mostafa; Rahimian, Mohammad Hassan; Fakhari, Abbas

    2017-05-01

    The available lattice Boltzmann (LB) models for combustion or phase change are focused on either single-phase flow combustion or two-phase flow with evaporation assuming a constant density for both liquid and gas phases. To pave the way towards simulation of spray combustion, we propose a two-phase LB method for modeling combustion of liquid fuel droplets. We develop an LB scheme to model phase change and combustion by taking into account the density variation in the gas phase and accounting for the chemical reaction based on the Cahn-Hilliard free-energy approach. Evaporation of liquid fuel is modeled by adding a source term, which is due to the divergence of the velocity field being nontrivial, in the continuity equation. The low-Mach-number approximation in the governing Navier-Stokes and energy equations is used to incorporate source terms due to heat release from chemical reactions, density variation, and nonluminous radiative heat loss. Additionally, the conservation equation for chemical species is formulated by including a source term due to chemical reaction. To validate the model, we consider the combustion of n-heptane and n-butanol droplets in stagnant air using overall single-step reactions. The diameter history and flame standoff ratio obtained from the proposed LB method are found to be in good agreement with available numerical and experimental data. The present LB scheme is believed to be a promising approach for modeling spray combustion.

  14. Meshless lattice Boltzmann method for the simulation of fluid flows.

    Science.gov (United States)

    Musavi, S Hossein; Ashrafizaadeh, Mahmud

    2015-02-01

    A meshless lattice Boltzmann numerical method is proposed. The collision and streaming operators of the lattice Boltzmann equation are separated, as in the usual lattice Boltzmann models. While the purely local collision equation remains the same, we rewrite the streaming equation as a pure advection equation and discretize the resulting partial differential equation using the Lax-Wendroff scheme in time and the meshless local Petrov-Galerkin scheme based on augmented radial basis functions in space. The meshless feature of the proposed method makes it a more powerful lattice Boltzmann solver, especially for cases in which using meshes introduces significant numerical errors into the solution, or when improving the mesh quality is a complex and time-consuming process. Three well-known benchmark fluid flow problems, namely the plane Couette flow, the circular Couette flow, and the impulsively started cylinder flow, are simulated for the validation of the proposed method. Excellent agreement with analytical solutions or with previous experimental and numerical results in the literature is observed in all the simulations. Although the computational resources required for the meshless method per node are higher compared to that of the standard lattice Boltzmann method, it is shown that for cases in which the total number of nodes is significantly reduced, the present method actually outperforms the standard lattice Boltzmann method.

  15. Bloch oscillations and Zener tunneling in two-dimensional photonic lattices.

    Science.gov (United States)

    Trompeter, Henrike; Krolikowski, Wieslaw; Neshev, Dragomir N; Desyatnikov, Anton S; Sukhorukov, Andrey A; Kivshar, Yuri S; Pertsch, Thomas; Peschel, Ulf; Lederer, Falk

    2006-02-10

    We report on the first experimental observation of photonic Bloch oscillations and Zener tunneling in two-dimensional periodic systems. We study the propagation of an optical beam in a square lattice superimposed on a refractive index ramp. We observe oscillations of the beam inside the first Brilloin zone and tunneling of light from the first to the higher-order bands of the lattice band gap spectrum.

  16. Tensor renormalization group approach to two-dimensional classical lattice models.

    Science.gov (United States)

    Levin, Michael; Nave, Cody P

    2007-09-21

    We describe a simple real space renormalization group technique for two-dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of the density matrix renormalization group method. We demonstrate the method - which we call the tensor renormalization group method - by computing the magnetization of the triangular lattice Ising model.

  17. A LATTICE BOLTZMANN SUBGRID MODEL FOR LID-DRIVEN CAVITY FLOW

    Institute of Scientific and Technical Information of China (English)

    YANG Fan; LIU Shu-hong; WU Yu-lin; TANG Xue-lin

    2005-01-01

    In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds number fluid flow applications, a subgrid turbulence model for LBM was introduced based on standard Smagorinsky subgrid model and Lattice Bhatnagar-Gross-Krook (LBGK) model. The subgrid LBGK model was subsequently used to simulate the two-dimensional driven cavity flow at high Reynolds numbers. The simulation results including distribution of stream lines, dimensionless velocities distribution, values of stream function, as well as location of vertex center, were compared with benchmark solutions, with satisfactory agreements.

  18. Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices

    NARCIS (Netherlands)

    Beugeling, W.; Everts, J.C.; de Morais Smith, C.

    2012-01-01

    For two-dimensional lattices in a tight-binding description, the intrinsic spin-orbit coupling, acting as a complex next-nearest-neighbor hopping, opens gaps that exhibit the quantum spin Hall effect. In this paper, we study the effect of a real next-nearest-neighbor hopping term on the band structu

  19. Lattice gas dynamics: application to driven vortices in two dimensional superconductors.

    Science.gov (United States)

    Gotcheva, Violeta; Wang, Albert T J; Teitel, S

    2004-06-18

    A continuous time Monte Carlo lattice gas dynamics is developed to model driven steady states of vortices in two dimensional superconducting networks. Dramatic differences are found when compared to a simpler Metropolis dynamics. Subtle finite size effects are found at low temperature, with a moving smectic that becomes unstable to an anisotropic liquid on sufficiently large length scales.

  20. Dipolar fermions in a two-dimensional lattice at non-zero temperature

    DEFF Research Database (Denmark)

    Larsen, Anne-Louise G.; Bruun, Georg

    2012-01-01

    We examine density-ordered and superfluid phases of fermionic dipoles in a two-dimensional square lattice at nonzero temperature. The critical temperature of the density-ordered phases is determined and is shown to be proportional to the coupling strength for strong coupling. We calculate...

  1. Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models

    Directory of Open Access Journals (Sweden)

    Xuemei Gao

    2014-01-01

    Full Text Available The aim of this paper is to extend the lattice method proposed by Ritchken and Trevor (1999 for pricing American options with one-dimensional stochastic volatility models to the two-dimensional cases with strangle payoff. This proposed method is compared with the least square Monte-Carlo method via numerical examples.

  2. Quantum computing via defect states in two-dimensional antidot lattices.

    Science.gov (United States)

    Flindt, Christian; Mortensen, Niels Asger; Jauho, Antti-Pekka

    2005-12-01

    We propose a new structure suitable for quantum computing in a solid-state environment: designed defect states in antidot lattices superimposed on a two-dimensional electron gas at a semiconductor heterostructure. State manipulation can be obtained with gate control. Model calculations indicate that it is feasible to fabricate structures whose energy level structure is robust against thermal dephasing.

  3. Lattice Boltzmann models for the grain growth in polycrystalline systems

    Directory of Open Access Journals (Sweden)

    Yonggang Zheng

    2016-08-01

    Full Text Available In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.

  4. Lattice Boltzmann models for the grain growth in polycrystalline systems

    Science.gov (United States)

    Zheng, Yonggang; Chen, Cen; Ye, Hongfei; Zhang, Hongwu

    2016-08-01

    In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.

  5. A dynamically adaptive lattice Boltzmann method for thermal convection problems

    Directory of Open Access Journals (Sweden)

    Feldhusen Kai

    2016-12-01

    Full Text Available Utilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM for forced and natural convection in two and three space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement (AMR procedure tailored for the LBM is applied to enable computationally efficient simulations of moderate to high Rayleigh number flows which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The objective of the latter is to advance the boundary conditions for an accurate treatment of curved boundaries and to demonstrate the effect on the solution. The effectiveness of the overall approach is demonstrated for the natural convection benchmark of a 2D cavity with differentially heated walls at Rayleigh numbers from 103 up to 108. To demonstrate the benefit of the employed AMR procedure for three-dimensional (3D problems, results from the natural convection in a cubic cavity at Rayleigh numbers from 103 up to 105 are compared with benchmark results.

  6. Boundary Conditions for Free Interfaces with the Lattice Boltzmann Method

    CERN Document Server

    Bogner, Simon; Rüde, Ulrich

    2014-01-01

    In this paper we analyze the boundary treatment of the Lattice Boltzmann method for simulating 3D flows with free surfaces. The widely used free surface boundary condition of K\\"orner et al. (2005) is shown to be first order accurate. The article presents new free surface boundary schemes that are suitable for the lattice Boltzmann method and that have second order spatial accuracy. The new method takes the free boundary position and orientation with respect to the computational lattice into account. Numerical experiments confirm the theoretical findings and illustrate the the difference between the old and the new method.

  7. One-dimensional lattices topologically equivalent to two-dimensional lattices within the context of the lattice gas model. II The triangular lattice

    Science.gov (United States)

    Costanza, E. F.; Costanza, G.

    2016-12-01

    Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to two-dimensional lattices is described in detail in the case of a triangular lattice. This example shows the general features that possess the procedure and extensions are also suggested in order to provide a wider insight in the present approach.

  8. One-dimensional lattices topologically equivalent to two-dimensional lattices within the context of the lattice gas model, III. The hexagonal lattice

    Science.gov (United States)

    Costanza, E. F.; Costanza, G.

    2017-02-01

    Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to two-dimensional lattices is described in detail in the case of a hexagonal lattice which has the particular feature that need four types of dynamical variables. This example shows additional features to the general procedure and some extensions are also suggested in order to provide a wider insight in the present approach.

  9. Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices.

    Science.gov (United States)

    Li, Q; Luo, K H; He, Y L; Gao, Y J; Tao, W Q

    2012-01-01

    In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard two-dimensional nine-velocity (D2Q9) lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small. Meanwhile, the simple structure and general features of the DDF LB approach are retained. The model is tested by numerical simulations of thermal Couette flow, attenuation-driven acoustic streaming, and natural convection in a square cavity with small and large temperature differences. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.

  10. Hofstadter butterfly evolution in the space of two-dimensional Bravais lattices

    Science.gov (United States)

    Yılmaz, F.; Oktel, M. Ö.

    2017-06-01

    The self-similar energy spectrum of a particle in a periodic potential under a magnetic field, known as the Hofstadter butterfly, is determined by the lattice geometry as well as the external field. Recent realizations of artificial gauge fields and adjustable optical lattices in cold-atom experiments necessitate the consideration of these self-similar spectra for the most general two-dimensional lattice. In a previous work [F. Yılmaz et al., Phys. Rev. A 91, 063628 (2015), 10.1103/PhysRevA.91.063628], we investigated the evolution of the spectrum for an experimentally realized lattice which was tuned by changing the unit-cell structure but keeping the square Bravais lattice fixed. We now consider all possible Bravais lattices in two dimensions and investigate the structure of the Hofstadter butterfly as the lattice is deformed between lattices with different point-symmetry groups. We model the optical lattice with a sinusoidal real-space potential and obtain the tight-binding model for any lattice geometry by calculating the Wannier functions. We introduce the magnetic field via Peierls substitution and numerically calculate the energy spectrum. The transition between the two most symmetric lattices, i.e., the triangular and the square lattices, displays the importance of bipartite symmetry featuring deformation as well as closing of some of the major energy gaps. The transitions from the square to rectangular lattice and from the triangular to centered rectangular lattices are analyzed in terms of coupling of one-dimensional chains. We calculate the Chern numbers of the major gaps and Chern number transfer between bands during the transitions. We use gap Chern numbers to identify distinct topological regions in the space of Bravais lattices.

  11. Two-dimensional Talbot self-imaging via Electromagnetically induced lattice

    Science.gov (United States)

    Wen, Feng; Wang, Wei; Ahmed, Irfan; Wang, Hongxing; Zhang, Yiqi; Zhang, Yanpeng; Mahesar, Abdul Rasheed; Xiao, Min

    2017-02-01

    We propose a lensless optical method for imaging two-dimensional ultra-cold atoms (or molecules) in which the image can be non-locally observed by coincidence recording of entangled photon pairs. In particular, we focus on the transverse and longitudinal resolutions of images under various scanning methods. In addition, the role of the induced nonmaterial lattice on the image contrast is investigated. Our work shows a non-destructive and lensless way to image ultra-cold atoms or molecules that can be further used for two-dimensional atomic super-resolution optical testing and sub-wavelength lithography.

  12. Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice

    Institute of Scientific and Technical Information of China (English)

    Yize Wang; Fengming Li; Yuesheng Wang; Kikuo Kishimoto; Wenhu Huang

    2009-01-01

    In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The gener-alized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet the-orem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the plane-wave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectric-ity with the larger lattice constant ratios and the filling frac-tions.

  13. On the Stability of the Finite Difference based Lattice Boltzmann Method

    KAUST Repository

    El-Amin, Mohamed

    2013-06-01

    This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.

  14. Numerical simulation of ski-jump jet motion using lattice Boltzmann method

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    Based on the lattice Boltzmann method,a lattice Boltzmann(LB) model of the ski-jump jet two-phase flow is developed first and the corresponding boundary conditions are studied.A simple case study of a droplet horizontal movement calculation is carried out to test and verify the model,where level set method is used to track and reconstruct the moving droplet free surface. Then,we numerically simulate a two dimensional flow field of the ski-jump jet with the LB model,derive the moving surface and velocity vector field of the jet flow.The simulation results are very consistent with the physical mechanisms.The effectiveness and reliability of the model are demonstrated by the numerical examples.

  15. Influence of asperities on fluid and thermal flow in a fracture: a coupled Lattice Boltzmann study

    CERN Document Server

    Neuville, Amélie; Toussaint, Renaud

    2013-01-01

    The characteristics of the hydro-thermal flow which occurs when a cold fluid is injected into a hot fractured bedrock depend on the morphology of the fracture. We consider a sharp triangular asperity, invariant in one direction, perturbing an otherwise flat fracture. We investigate its influence on the macroscopic hydraulic transmissivity and heat transfer efficiency, at fixed low Reynolds number. In this study, numerical simulations are done with a coupled lattice Boltzmann method that solves both the complete Navier-Stokes and advection-diffusion equations in three dimensions. The results are compared with those obtained under lubrication approximations which rely on many hypotheses and neglect the three-dimensional (3D) effects. The lubrication results are obtained by analytically solving the Stokes equation and a two-dimensional (integrated over the thickness) advection-diffusion equation. We use a lattice Boltzmann method with a double distribution (for mass and energy transport) on hypercubic and cubic ...

  16. Numerical simulation of direct methanol fuel cells using lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

    Delavar, Mojtaba Aghajani; Farhadi, Mousa; Sedighi, Kurosh [Faculty of Mechanical Engineering, Babol University of Technology, Babol, P.O. Box 484 (Iran)

    2010-09-15

    In this study Lattice Boltzmann Method (LBM) as an alternative of conventional computational fluid dynamics method is used to simulate Direct Methanol Fuel Cell (DMFC). A two dimensional lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the problem. The computational domain includes all seven parts of DMFC: anode channel, catalyst and diffusion layers, membrane and cathode channel, catalyst and diffusion layers. The model has been used to predict the flow pattern and concentration fields of different species in both clear and porous channels to investigate cell performance. The results have been compared well with results in literature for flow in porous and clear channels and cell polarization curves of the DMFC at different flow speeds and feed methanol concentrations. (author)

  17. Double MRT Thermal Lattice Boltzmann Method for Simulating Natural Convection of Low Prandtl Number Fluids

    CERN Document Server

    Li, Zheng; Zhang, Yuwen

    2016-01-01

    The purposes of this paper are testing an efficiency algorithm based on LBM and using it to analyze two-dimensional natural convection with low Prandtl number. Steady state or oscillatory results are obtained using double multiple-relaxation-time thermal lattice Boltzmann method. The velocity and temperature fields are solved using D2Q9 and D2Q5 models, respectively. With different Rayleigh number, the tested natural convection can either achieve to steady state or oscillatory. With fixed Rayleigh number, lower Prandtl number leads to a weaker convection effect, longer oscillation period and higher oscillation amplitude for the cases reaching oscillatory solutions. At fixed Prandtl number, higher Rayleigh number leads to a more notable convection effect and longer oscillation period. Double multiple-relaxation-time thermal lattice Boltzmann method is applied to simulate the low Prandtl number fluid natural convection. Rayleigh number and Prandtl number effects are also investigated when the natural convection...

  18. Stabilizing the thermal lattice Boltzmann method by spatial filtering.

    Science.gov (United States)

    Gillissen, J J J

    2016-10-01

    We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions.

  19. An integrable 3D lattice model with positive Boltzmann weights

    CERN Document Server

    Mangazeev, Vladimir V; Sergeev, Sergey M

    2013-01-01

    In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D generalisation of the Yang-Baxter equation. The weights depend on a free parameter 0lattice model with non-negative Boltzmann weights.

  20. Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi-Pasta-Ulam lattice

    Institute of Scientific and Technical Information of China (English)

    Xu Quan; Tian Qiang

    2013-01-01

    Using numerical method,we investigate whether periodic,quasiperiodic,and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam (FPU) lattice with linear dispersion term.The spatial profile and time evolution of the two-dimensional discrete β-FPU lattice are segregated by the method of separation of variables,and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system.By introducing a periodic interaction into the linear interaction between the atoms,we achieve the coupling of two incommensurate frequencies for a single DB,and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system,too.

  1. Non-classical photon correlation in a two-dimensional photonic lattice

    CERN Document Server

    Gao, Jun; Lin, Xiao-Feng; Jiao, Zhi-Qiang; Feng, Zhen; Zhou, Zheng; Gao, Zhen-Wei; Xu, Xiao-Yun; Chen, Yuan; Tang, Hao; Jin, Xian-Min

    2016-01-01

    Quantum interference and quantum correlation, as two main features of quantum optics, play an essential role in quantum information applications, such as multi-particle quantum walk and boson sampling. While many experimental demonstrations have been done in one-dimensional waveguide arrays, it remains unexplored in higher dimensions due to tight requirement of manipulating and detecting photons in large-scale. Here, we experimentally observe non-classical correlation of two identical photons in a fully coupled two-dimensional structure, i.e. photonic lattice manufactured by three-dimensional femtosecond laser writing. Photon interference consists of 36 Hong-Ou-Mandel interference and 9 bunching. The overlap between measured and simulated distribution is up to $0.890\\pm0.001$. Clear photon correlation is observed in the two-dimensional photonic lattice. Combining with controllably engineered disorder, our results open new perspectives towards large-scale implementation of quantum simulation on integrated phot...

  2. Tunable band topology reflected by fractional quantum Hall States in two-dimensional lattices.

    Science.gov (United States)

    Wang, Dong; Liu, Zhao; Cao, Junpeng; Fan, Heng

    2013-11-01

    Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from the Hofstadter model and demonstrate that the band topology transitions can be realized by simply introducing tunable longer-range hopping. The rich phase diagram of band Chern numbers is obtained for the simple rational flux density and a classification of phases is presented. In the presence of interactions, the existence of fractional quantum Hall states in both |C| = 1 and |C| > 1 bands is confirmed, which can reflect the band topologies in different phases. In contrast, when our model reduces to a one-dimensional lattice, the ground states are crucially different from fractional quantum Hall states. Our results may provide insights into the study of new fractional quantum Hall states and experimental realizations of various topological phases in optical lattices.

  3. Two-Dimensional Photonic Band-Gap Defect Modes with Deformed Lattice

    Institute of Scientific and Technical Information of China (English)

    CAI Xiang-Hua; ZHENG Wan-Hua; MA Xiao-Tao; REN Gang; XIA Jian-Bai

    2005-01-01

    @@ A numerical study of the defect modes in two-dimensional photonic crystals with deformed triangular lattice is presented by using the supercell method and the finite-difference time-domain method We find the stretch or shrink of the lattice can bring the change not only on the frequencies of the defect modes but also on their magnetic field distributions. We obtain the separation of the doubly degenerate dipole modes with the change of the lattice and find that both the stretch and the shrink of the lattice can make the dipole modes separate large enough to realize the single-mode emission. These results may be advantageous to the manufacture of photonic crystal lasers and provide a new way to realize the single-mode operation in photonic crystal lasers.

  4. The mean field study of phase transitions in two dimensional Kagome lattice under local anisotropy

    Directory of Open Access Journals (Sweden)

    S. Mortezapour

    2007-06-01

    Full Text Available  In this work we investigated the critical properties of the anti-ferromagnetic XY model on a two dimensional Kagome lattice under single-ion easy-axes anisotropy. Employing the mean field theory, we found that this model shows a second order phase transition from disordered to all-in all-out state for any value of anisotropy.

  5. Light-Induced Hofstadter's Butterfly Spectrum of Ultracold Atoms on the Two-Dimensional Kagome Lattice

    Institute of Scientific and Technical Information of China (English)

    HOU Jing-Min

    2009-01-01

    We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagome optical lattice under an effective magnetic field,which can be realized with laser beams.We derive the generalized Harper's equations from the Schr(o)dinger equation.The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper's equations.We analyze the properties of the Hofstadter's butterfly spectrum and discuss its observability.

  6. Quantum Monte Carlo simulation of a two-dimensional Majorana lattice model

    Science.gov (United States)

    Hayata, Tomoya; Yamamoto, Arata

    2017-07-01

    We study interacting Majorana fermions in two dimensions as a low-energy effective model of a vortex lattice in two-dimensional time-reversal-invariant topological superconductors. For that purpose, we implement ab initio quantum Monte Carlo simulation to the Majorana fermion system in which the path-integral measure is given by a semipositive Pfaffian. We discuss spontaneous breaking of time-reversal symmetry at finite temperatures.

  7. Closed-form evaluation of two-dimensional static lattice sums

    Science.gov (United States)

    Yakubovich, S.; Drygas, P.; Mityushev, V.

    2016-11-01

    Closed-form formulae for the conditionally convergent two-dimensional (2D) static lattice sums S2 (for conductivity) and T2 (for elasticity) are deduced in terms of the complete elliptic integrals of the first and second kind. The obtained formulae yield asymptotic analytical formulae for the effective tensors of 2D composites with circular inclusions up to the third order in concentration. Exact relations between S2 and T2 for different lattices are established. In particular, the value S2=π for the square and hexagonal arrays is discussed and T2=π/2 for the hexagonal is deduced.

  8. Competitive irreversible random one-, two-, three-, . . . point adsorption on two-dimensional lattices

    Science.gov (United States)

    Evans, J. W.; Nord, R. S.

    1985-02-01

    An analytic treatment of competitive, irreversible (immobile) random one-, two-, three-, . . . point adsorption (or monomer, dimer, trimer, . . . filling) on infinite, uniform two-dimensional lattices is provided by applying previously developed truncation schemes to the hierarchial form of the appropriate master equations. The behavior of these processes for two competing species is displayed by plotting families of ``filling trajectories'' in the partial-coverage plane for various ratios of adsorption rates. The time or coverage dependence of various subconfiguration probabilities can also be analyzed. For processes where no one-point (monomer) adsorption occurs, the lattice cannot fill completely; accurate estimates of the total (and partial) saturation coverages can be obtained.

  9. Fundamental and vortex solitons in a two-dimensional optical lattice

    CERN Document Server

    Yang, J; Yang, Jianke; Musslimani, Ziad

    2003-01-01

    Fundamental and vortex solitons in a two-dimensional optically induced waveguide array are reported. In the strong localization regime, the fundamental soliton is largely confined to one lattice site, while the vortex state comprises of four fundamental modes superimposed in a square configuration with a phase structure that is topologically equivalent to the conventional vortex. However, in the weak localization regime, both the fundamental and vortex solitons spread over many lattice sites. We further show that fundamental and vortex solitons are stable against small perturbations in the strong localization regime.

  10. Dynamic Effective Medium Theory for Two-Dimensional Non-Magnetic Metamaterial Lattices using Multipole Expansion

    CERN Document Server

    Chremmos, Ioannis; Giamalaki, Melpomeni; Yannopapas, Vassilios; Paspalakis, Emmanuel

    2014-01-01

    We present a formulation for deriving effective medium properties of infinitely periodic two-dimensional metamaterial lattice structures beyond the static and quasi-static limits. We utilize the multipole expansions, where the polarization currents associated with the supported Bloch modes are expressed via the electric dipole, magnetic dipole, and electric quadrupole moments per unit length. We then propose a method to calculate the Bloch modes based on the lattice geometry and individual unit element structure. The results revert to well-known formulas in the quasistatic limit and are useful for the homogenization of nanorod-type metamaterials which are frequently used in optical applications.

  11. Configurational entropy of a set of dipoles placed on a two-dimensional lattice

    Science.gov (United States)

    Dammig Quiña, P. L.; Irurzun, I. M.; Mola, E. E.

    2017-01-01

    In the present work we calculate the configurational entropy of an arbitrary number of dipoles placed on a square lattice. We use a quasi-two-dimensional (Q2D) space to capture the main features determining the occupation statistics of this system. We show that our result is in agreement with both, lattice-gas predictions at low coverages and the exact value derived in the close-packed limit as well. Therefore our equation provides a substantial improvement to the most recent calculations based on semiempirical models and Monte Carlo simulations.

  12. Heteroepitaxial growth modes with dislocations in a two-dimensional elastic lattice model

    Science.gov (United States)

    Katsuno, Hiroyasu; Uwaha, Makio; Saito, Yukio

    2008-11-01

    We study equilibrium shapes of adsorbate crystals by allowing a possibility of dislocations on an elastic substrate in a two-dimensional lattice model. The ground state energy is calculated numerically with the use of an elastic lattice Green's function. From the equilibrium shapes determined for various coverages, we infer the growth mode. As the misfit parameter increases, the growth mode changes from the Frank-van der Merwe (FM) to the Stranski-Krastanov (SK), further to the FM with dislocations for a parameter range of ordinary semiconductor materials. Conceivable growth modes such as the SK with dislocations appear in a parameter range between the SK and the FM with dislocations.

  13. Contact line dynamics in binary lattice Boltzmann simulations

    CERN Document Server

    Pooley, C M; Yeomans, J M; 10.1103/PhysRevE.78.056709

    2008-01-01

    We show that, when a single relaxation time lattice Boltzmann algorithm is used to solve the hydrodynamic equations of a binary fluid for which the two components have different viscosities, strong spurious velocities in the steady state lead to incorrect results for the equilibrium contact angle. We identify the origins of these spurious currents, and demonstrate how the results can be greatly improved by using a lattice Boltzmann method based on a multiple-relaxation-time algorithm. By considering capillary filling we describe the dependence of the advancing contact angle on the interface velocity.

  14. Axisymmetric multiphase Lattice Boltzmann method for generic equations of state

    CERN Document Server

    Reijers, Sten A; Toschi, Federico

    2015-01-01

    We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid-gas density ratios up to $10^3$. Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymmetric multiphase conservation equations. We validate the model by showing that a stationary droplet obeys the Young-Laplace law, comparing the second oscillation mode of a droplet with respect to an analytical solution and showing correct mass conservation of a propagating density wave.

  15. Boundaries determine the formation energies of lattice defects in two-dimensional buckled materials

    Science.gov (United States)

    Jain, Sandeep K.; Juričić, Vladimir; Barkema, Gerard T.

    2016-07-01

    Lattice defects are inevitably present in two-dimensional materials, with direct implications on their physical and chemical properties. We show that the formation energy of a lattice defect in buckled two-dimensional crystals is not uniquely defined as it takes different values for different boundary conditions even in the thermodynamic limit, as opposed to their perfectly planar counterparts. Also, the approach to the thermodynamic limit follows a different scaling: inversely proportional to the logarithm of the system size for buckled materials, rather than the usual power-law approach. In graphene samples of ˜1000 atoms, different boundary conditions can cause differences exceeding 10 eV. Besides presenting numerical evidence in simulations, we show that the universal features in this behavior can be understood with simple bead-spring models. Fundamentally, our findings imply that it is necessary to specify the boundary conditions for the energy of the lattice defects in the buckled two-dimensional crystals to be uniquely defined, and this may explain the lack of agreement in the reported values of formation energies in graphene. We argue that boundary conditions may also have an impact on other physical observables such as the melting temperature.

  16. Lattice Boltzmann method and its applications in engineering thermophysics

    Institute of Scientific and Technical Information of China (English)

    HE YaLing; LI Qing; WANG Yong; TANG GuiHua

    2009-01-01

    The lattice Boltzmann method (LBM),a mesoscopic method between the molecular dynamics method and the conventional numerical methods,has been developed into a very efficient numerical alternative in the past two decades.Unlike conventional numerical methods,the kinetic theory based LBM simulates fluid flows by tracking the evolution of the particle distribution function,and then accumulates the distribution to obtain macroscopic averaged properties.In this article we review some work on LBM applications in engineering thermophysics:(1) brief introduction to the development of the LBM; (2)fundamental theory of LBM including the Boltzmann equation,Maxwell distribution function,Boltzmann-BGK equation,and the lattice Boltzmann-BGK equation; (3) lattice Boltzmann models for compressible flows and non-equilibrium gas flows,bounce back-specular-reflection boundary scheme for microscale gaseous flows,the mass modified outlet boundary scheme for fully developed flows,and an implicit-explicit finite-difference-based LBM; and (4) applications of the LBM to oscillating flow,compressible flow,porous media flow,non-equilibrium flow,and gas resonant oscillating flow.

  17. Multiple-relaxation-time lattice Boltzmann kinetic model for combustion.

    Science.gov (United States)

    Xu, Aiguo; Lin, Chuandong; Zhang, Guangcai; Li, Yingjun

    2015-04-01

    To probe both the hydrodynamic nonequilibrium (HNE) and thermodynamic nonequilibrium (TNE) in the combustion process, a two-dimensional multiple-relaxation-time (MRT) version of lattice Boltzmann kinetic model (LBKM) for combustion phenomena is presented. The chemical energy released in the progress of combustion is dynamically coupled into the system by adding a chemical term to the LB kinetic equation. Aside from describing the evolutions of the conserved quantities, the density, momentum, and energy, which are what the Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained description on the evolutions of some nonconserved quantities. The current model works for both subsonic and supersonic flows with or without chemical reaction. In this model, both the specific-heat ratio and the Prandtl number are flexible, the TNE effects are naturally presented in each simulation step. The model is verified and validated via well-known benchmark tests. As an initial application, various nonequilibrium behaviors, including the complex interplays between various HNEs, between various TNEs, and between the HNE and TNE, around the detonation wave in the unsteady and steady one-dimensional detonation processes are preliminarily probed. It is found that the system viscosity (or heat conductivity) decreases the local TNE, but increases the global TNE around the detonation wave, that even locally, the system viscosity (or heat conductivity) results in two kinds of competing trends, to increase and to decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses.

  18. Peristaltic particle transport using the Lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

    Connington, Kevin William [Los Alamos National Laboratory; Kang, Qinjun [Los Alamos National Laboratory; Viswanathan, Hari S [Los Alamos National Laboratory; Abdel-fattah, Amr [Los Alamos National Laboratory; Chen, Shiyi [JOHNS HOPKINS UNIV.

    2009-01-01

    Peristaltic transport refers to a class of internal fluid flows where the periodic deformation of flexible containing walls elicits a non-negligible fluid motion. It is a mechanism used to transport fluid and immersed solid particles in a tube or channel when it is ineffective or impossible to impose a favorable pressure gradient or desirous to avoid contact between the transported mixture and mechanical moving parts. Peristaltic transport occurs in many physiological situations and has myriad industrial applications. We focus our study on the peristaltic transport of a macroscopic particle in a two-dimensional channel using the lattice Boltzmann method. We systematically investigate the effect of variation of the relevant dimensionless parameters of the system on the particle transport. We find, among other results, a case where an increase in Reynolds number can actually lead to a slight increase in particle transport, and a case where, as the wall deformation increases, the motion of the particle becomes non-negative only. We examine the particle behavior when the system exhibits the peculiar phenomenon of fluid trapping. Under these circumstances, the particle may itself become trapped where it is subsequently transported at the wave speed, which is the maximum possible transport in the absence of a favorable pressure gradient. Finally, we analyze how the particle presence affects stress, pressure, and dissipation in the fluid in hopes of determining preferred working conditions for peristaltic transport of shear-sensitive particles. We find that the levels of shear stress are most hazardous near the throat of the channel. We advise that shear-sensitive particles should be transported under conditions where trapping occurs as the particle is typically situated in a region of innocuous shear stress levels.

  19. Designing artificial two dimensional electron lattice on metal surface: a Kagome-like lattice as an example.

    Science.gov (United States)

    Li, Shuai; Qiu, Wen-Xuan; Gao, Jin-Hua

    2016-07-07

    Recently, a new kind of artificial two dimensional (2D) electron lattice on the nanoscale, i.e. molecular graphene, has drawn a lot of interest, where the metal surface electrons are transformed into a honeycomb lattice via absorbing a molecular lattice on the metal surface [Gomes et al., Nature, 2012, 438, 306; Wang et al., Phys. Rev. Lett., 2014, 113, 196803]. In this work, we theoretically demonstrate that this technique can be readily used to build other complex 2D electron lattices on a metal surface, which are of high interest in the field of condensed matter physics. The main challenge to build a complex 2D electron lattice is that this is a quantum antidot system, where the absorbed molecule normally exerts a repulsive potential on the surface electrons. Thus, there is no straightforward corresponding relation between the molecular lattice pattern and the desired 2D lattice of surface electrons. Here, we give an interesting example about the Kagome lattice, which has exotic correlated electronic states. We design a special molecular pattern and show that this molecular lattice can transform the surface electrons into a Kagome-like lattice. The numerical simulation is conducted using a Cu(111) surface and CO molecules. We first estimate the effective parameters of the Cu/CO system by fitting experimental data of the molecular graphene. Then, we calculate the corresponding energy bands and LDOS of the surface electrons in the presence of the proposed molecular lattice. Finally, we interpret the numerical results by the tight binding model of the Kagome lattice. We hope that our work can stimulate further theoretical and experimental interest in this novel artificial 2D electron lattice system.

  20. A Parallel Lattice Boltzmann Model of a Carotid Artery

    Science.gov (United States)

    Boyd, J.; Ryan, S. J.; Buick, J. M.

    2008-11-01

    A parallel implementation of the lattice Boltzmann model is considered for a three dimensional model of the carotid artery. The computational method and its parallel implementation are described. The performance of the parallel implementation on a Beowulf cluster is presented, as are preliminary hemodynamic results.

  1. The lattice Boltzmann method and the problem of turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Djenidi, L. [School of Engineering The University of Newcastle, Callaghan NSW 2308 (Australia)

    2015-03-10

    This paper reports a brief review of numerical simulations of homogeneous isotopic turbulence (HIT) using the lattice Boltzmann method (LBM). The LBM results shows that the details of HIT are well captured and in agreement with existing data. This clearly indicates that the LBM is as good as current Navier-Stokes solvers and is very much adequate for investigating the problem of turbulence.

  2. EXTERNAL BODY FORCE IN FINITE DIFFERENCE LATTICE BOLTZMANN METHOD

    Institute of Scientific and Technical Information of China (English)

    CHEN Sheng; LIU Zhao-hui; SHI Bao-chang; ZHENG Chu-guang

    2005-01-01

    A new finite difference lattice Boltzmann scheme is developed. Because of analyzing the influence of external body force roundly, the correct Navier-Stokes equations with the external body force are recovered, without any additional unphysical terms. And some numerical results are presented. The result which close agreement with analytical data shows the good performance of the model.

  3. Lattice Boltzmann simulations of droplet formation during microchannel emulsification

    NARCIS (Netherlands)

    Zwan, van der E.A.; Sman, van der R.G.M.; Schroën, C.G.P.H.; Boom, R.M.

    2009-01-01

    In this study, we compared microchannel droplet formation in a microfluidics device with a two phase lattice Boltzmann simulation. The droplet formation was found to be qualitatively described, with a slightly smaller droplet in the simulation. This was due to the finite thickness of the interface i

  4. Performance evaluation of a parallel sparse lattice Boltzmann solver

    NARCIS (Netherlands)

    Axner, L.; Bernsdorf, J.; Zeiser, T.; Lammers, P.; Linxweiler, J.; Hoekstra, A.G.

    2008-01-01

    We develop a performance prediction model for a parallelized sparse lattice Boltzmann solver and present performance results for simulations of flow in a variety of complex geometries. A special focus is on partitioning and memory/load balancing strategy for geometries with a high solid fraction and

  5. Lattice Boltzmann solution of the transient Boltzmann transport equation in radiative and neutron transport.

    Science.gov (United States)

    Wang, Yahui; Yan, Liming; Ma, Yu

    2017-06-01

    Applications of the transient Boltzmann transport equation (BTE) have undergone much investigation, such as radiative heat transfer and neutron transport. This paper provides a lattice Boltzmann model to efficiently resolve the multidimensional transient BTE. For a higher angular resolution, enough transport directions are considered while the transient BTE in each direction is treated as a conservation law equation and solved independently. Both macroscopic equations recovered from a Chapman-Enskog expansion and simulated results of typical benchmark problems show not only the second-order accuracy but also the flexibility and applicability of the proposed lattice Boltzmann model. This approach may contribute a powerful technique for the parallel simulation of large-scale engineering and some alternative perspectives for solving the nonlinear transport problem further.

  6. High-accuracy approximation of high-rank derivatives: isotropic finite differences based on lattice-Boltzmann stencils.

    Science.gov (United States)

    Mattila, Keijo Kalervo; Hegele Júnior, Luiz Adolfo; Philippi, Paulo Cesar

    2014-01-01

    We propose isotropic finite differences for high-accuracy approximation of high-rank derivatives. These finite differences are based on direct application of lattice-Boltzmann stencils. The presented finite-difference expressions are valid in any dimension, particularly in two and three dimensions, and any lattice-Boltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of lattice-Boltzmann stencils in the approximation of high-rank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing lattice-Boltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th-, 6th-, and 8th-order two-dimensional lattice-Boltzmann stencils.

  7. Theoretical and numerical investigation of HF elastic wave propagation in two-dimensional periodic beam lattices

    Science.gov (United States)

    Tie, B.; Tian, B. Y.; Aubry, D.

    2013-12-01

    The elastic wave propagation phenomena in two-dimensional periodic beam lattices are studied by using the Bloch wave transform. The numerical modeling is applied to the hexagonal and the rectangular beam lattices, in which, both the in-plane (with respect to the lattice plane) and out-of-plane waves are considered. The dispersion relations are obtained by calculating the Bloch eigenfrequencies and eigenmodes. The frequency bandgaps are observed and the influence of the elastic and geometric properties of the primitive cell on the bandgaps is studied. By analyzing the phase and the group velocities of the Bloch wave modes, the anisotropic behaviors and the dispersive characteristics of the hexagonal beam lattice with respect to the wave propagation are highlighted in high frequency domains. One important result presented herein is the comparison between the first Bloch wave modes to the membrane and bending/transverse shear wave modes of the classical equivalent homogenized orthotropic plate model of the hexagonal beam lattice. It is shown that, in low frequency ranges, the homogenized plate model can correctly represent both the in-plane and out-of-plane dynamic behaviors of the beam lattice, its frequency validity domain can be precisely evaluated thanks to the Bloch modal analysis. As another important and original result, we have highlighted the existence of the retropropagating Bloch wave modes with a negative group velocity, and of the corresponding "retro-propagating" frequency bands.

  8. Lattice Boltzmann technique for heat transport phenomena coupled with melting process

    Science.gov (United States)

    Ibrahem, A. M.; El-Amin, M. F.; Mohammadein, A. A.; Gorla, Rama Subba Reddy

    2016-04-01

    In this work, the heat transport phenomena coupled with melting process are studied by using the enthalpy-based lattice Boltzmann method (LBM). The proposed model is a modified version of thermal LB model, where could avoid iteration steps and ensures high accuracy. The Bhatnagar-Gross-Krook (BGK) approximation with a D1Q2 lattice was used to determine the temperature field for one-dimensional melting by conduction and multi-distribution functions (MDF) with D2Q9 lattice was used to determine the density, velocity and temperature fields for two-dimensional melting by natural convection. Different boundary conditions including Dirichlet, adiabatic and bounce-back boundary conditions were used. The influence of increasing Rayleigh number (from 103 to 105) on temperature distribution and melting process is studied. The obtained results show that a good agreement with the analytical solution for melting by conduction case and with the benchmark solution for melting by convection.

  9. Lattice Boltzmann technique for heat transport phenomena coupled with melting process

    Science.gov (United States)

    Ibrahem, A. M.; El-Amin, M. F.; Mohammadein, A. A.; Gorla, Rama Subba Reddy

    2017-01-01

    In this work, the heat transport phenomena coupled with melting process are studied by using the enthalpy-based lattice Boltzmann method (LBM). The proposed model is a modified version of thermal LB model, where could avoid iteration steps and ensures high accuracy. The Bhatnagar-Gross-Krook (BGK) approximation with a D1Q2 lattice was used to determine the temperature field for one-dimensional melting by conduction and multi-distribution functions (MDF) with D2Q9 lattice was used to determine the density, velocity and temperature fields for two-dimensional melting by natural convection. Different boundary conditions including Dirichlet, adiabatic and bounce-back boundary conditions were used. The influence of increasing Rayleigh number (from 103 to 105) on temperature distribution and melting process is studied. The obtained results show that a good agreement with the analytical solution for melting by conduction case and with the benchmark solution for melting by convection.

  10. Lattice Boltzmann method for multimode wave propagation in viscoelastic media and in elastic solids.

    Science.gov (United States)

    Frantziskonis, George N

    2011-06-01

    This paper reports the lattice Boltzmann method (LBM) based formulation for viscoelastic fluids with both volumetric and shear viscoelasticity. The relaxation limit of the viscoelastic fluid formulation yields the LBM for elastic solids with both volumetric or pressure (p) and shear (s) wave propagation modes. The reflection of a two-dimensional p wave from an obstacle (wedge) inclined to the propagation direction of the p wave is studied together with the convergence and stability behavior of the LBM as the lattice size and lattice time step decrease. The model is capable of accurately predicting the mode change (p to s) due to the reflection. The model provides a unique unified approach capable of simulating fluids, viscoelastic fluids, and solids within a single LBM framework, thus avoiding interface problems between different simulation methods. The paper concentrates on the wave propagation part of the model, in the quasielastic regime.

  11. A numerical theory of lattice gas and lattice Boltzmann methods in the computation of solutions to nonlinear advective-diffusive systems

    Energy Technology Data Exchange (ETDEWEB)

    Elton, A.B.H.

    1990-09-24

    A numerical theory for the massively parallel lattice gas and lattice Boltzmann methods for computing solutions to nonlinear advective-diffusive systems is introduced. The convergence theory is based on consistency and stability arguments that are supported by the discrete Chapman-Enskog expansion (for consistency) and conditions of monotonicity (in establishing stability). The theory is applied to four lattice methods: Two of the methods are for some two-dimensional nonlinear diffusion equations. One of the methods is for the one-dimensional lattice method for the one-dimensional viscous Burgers equation. And one of the methods is for a two-dimensional nonlinear advection-diffusion equation. Convergence is formally proven in the L{sub 1}-norm for the first three methods, revealing that they are second-order, conservative, conditionally monotone finite difference methods. Computational results which support the theory for lattice methods are presented. In addition, a domain decomposition strategy using mesh refinement techniques is presented for lattice gas and lattice Boltzmann methods. The strategy allows concentration of computational resources on regions of high activity. Computational evidence is reported for the strategy applied to the lattice gas method for the one-dimensional viscous Burgers equation. 72 refs., 19 figs., 28 tabs.

  12. Quantum State Transfer in a Two-dimensional Regular Spin Lattice of Triangular Shape

    CERN Document Server

    Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei

    2012-01-01

    Quantum state transfer in a triangular domain of a two-dimensional, equally-spaced, spin lat- tice with non-homogeneous nearest-neighbor couplings is analyzed. An exact solution of the one- excitation dynamics is provided in terms of 2-variable Krawtchouk orthogonal polynomials that have been recently defined. The probability amplitude for an excitation to transit from one site to another is given. For some values of the parameters, perfect transfer is shown to take place from the apex of the lattice to the boundary hypotenuse.

  13. High applicability of two-dimensional phosphorous in Kagome lattice predicted from first-principles calculations

    OpenAIRE

    Peng-Jen Chen; Horng-Tay Jeng

    2016-01-01

    A new semiconducting phase of two-dimensional phosphorous in the Kagome lattice is proposed from first-principles calculations. The band gaps of the monolayer (ML) and bulk Kagome phosphorous (Kagome-P) are 2.00 and 1.11 eV, respectively. The magnitude of the band gap is tunable by applying the in-plane strain and/or changing the number of stacking layers. High optical absorption coefficients at the visible light region are predicted for multilayer Kagome-P, indicating potential applications ...

  14. Hamiltonian dynamics of the two-dimensional lattice {phi}{sup 4} model

    Energy Technology Data Exchange (ETDEWEB)

    Caiani, Lando [Scuola Internazionale Superiore di Studi Avanzati (SISSA/ISAS), Trieste (Italy); Casetti, Lapo [Istituto Nazionale di Fisica della Materia (INFM), Unita di Ricerca del Politecnico di Torino, Dipartimento di Fisica, Politecnico di Torino, Turin (Italy); Pettini, Marco [Osservatorio Astrofisico di Arcetri, Florence (Italy)

    1998-04-17

    The Hamiltonian dynamics of the classical {phi}{sup 4} model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics. (author)

  15. Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice

    CERN Document Server

    Giguère, Eric

    2015-01-01

    We perform lattice simulations of two-dimensional supersymmetric Yang-Mills theory with sixteen supercharges with a lattice action which has two exact supercharges (Sugino lattice action). According to the gauge/gravity duality, the theory at finite temperature is expected to be well described by the corresponding black 1-branes, at low temperature in the large N limit. We aim to confirm the duality conjecture by comparing the lattice results with the theoretical predictions obtained in the gravity side. In this article, at the beginning of this study, we examine the supersymmetric Ward-Takahashi identity to test whether the lattice action reproduces the correct continuum theory. Numerical results of the SUSY WTI strongly suggest us that any cut-off effects, which break supersymmetry, disappear in the continuum limit. In addition, we study the issue of degenerate vacua and find that the admissiblilty condition or any other constraints of the link fields which guarantee the unique vacuum are not always needed.

  16. Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice

    Energy Technology Data Exchange (ETDEWEB)

    Giguère, Eric [Department of Physics, University of Hokkaido,Sapporo, Hokkaido 060-0810 (Japan); Kadoh, Daisuke [KEK Theory Center, High Energy Accelerator Research Organization (KEK),Tsukuba, Ibaraki 305-0801 (Japan)

    2015-05-18

    We perform lattice simulations of two-dimensional supersymmetric Yang-Mills theory with sixteen supercharges with a lattice action which has two exact supercharges (Sugino lattice action). According to the gauge/gravity duality, the theory at finite temperature is expected to be well described by the corresponding black 1-branes, at low temperature in the large N limit. We aim to confirm the duality conjecture by comparing the lattice results with the theoretical predictions obtained in the gravity side. In this article, at the beginning of this study, we examine the supersymmetric Ward-Takahashi identity to test whether the lattice action reproduces the correct continuum theory. Numerical results of the SUSY WTI strongly suggest us that any cut-off effects, which break supersymmetry, disappear in the continuum limit. In addition, we study the issue of degenerate vacua and find that the admissiblilty condition or any other constraints of the link fields which guarantee the unique vacuum are not always needed.

  17. Hydration of an apolar solute in a two-dimensional waterlike lattice fluid.

    Science.gov (United States)

    Buzano, C; De Stefanis, E; Pretti, M

    2005-05-01

    In a previous work, we investigated a two-dimensional lattice-fluid model, displaying some waterlike thermodynamic anomalies. The model, defined on a triangular lattice, is now extended to aqueous solutions with apolar species. Water molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three equivalent bonding arms. Bond formation depends both on orientation and local density. The insertion of inert molecules displays typical signatures of hydrophobic hydration: large positive transfer free energy, large negative transfer entropy (at low temperature), strong temperature dependence of the transfer enthalpy and entropy, i.e., large (positive) transfer heat capacity. Model properties are derived by a generalized first order approximation on a triangle cluster.

  18. Entanglement entropy for a Maxwell field: Numerical calculation on a two dimensional lattice

    CERN Document Server

    Casini, Horacio

    2014-01-01

    We study entanglement entropy (EE) for a Maxwell field in 2+1 dimensions. We do numerical calculations in two dimensional lattices. This gives a concrete example of the general results of our recent work on entropy for lattice gauge fields using an algebraic approach. To evaluate the entropies we extend the standard calculation methods for the entropy of Gaussian states in canonical commutation algebras to the more general case of algebras with center and arbitrary numerical commutators. We find that while the entropy depends on the details of the algebra choice, mutual information has a well defined continuum limit. We study several universal terms for the entropy of the Maxwell field and compare with the case of a massless scalar field. We find some interesting new phenomena: An "evanescent" logarithmically divergent term in the entropy with topological coefficient which does not have any correspondence with ultraviolet entanglement in the universal quantities, and a non standard way in which strong subaddi...

  19. Competitive irreversible random one-, two-, three-,. point adsorption on two-dimensional lattices

    Energy Technology Data Exchange (ETDEWEB)

    Evans, J.W.; Nord, R.S.

    1985-02-15

    An analytic treatment of competitive, irreversible (immobile) random one-, two-, three-, . . . point adsorption (or monomer, dimer, trimer, . . . filling) on infinite, uniform two-dimensional lattices is provided by applying previously developed truncation schemes to the hierarchial form of the appropriate master equations. The behavior of these processes for two competing species is displayed by plotting families of ''filling trajectories'' in the partial-coverage plane for various ratios of adsorption rates. The time or coverage dependence of various subconfiguration probabilities can also be analyzed. For processes where no one-point (monomer) adsorption occurs, the lattice cannot fill completely; accurate estimates of the total (and partial) saturation coverages can be obtained.

  20. Spin superconductivity in the frustrated two-dimensional antiferromagnet in the square lattice

    Science.gov (United States)

    Lima, L. S.

    2017-02-01

    We use the SU(2) Schwinger boson formalism to study the spin transport in the two-dimensional S = 1 / 2 frustrated Heisenberg antiferromagnet in a square lattice, considering the second-neighbors interactions in the diagonal. We have obtained a spin superfluid behavior for the spin transport to this system similar to obtained recently to the triangular lattice. We consider an antiferromagnetic inter-chain coupling on the diagonal, J2 > 0 , and the nearest-neighbor coupling antiferromagnetic J1 > 0 . We also have in the critical temperature T0, where the correlation length ξ → 0 , that the system suffers a transition from an ordered ground state to a disordered ground state.

  1. Vector meson masses in two-dimensional SU(NC) lattice gauge theory with massive quarks

    Institute of Scientific and Technical Information of China (English)

    JIANG Jun-Qin

    2008-01-01

    Using an improved lattice Hamiltonian with massive Wilson quarks a variational method is applied to study the dependence of the vector meson mass Mv on the quark mass m and the Wilson parameter r in in the scaling window 1 ≤ 1/g2 ≤ 2, Mv/g is approximately linear in m, but Mv/g obviously does not depend on r (this differs from the quark condensate). Particularly for m → 0 our numerical results agree very well with Bhattacharya's analytical strong coupling result in the continuum, and the value of ((e)Mv/(e)m) |mm=0 in two-dimensional SU(NC) lattice gauge theory is very close to that in Schwinger model.

  2. Two-dimensional-lattice spin models with long-range antiferromagnetic interactions

    Science.gov (United States)

    Romano, S.

    1991-10-01

    We consider a classical system, consisting of m-component unit vectors (m=2,3), associated with a two-dimensional lattice \\{uk||k∈openZ2\\} and interacting via translationally and rotationally invariant antiferromagnetic pair potentials of the long-range form W=Wjk=ɛ||xj-xk||-puj.uk, p>2, where ɛ is a positive quantity, setting energy and temperature scales (i.e., T*=kBT/ɛ), and xk are the coordinates of the lattice sites. A spin-wave approach predicts orientational disorder (in the thermodynamic limit) at all finite temperatures and for all p>2 this agrees with available rigorous results for p>=4, whereas no such theorems are known in the literature when 22.

  3. Piezoelectricity in two-dimensional materials: Comparative study between lattice dynamics and ab initio calculations

    Science.gov (United States)

    Michel, K. H.; ćakır, D.; Sevik, C.; Peeters, F. M.

    2017-03-01

    The elastic constant C11 and piezoelectric stress constant e1 ,11 of two-dimensional (2D) dielectric materials comprising h-BN, 2 H -MoS2 , and other transition-metal dichalcogenides and dioxides are calculated using lattice dynamical theory. The results are compared with corresponding quantities obtained with ab initio calculations. We identify the difference between clamped-ion and relaxed-ion contributions with the dependence on inner strains which are due to the relative displacements of the ions in the unit cell. Lattice dynamics allows us to express the inner-strain contributions in terms of microscopic quantities such as effective ionic charges and optoacoustical couplings, which allows us to clarify differences in the piezoelectric behavior between h-BN and MoS2. Trends in the different microscopic quantities as functions of atomic composition are discussed.

  4. Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices.

    Science.gov (United States)

    Chong, C; Kevrekidis, P G; Ablowitz, M J; Ma, Yi-Ping

    2016-01-01

    Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. For weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. The transition between these two types of propagation is explored.

  5. Identification of the dynamics of a two-dimensional grid structure using least square lattice filters

    Science.gov (United States)

    Montgomery, R. C.; Sundararajan, N.

    1984-01-01

    The basic theory of least square lattice filters and their use in identification of structural dynamics systems is summarized. Thereafter, this theory is applied to a two-dimensional grid structure made of overlapping bars. Previously, this theory has been applied to an integral beam. System identification results are presented for both simulated and experimental tests and they are compared with those predicted using finite element modelling. The lattice filtering approach works well for simulated data based on finite element modelling. However, considerable discrepancy exists between estimates obtained from experimental data and the finite element analysis. It is believed that this discrepancy is the result of inadequacies in the finite element modelling to represent the damped motion of the laboratory apparatus.

  6. Suppression of photothermal convection of microparticles in two dimensional nanoplasmonic optical lattice

    Science.gov (United States)

    Chen, Yi-Chung; Yossifon, Gilad; Yang, Ya-Tang

    2016-11-01

    Photothermal convection has been a major obstacle for stable particle trapping in plasmonic optical tweezer at high optical power. Here, we demonstrate a strategy to suppress the plasmonic photothermal convection by using vanishingly small thermal expansion coefficient of water at low temperature. A simple square nanoplasmonic array is illuminated with a loosely Gaussian beam to produce a two dimensional optical lattice for trapping of micro particles. We observe stable particle trapping due to near-field optical gradient forces at elevated optical power at low temperature. In contrast, for the same optical power at room temperature, the particles are convected away from the center of the optical lattice without their accumulation. This technique will greatly increase usable optical power and enhance the trapping capability of plasmonic optical tweezer.

  7. An improvement of the lattice theory of dislocation for a two-dimensional triangular crystal

    Institute of Scientific and Technical Information of China (English)

    Wang Shao-Feng

    2005-01-01

    The structure of dislocation in a two-dimensional triangular crystal has been studied theoretically on the basis of atomic interaction and lattice statics. The theory presented in this paper is an improvement to that published previously.Within a reasonable interaction approximation, a new dislocation equation is obtained, which remedies a fault existing in the lattice theory of dislocation. A better simplification of non-diagonal terms of the kernel is given. The solution of the new dislocation equation asymptotically becomes the same as that obtained in the elastic theory, and agrees with experimental data. It is found that the solution is formally identical with that proposed phenomenologically by Foreman et al, where the parameter can be chosen freely, but cannot uniquely determined from theory. Indeed, if the parameter in the expression of the solution is selected suitably, the expression can be well applied to describe the fine structure of the dislocation.

  8. Dual geometric worm algorithm for two-dimensional discrete classical lattice models

    Science.gov (United States)

    Hitchcock, Peter; Sørensen, Erik S.; Alet, Fabien

    2004-07-01

    We present a dual geometrical worm algorithm for two-dimensional Ising models. The existence of such dual algorithms was first pointed out by Prokof’ev and Svistunov [N. Prokof’ev and B. Svistunov, Phys. Rev. Lett. 87, 160601 (2001)]. The algorithm is defined on the dual lattice and is formulated in terms of bond variables and can therefore be generalized to other two-dimensional models that can be formulated in terms of bond variables. We also discuss two related algorithms formulated on the direct lattice, applicable in any dimension. These latter algorithms turn out to be less efficient but of considerable intrinsic interest. We show how such algorithms quite generally can be “directed” by minimizing the probability for the worms to erase themselves. Explicit proofs of detailed balance are given for all the algorithms. In terms of computational efficiency the dual geometrical worm algorithm is comparable to well known cluster algorithms such as the Swendsen-Wang and Wolff algorithms, however, it is quite different in structure and allows for a very simple and efficient implementation. The dual algorithm also allows for a very elegant way of calculating the domain wall free energy.

  9. Long-range ferrimagnetic order in a two-dimensional supramolecular Kondo lattice

    Science.gov (United States)

    Girovsky, Jan; Nowakowski, Jan; Ali, Md. Ehesan; Baljozovic, Milos; Rossmann, Harald R.; Nijs, Thomas; Aeby, Elise A.; Nowakowska, Sylwia; Siewert, Dorota; Srivastava, Gitika; Wäckerlin, Christian; Dreiser, Jan; Decurtins, Silvio; Liu, Shi-Xia; Oppeneer, Peter M.; Jung, Thomas A.; Ballav, Nirmalya

    2017-05-01

    Realization of long-range magnetic order in surface-supported two-dimensional systems has been challenging, mainly due to the competition between fundamental magnetic interactions as the short-range Kondo effect and spin-stabilizing magnetic exchange interactions. Spin-bearing molecules on conducting substrates represent a rich platform to investigate the interplay of these fundamental magnetic interactions. Here we demonstrate the direct observation of long-range ferrimagnetic order emerging in a two-dimensional supramolecular Kondo lattice. The lattice consists of paramagnetic hexadeca-fluorinated iron phthalocyanine (FeFPc) and manganese phthalocyanine (MnPc) molecules co-assembled into a checkerboard pattern on single-crystalline Au(111) substrates. Remarkably, the remanent magnetic moments are oriented in the out-of-plane direction with significant contribution from orbital moments. First-principles calculations reveal that the FeFPc-MnPc antiferromagnetic nearest-neighbour coupling is mediated by the Ruderman-Kittel-Kasuya-Yosida exchange interaction via the Au substrate electronic states. Our findings suggest the use of molecular frameworks to engineer novel low-dimensional magnetically ordered materials and their application in molecular quantum devices.

  10. Long-range ferrimagnetic order in a two-dimensional supramolecular Kondo lattice.

    Science.gov (United States)

    Girovsky, Jan; Nowakowski, Jan; Ali, Md Ehesan; Baljozovic, Milos; Rossmann, Harald R; Nijs, Thomas; Aeby, Elise A; Nowakowska, Sylwia; Siewert, Dorota; Srivastava, Gitika; Wäckerlin, Christian; Dreiser, Jan; Decurtins, Silvio; Liu, Shi-Xia; Oppeneer, Peter M; Jung, Thomas A; Ballav, Nirmalya

    2017-05-22

    Realization of long-range magnetic order in surface-supported two-dimensional systems has been challenging, mainly due to the competition between fundamental magnetic interactions as the short-range Kondo effect and spin-stabilizing magnetic exchange interactions. Spin-bearing molecules on conducting substrates represent a rich platform to investigate the interplay of these fundamental magnetic interactions. Here we demonstrate the direct observation of long-range ferrimagnetic order emerging in a two-dimensional supramolecular Kondo lattice. The lattice consists of paramagnetic hexadeca-fluorinated iron phthalocyanine (FeFPc) and manganese phthalocyanine (MnPc) molecules co-assembled into a checkerboard pattern on single-crystalline Au(111) substrates. Remarkably, the remanent magnetic moments are oriented in the out-of-plane direction with significant contribution from orbital moments. First-principles calculations reveal that the FeFPc-MnPc antiferromagnetic nearest-neighbour coupling is mediated by the Ruderman-Kittel-Kasuya-Yosida exchange interaction via the Au substrate electronic states. Our findings suggest the use of molecular frameworks to engineer novel low-dimensional magnetically ordered materials and their application in molecular quantum devices.

  11. Quantum spin liquid and magnetic order in a two-dimensional nonsymmorphic lattice: Considering the distorted kagome lattice of volborthite

    Science.gov (United States)

    Chern, Li Ern; Hwang, Kyusung; Mizoguchi, Tomonari; Huh, Yejin; Kim, Yong Baek

    2017-07-01

    The Kagome-lattice-based material, volborthite, Cu3V2O7(OH) 2.2 H2O , has been considered as a promising platform for discovery of unusual quantum ground states due to the frustrated nature of spin interaction. We explore possible quantum spin liquid and magnetically ordered phases in a two-dimensional nonsymmorphic lattice, which is described by the plane group p 2 g g , consistent with the spatial anisotropy of the spin model derived from density functional theory (DFT) for volborthite. Using the projective symmetry group (PSG) analysis and Schwinger boson mean field theory, we classify possible spin liquid phases with bosonic spinons and investigate magnetically ordered phases connected to such states. It is shown, in general, that only translationally invariant mean field spin liquid ansatzes are allowed in two-dimensional nonsymmorphic lattices. We study the mean field phase diagram of the DFT-derived spin model and find that possible quantum spin liquid phases are connected to two types of magnetically ordered phases, a coplanar incommensurate (q ,0 ) spiral order as the ground state and a closely competing coplanar commensurate (π ,π ) spin density wave order. In addition, periodicity enhancement of the two-spinon continuum, a consequence of symmetry fractionalization, is found in the spin liquid state connected to the (π ,π ) spin density wave order. We discuss relevance of these results to recent and future experiments on volborthite.

  12. Dipolar matter-wave solitons in two-dimensional anisotropic discrete lattices

    Science.gov (United States)

    Chen, Huaiyu; Liu, Yan; Zhang, Qiang; Shi, Yuhan; Pang, Wei; Li, Yongyao

    2016-05-01

    We numerically demonstrate two-dimensional (2D) matter-wave solitons in the disk-shaped dipolar Bose-Einstein condensates (BECs) trapped in strongly anisotropic optical lattices (OLs) in a disk's plane. The considered OLs are square lattices which can be formed by interfering two pairs of plane waves with different intensities. The hopping rates of the condensates between two adjacent lattices in the orthogonal directions are different, which gives rise to a linearly anisotropic system. We find that when the polarized orientation of the dipoles is parallel to disk's plane with the same direction, the combined effects of the linearly anisotropy and the nonlocal nonlinear anisotropy strongly influence the formations, as well as the dynamics of the lattice solitons. Particularly, the isotropy-pattern solitons (IPSs) are found when these combined effects reach a balance. Motion, collision, and rotation of the IPSs are also studied in detail by means of systematic simulations. We further find that these IPSs can move freely in the 2D anisotropic discrete system, hence giving rise to an anisotropic effective mass. Four types of collisions between the IPSs are identified. By rotating an external magnetic field up to a critical angular velocity, the IPSs can still remain localized and play as a breather. Finally, the influences from the combined effects between the linear and the nonlocal nonlinear anisotropy with consideration of the contact and/or local nonlinearity are discussed too.

  13. Bandgaps and directional properties of two-dimensional square beam-like zigzag lattices

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Yan-Feng; Wang, Yue-Sheng, E-mail: yswang@bjtu.edu.cn [Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044 (China); Zhang, Chuanzeng [Department of Civil Engineering, University of Siegen, Siegen 57068 (Germany)

    2014-12-15

    In this paper we propose four kinds of two-dimensional square beam-like zigzag lattice structures and study their bandgaps and directional propagation of elastic waves. The band structures are calculated by using the finite element method. Both the in-plane and out-of-plane waves are investigated simultaneously via the three-dimensional Euler beam elements. The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges. The effects of the geometry parameters of the xy- and z-zigzag lattices on the bandgaps are investigated and discussed. Multiple complete bandgaps are found owing to the separation of the degeneracy by introducing bending arms. The bandgaps are sensitive to the geometry parameters of the periodic systems. The deformed displacement fields of the harmonic responses of a finite lattice structure subjected to harmonic loads at different positions are illustrated to show the directional wave propagation. An extension of the proposed concept to the hexagonal lattices is also presented. The research work in this paper is relevant to the practical design of cellular structures with enhanced vibro-acoustics performance.

  14. LATTICE-BOLTZMANN MODEL FOR COMPRESSIBLE PERFECT GASES

    Institute of Scientific and Technical Information of China (English)

    Sun Chenghai

    2000-01-01

    We present an adaptive lattice Boltzmann model to simulate super sonic flows. The particle velocities are determined by the mean velocity and internal energy. The adaptive nature of particle velocities permits the mean flow to have high Mach number. A particle potential energy is introduced so that the model is suitable for the perfect gas with arbitrary specific heat ratio. The Navier-Stokes equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation.As preliminary tests, two kinds of simulations have been performed on hexagonal lattices. One is the one-dimensional simulation for sinusoidal velocity distributions.The velocity distributions are compared with the analytical solution and the mea sured viscosity is compared with the theoretical values. The agreements are basically good. However, the discretion error may cause some non-isotropic effects. The other simulation is the 29 degree shock reflection.

  15. Contact angles in the pseudopotential lattice Boltzmann modeling of wetting

    CERN Document Server

    Li, Q; Kang, Q J; Chen, Q

    2014-01-01

    In this paper, we aim to investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio. The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994)] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model, the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions: the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction formulated in the present paper, are numerically investigated and compared in terms of the achievable contact angles, the maximum and the minimum densities, and the spurious currents. It is found that the pseudopotential-based interaction works well for simulating small static (liquid) contact angles, however, is unable to reproduce static contact angles close to 180 degrees. Meanwhile, it is found that the proposed modif...

  16. Effects of anisotropy and magnetic fields on the specific heat of a quasi-two-dimensional Boltzmann gas in an elliptical parabolic quantum dot

    Institute of Scientific and Technical Information of China (English)

    Zhai Zhi-Yuan; Li Yu-Qi; Pan Xiao-Yin

    2012-01-01

    We investigate the effects due to anisotropy and magnetic field interaction for a quasi-two-dimensional Boltzmann gas in an elliptical parabolic quantum dot.The specific heat is studied with varying temperature,anisotropy,and magnetic field strength.The cases without and with the inclusion of the spin Zeeman interaction are considered.

  17. A Lattice Boltzmann Model of Binary Fluid Mixture

    CERN Document Server

    Orlandini, E; Yeomans, J M; Orlandini, Enzo; Swift, Michael R.

    1995-01-01

    We introduce a lattice Boltzmann for simulating an immiscible binary fluid mixture. Our collision rules are derived from a macroscopic thermodynamic description of the fluid in a way motivated by the Cahn-Hilliard approach to non-equilibrium dynamics. This ensures that a thermodynamically consistent state is reached in equilibrium. The non-equilibrium dynamics is investigated numerically and found to agree with simple analytic predictions in both the one-phase and the two-phase region of the phase diagram.

  18. A non-slip boundary condition for lattice Boltzmann simulations

    CERN Document Server

    Inamuro, T; Ogino, F; Inamuro, Takaji; Yoshino, Masato; Ogino, Fumimaru

    1995-01-01

    A non-slip boundary condition at a wall for the lattice Boltzmann method is presented. In the present method unknown distribution functions at the wall are assumed to be an equilibrium distribution function with a counter slip velocity which is determined so that fluid velocity at the wall is equal to the wall velocity. Poiseuille flow and Couette flow are calculated with the nine-velocity model to demonstrate the accuracy of the present boundary condition.

  19. A lattice Boltzmann method based on generalized polynomials

    CERN Document Server

    Coelho, Rodrigo C V; Doria, Mauro M

    2015-01-01

    We propose a lattice Boltzmann method based on the expansion of the equilibrium distribution function in powers of generalized orthonormal polynomials which are weighted by the equilibrium distribution function itself. The D-dimensional Euclidean space Hermite polynomials correspond to the particular weight of a gaussian function. The proposed polynomials give a general method to obtain an expansion of the equilibrium distribution function in powers of the ratio between the displacement velocity and the local scale velocity of the fluid.

  20. Lattice Boltzmann simulation of droplet formation in T-junction geometries

    Science.gov (United States)

    Busuioc, Sergiu; Ambruş, Victor E.; Sofonea, Victor

    2017-01-01

    The formation of droplets in T-junction configurations is investigated using a two-dimensional Lattice Boltzmann model for liquid-vapor systems. We use an expansion of the equilibrium distribution function with respect to Hermite polynomials and an off-lattice velocity set. To evolve the distribution functions we use the second order corner transport upwind numerical scheme and a third order scheme is used to compute the gradient operators in the force term. The droplet formation successfully recovers the squeezing, dripping and jetting regimes. We find that the droplet length decreases proportionally with the flow rate of the continuous phase and increases with the flow rate of the dispersed phase in all simulation configurations and has a linear dependency on the surface tension parameter κ.

  1. Non-orthogonal multiple-relaxation-time lattice Boltzmann method for incompressible thermal flows

    CERN Document Server

    Liu, Qing; Li, Dong

    2015-01-01

    In this paper, a non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) method for simulating incompressible thermal flows is presented. In the method, the incompressible Navier-Stokes equations and temperature equation (or convection-diffusion equation) are solved separately by two different MRT-LB models, which are proposed based on non-orthogonal transformation matrices constructed in terms of some proper non-orthogonal basis vectors obtained from the combinations of the lattice velocity components. The macroscopic equations for incompressible thermal flows can be recovered from the present method through the Chapman-Enskog analysis in the incompressible limit. Numerical simulations of several typical two-dimensional problems are carried out to validate the present method. It is found that the present numerical results are in good agreement with the analytical solutions or other numerical results of previous studies. Furthermore, the grid convergence tests indicate that the present MRT-LB met...

  2. Lattice Boltzmann Model for Electronic Structure Simulations

    CERN Document Server

    Mendoza, M; Succi, S

    2015-01-01

    Recently, a new connection between density functional theory and kinetic theory has been proposed. In particular, it was shown that the Kohn-Sham (KS) equations can be reformulated as a macroscopic limit of the steady-state solution of a suitable single-particle kinetic equation. By using a discrete version of this new formalism, the exchange and correlation energies of simple atoms and the geometrical configuration of the methane molecule were calculated accurately. Here, we discuss the main ideas behind the lattice kinetic approach to electronic structure computations, offer some considerations for prospective extensions, and also show additional numerical results, namely the geometrical configuration of the water molecule.

  3. Deviations from Boltzmann-Gibbs Statistics in Confined Optical Lattices.

    Science.gov (United States)

    Dechant, Andreas; Kessler, David A; Barkai, Eli

    2015-10-23

    We investigate the semiclassical phase-space probability distribution P(x,p) of cold atoms in a Sisyphus cooling lattice with an additional harmonic confinement. We pose the question of whether this nonequilibrium steady state satisfies the equivalence of energy and probability. This equivalence is the foundation of Boltzmann-Gibbs and generalized thermostatic statistics, and a prerequisite for the description in terms of a temperature. At large energies, P(x,p) depends only on the Hamiltonian H(x,p) and the answer to the question is yes. In distinction to the Boltzmann-Gibbs state, the large-energy tails are power laws P(x,p)∝H(x,p)(-1/D), where D is related to the depth of the optical lattice. At intermediate energies, however, P(x,p) cannot be expressed as a function of the Hamiltonian and the equivalence between energy and probability breaks down. As a consequence the average potential and kinetic energy differ and no well-defined temperature can be assigned. The Boltzmann-Gibbs state is regained only in the limit of deep optical lattices. For strong confinement relative to the damping, we derive an explicit expression for the stationary phase-space distribution.

  4. A lattice Boltzmann method for dilute polymer solutions.

    Science.gov (United States)

    Singh, Shiwani; Subramanian, Ganesh; Ansumali, Santosh

    2011-06-13

    We present a lattice Boltzmann approach for the simulation of non-Newtonian fluids. The method is illustrated for the specific case of dilute polymer solutions. With the appropriate local equilibrium distribution, phase-space dynamics on a lattice, driven by a Bhatnagar-Gross-Krook (BGK) relaxation term, leads to a solution of the Fokker-Planck equation governing the probability density of polymer configurations. Results for the bulk rheological characteristics for steady and start-up shear flow are presented, and compare favourably with those obtained using Brownian dynamics simulations. The new method is less expensive than stochastic simulation techniques, particularly in the range of small to moderate Weissenberg numbers (Wi).

  5. Magnetic properties of two dimensional silicon carbide triangular nanoflakes-based kagome lattices

    Energy Technology Data Exchange (ETDEWEB)

    Li Xiaowei [Peking University, Center for Applied Physics and Technology, College of Engineering (China); Zhou Jian [Peking University, Department of Materials Science and Engineering (China); Wang Qian, E-mail: qianwang2@pku.edu.cn [Peking University, Center for Applied Physics and Technology, College of Engineering (China); Jena, Puru [Virginia Commonwealth University, Department of Physics (United States)

    2012-08-15

    Two-dimensional (2D) magnetic kagome lattices are constructed using silicon carbide triangular nanoflakes (SiC-TNFs). Two types of structures with alternating Si and C atoms are studied: the first one is constructed using the C-edged SiC-TNFs as the building blocks and C atoms as the linkers of kagome sites (TNF{sub N}-C-TNF{sub N}) while the second one is composed of the Si-edged SiC-TNFs with Si atoms as linkers (TNF{sub N}-Si-TNF{sub N}). Using density functional theory-based calculations, we show that the fully relaxed TNF{sub N}-C-TNF{sub N} retains the morphology of regular kagome lattice and is ferromagnetism. On the other hand, the TNF{sub N}-Si-TNF{sub N} structure is deformed and antiferromagnetic. However, the ground state of TNF{sub N}-Si-TNF{sub N} structure can be transformed from the antiferromagnetic to ferromagnetic state by applying tensile strain. Monte Carlo simulations indicate that the SiC-TNFs-based kagome lattices can be ferromagnetic at room temperature.

  6. Differentiated heated lid driven cavity interacting with tube: A lattice Boltzmann study

    Directory of Open Access Journals (Sweden)

    Bennacer Rachid

    2017-01-01

    Full Text Available The multiple-relaxation-time (MRT lattice-Boltzmann method is implemented to investigate combined natural and forced convection occurring in a two-dimensional square cavity. The top wall slides to the right at constant speed, while the other three remain stationary. The solution is performed for a left vertical wall at a constant temperature, which is higher than of the right wall. This yields a “cooperating” case, in which dynamic and buoyancy forces are added together. The enclosure is filled with air and contains a heat conducting circular cylinder, which is placed at various positions. The double distribution model used in lattice Boltzmann methods has been adopted to simulate the hydrodynamic and thermal fields, with the D2Q9 and D2Q5 lattices selected to perform the corresponding computations. Simulations have been conducted over a wide range of Rayleigh (Ra and Reynolds (Re numbers, and the features of dynamic and thermal fields are presented for the spectra of this mixed convection phenomenon. The flow and heat transfer characteristics of the cylinder position are described and analyzed in terms of the average Nusselt number (Nu. The computed results show the influence of the cylinder on the corresponding heat transfer in the enclosure. It has been found that the power (i.e. shear stress needed to lid the upper surface will depend on the governing parameters.

  7. Pythagoras's theorem on a two-dimensional lattice from a `natural' Dirac operator and Connes's distance formula

    Science.gov (United States)

    Dai, Jian; Song, Xing-Chang

    2001-07-01

    One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.

  8. Filter-matrix lattice Boltzmann model for microchannel gas flows.

    Science.gov (United States)

    Zhuo, Congshan; Zhong, Chengwen

    2013-11-01

    The lattice Boltzmann method has been shown to be successful for microscale gas flows, and it has attracted significant research interest. In this paper, the recently proposed filter-matrix lattice Boltzmann (FMLB) model is first applied to study the microchannel gas flows, in which a Bosanquet-type effective viscosity is used to capture the flow behaviors in the transition regime. A kinetic boundary condition, the combined bounce-back and specular-reflection scheme with the second-order slip scheme, is also designed for the FMLB model. By analyzing a unidirectional flow, the slip velocity and the discrete effects related to the boundary condition are derived within the FMLB model, and a revised scheme is presented to overcome such effects, which have also been validated through numerical simulations. To gain an accurate simulation in a wide range of Knudsen numbers, covering the slip and the entire transition flow regimes, a set of slip coefficients with an introduced fitting function is adopted in the revised second-order slip boundary condition. The periodic and pressure-driven microchannel flows have been investigated by the present model in this study. The numerical results, including the velocity profile and the mass flow rate, as well as the nonlinear pressure distribution along the channel, agree fairly well with the solutions of the linearized Boltzmann equation, the direct simulation Monte Carlo results, the experimental data, and the previous results of the multiple effective relaxation lattice Boltzmann model. Also, the present results of the velocity profile and the mass flow rate show that the present model with the fitting function can yield improved predictions for the microchannel gas flow with higher Knudsen numbers in the transition flow regime.

  9. Analysis of Photonic Band Gaps in a Two-Dimensional Triangular Lattice with Superconducting Hollow Rods

    Science.gov (United States)

    Diaz-Valencia, B. F.; Calero, J. M.

    2017-02-01

    In this work, we use the plane wave expansion method to calculate photonic band structures in two-dimensional photonic crystals which consist of high-temperature superconducting hollow rods arranged in a triangular lattice. The variation of the photonic band structure with respect to both, the inner radius and the system temperature, is studied, taking into account temperatures below the critical temperature of the superconductor in the low frequencies regime and assuming E polarization of the incident light. Permittivity contrast and nontrivial geometry of the hollow rods lead to the appearance of new band gaps as compared with the case of solid cylinders. Such band gaps can be modulated by means of the inner radius and system temperature.

  10. Two-dimensional novel optical lattices with multi-well traps for cold atoms or molecules

    Institute of Scientific and Technical Information of China (English)

    Junfa Lu; Xianming Ji; Jianping Yin

    2006-01-01

    We propose some new schemes to constitute two-dimensional (2D) array of multi-well optical dipole traps for cold atoms (or molecules) by using an optical system consisting of a binary π-phase grating and a 2D array of rectangle microlens. We calculate the intensity distribution of each optical well in 2D array of multi-well traps and its geometric parameters and so on. The proposed 2D array of multi-well traps can be used to form novel 2D optical lattices with cold atoms (or molecules), and form various novel optical crystals with cold atoms (or molecules), or to perform quantum computing and quantum information processing on an atom chip, even to realize an array of all-optical multi-well atomic (or molecular) BoseEinstein condensates (BECs) on an all-optical integrated atom (or molecule) chip.

  11. Pair formation in Fermi systems with population imbalance in one- and two-dimensional optical lattices

    Science.gov (United States)

    Batrouni, George

    2011-03-01

    I will discuss pairing in fermionic systems in one- and two-dimensional optical lattices with population imbalance. This will be done in the context of the attractive fermionic Hubbard model using the Stochastic Green Function algorithm in d=1 while for d=2 we use Determinant Quantum Monte Carlo. This is the first exact QMC study examining the effects of finite temperature which is very important in experiments on ultra-cold atoms. Our results show that, in the ground state, the dominant pairing mechanism is at nonzero center of mass momentum, i.e. FFLO. I will then discuss the effect of finite temperature in the uniform and confined systems and present finite temperature phase diagrams. The numerical results will be compared with experiments. With M. J. Wolak (CQT, National University of Singapore) and V. G. Rousseau (Department of Physics and Astronomy, Louisiana State University).

  12. Piecewise parabolic negative magnetoresistance of two-dimensional electron gas with triangular antidot lattice

    Energy Technology Data Exchange (ETDEWEB)

    Budantsev, M. V., E-mail: budants@isp.nsc.ru; Lavrov, R. A.; Pogosov, A. G.; Zhdanov, E. Yu.; Pokhabov, D. A. [Russian Academy of Sciences, Rzhanov Institute of Semiconductor Physics, Siberian Branch (Russian Federation)

    2011-02-15

    Extraordinary piecewise parabolic behavior of the magnetoresistance has been experimentally detected in the two-dimensional electron gas with a dense triangular lattice of antidots, where commensurability magnetoresistance oscillations are suppressed. The magnetic field range of 0-0.6 T can be divided into three wide regions, in each of which the magnetoresistance is described by parabolic dependences with high accuracy (comparable to the experimental accuracy) and the transition regions between adjacent regions are much narrower than the regions themselves. In the region corresponding to the weakest magnetic fields, the parabolic behavior becomes almost linear. The observed behavior is reproducible as the electron gas density changes, which results in a change in the resistance by more than an order of magnitude. Possible physical mechanisms responsible for the observed behavior, including so-called 'memory effects,' are discussed.

  13. Duality and Fisher zeros in the two-dimensional Potts model on a square lattice.

    Science.gov (United States)

    Astorino, Marco; Canfora, Fabrizio

    2010-05-01

    A phenomenological approach to the ferromagnetic two-dimensional (2D) Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q-state Potts model. The duality symmetry of the 2D Potts model together with the known results on its critical exponent α allows us to fix consistently the details of the proposed expression for the free energy. The agreement of the analytic ansatz with numerical data in the q=3 case is very good at high and low temperatures as well as at the critical point. It is shown that the q>4 cases naturally fit into the same scheme and that one should also expect a good agreement with numerical data. The limiting q=4 case is shortly discussed.

  14. Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices

    Energy Technology Data Exchange (ETDEWEB)

    Rojas-Rojas, Santiago, E-mail: srojas@cefop.cl [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Naether, Uta [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, 50009 Zaragoza (Spain); Delgado, Aldo [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Vicencio, Rodrigo A. [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago (Chile)

    2016-09-16

    Highlights: • We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates. • Important differences in the properties of three fundamental modes are found. • Norm threshold for existence of 2D breathers varies with dipolar interaction. • The Effective Potential Method is implemented for stability analysis. • Uncommon mobility of 2D discrete solitons is observed. - Abstract: We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.

  15. Moving charged particles in lattice Boltzmann-based electrokinetics.

    Science.gov (United States)

    Kuron, Michael; Rempfer, Georg; Schornbaum, Florian; Bauer, Martin; Godenschwager, Christian; Holm, Christian; de Graaf, Joost

    2016-12-07

    The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann algorithm for the simulation of hydrodynamic flow and exploits computational locality. However, thus far, a description of how to incorporate moving boundary conditions into the Capuani scheme has been lacking. Moving boundary conditions are needed to simulate multiple arbitrarily moving colloids. In this paper, we detail how to introduce such a particle coupling scheme, based on an analogue to the moving boundary method for the pure lattice Boltzmann solver. The key ingredients in our method are mass and charge conservation for the solute species and a partial-volume smoothing of the solute fluxes to minimize discretization artifacts. We demonstrate our algorithm's effectiveness by simulating the electrophoresis of charged spheres in an external field; for a single sphere we compare to the equivalent electro-osmotic (co-moving) problem. Our method's efficiency and ease of implementation should prove beneficial to future simulations of the dynamics in a wide range of complex nanoscopic and colloidal systems that were previously inaccessible to lattice-based continuum algorithms.

  16. Lattice Boltzmann method for linear oscillatory noncontinuum flows.

    Science.gov (United States)

    Shi, Yong; Yap, Ying Wan; Sader, John E

    2014-03-01

    Oscillatory gas flows are commonly generated by micro- and nanoelectromechanical systems. Due to their small size and high operating frequencies, these devices often produce noncontinuum gas flows. Theoretical analysis of such flows requires solution of the unsteady Boltzmann equation, which can present a formidable challenge. In this article, we explore the applicability of the lattice Boltzmann (LB) method to such linear oscillatory noncontinuum flows; this method is derived from the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation. We formulate four linearized LB models in the frequency domain, based on Gaussian-Hermite quadratures of different algebraic precision (AP). The performance of each model is assessed by comparison to high-accuracy numerical solutions to the linearized Boltzmann-BGK equation for oscillatory Couette flow. The numerical results demonstrate that high even-order LB models provide superior performance over the greatest noncontinuum range. Our results also highlight intrinsic deficiencies in the current LB framework, which is incapable of capturing noncontinuum behavior at high oscillation frequencies, regardless of quadrature AP and the Knudsen number.

  17. Lattice Boltzmann method for linear oscillatory noncontinuum flows

    Science.gov (United States)

    Shi, Yong; Yap, Ying Wan; Sader, John E.

    2014-03-01

    Oscillatory gas flows are commonly generated by micro- and nanoelectromechanical systems. Due to their small size and high operating frequencies, these devices often produce noncontinuum gas flows. Theoretical analysis of such flows requires solution of the unsteady Boltzmann equation, which can present a formidable challenge. In this article, we explore the applicability of the lattice Boltzmann (LB) method to such linear oscillatory noncontinuum flows; this method is derived from the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation. We formulate four linearized LB models in the frequency domain, based on Gaussian-Hermite quadratures of different algebraic precision (AP). The performance of each model is assessed by comparison to high-accuracy numerical solutions to the linearized Boltzmann-BGK equation for oscillatory Couette flow. The numerical results demonstrate that high even-order LB models provide superior performance over the greatest noncontinuum range. Our results also highlight intrinsic deficiencies in the current LB framework, which is incapable of capturing noncontinuum behavior at high oscillation frequencies, regardless of quadrature AP and the Knudsen number.

  18. Creating tuneable microwave media from a two-dimensional lattice of re-entrant posts

    Science.gov (United States)

    Goryachev, Maxim; Tobar, Michael E.

    2015-11-01

    The potential capabilities of resonators based on two dimensional arrays of re-entrant posts is demonstrated. Such posts may be regarded as magnetically coupled lumped element microwave harmonic oscillators, arranged in a 2D lattices structure, which is enclosed in a 3D cavity. By arranging these elements in certain 2D patterns, we demonstrate how to achieve certain requirements with respect to field localisation and device spectra. Special attention is paid to symmetries of the lattices, mechanical tuning, design of areas of high localisation of magnetic energy; this in turn creates unique discrete mode spectra. We demonstrate analogies between systems designed on the proposed platform and well known physical phenomena such as polarisation, frustration, and Whispering Gallery Modes. The mechanical tunability of the cavity with multiple posts is analysed, and its consequences to optomechanical applications is calculated. One particular application to quantum memory is demonstrated with a cavity design consisting of separate resonators analogous to discrete Fabry-Pérot resonators. Finally, we propose a generalised approach to a microwave system design based on the concept of Programmable Cavity Arrays.

  19. Ground State and Collective Modes of Magnetic Dipoles Fixed on Two-Dimensional Lattice Sites

    Science.gov (United States)

    Feldmann, John; Kalman, Gabor; Hartmann, Peter; Rosenberg, Marlene

    2006-10-01

    In complex (dusty) plasmas the grains may be endowed with intrinsic dipole moments. We present here our results of theoretical calculations accompanied by and Molecular Dynamics simulation findings on the ground state configuration and on the collective modes mode spectrum of a system of magnetic dipoles, interacting via the magnetic dipole pair-dipole potential, fixed on two-dimensional (2D) lattice sites. In particular, we We study a family of lattices that can be characterized by two parameters: (parallelogram)---the aspect ratio, c/a, and the rhombic angle, phi. The The new collective modes of in the system associated with the dipole-dipole interaction are the angular oscillations (or wobbling) of the direction of the dipoles about their equilibrium configurations. We identify in-plane and out-of-plane modes and display their dispersions. Orders of magnitudes of the parameters of the system relevant to possible future experiments will be discussed. JD Feldmann, G J Kalman and M Rosenberg, J. Phys. A: Math. Gen. 39 (2006) 4549-4553

  20. Creating tuneable microwave media from a two-dimensional lattice of re-entrant posts

    Energy Technology Data Exchange (ETDEWEB)

    Goryachev, Maxim; Tobar, Michael E. [ARC Centre of Excellence for Engineered Quantum Systems, University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009 (Australia)

    2015-11-28

    The potential capabilities of resonators based on two dimensional arrays of re-entrant posts is demonstrated. Such posts may be regarded as magnetically coupled lumped element microwave harmonic oscillators, arranged in a 2D lattices structure, which is enclosed in a 3D cavity. By arranging these elements in certain 2D patterns, we demonstrate how to achieve certain requirements with respect to field localisation and device spectra. Special attention is paid to symmetries of the lattices, mechanical tuning, design of areas of high localisation of magnetic energy; this in turn creates unique discrete mode spectra. We demonstrate analogies between systems designed on the proposed platform and well known physical phenomena such as polarisation, frustration, and Whispering Gallery Modes. The mechanical tunability of the cavity with multiple posts is analysed, and its consequences to optomechanical applications is calculated. One particular application to quantum memory is demonstrated with a cavity design consisting of separate resonators analogous to discrete Fabry–Pérot resonators. Finally, we propose a generalised approach to a microwave system design based on the concept of Programmable Cavity Arrays.

  1. Quadrature-based Lattice Boltzmann Model for Relativistic Flows

    CERN Document Server

    Blaga, Robert

    2016-01-01

    A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.

  2. Lattice Boltzmann method with the cell-population equilibrium

    Institute of Scientific and Technical Information of China (English)

    Zhou Xiao-Yang; Cheng Bing; Shi Bao-Chang

    2008-01-01

    The central problem of the lattice Boltzmann method (LBM) is to construct a discrete equilibrium.In this paper,a multi-speed 1D cell-model of Boltzmann equation is proposed,in which the cell-population equilibrium,a direct nonnegative approximation to the continuous Maxwellian distribution,plays an important part.By applying the explicit one-order Chapman-Enskog distribution,the model reduces the transportation and collision,two basic evolution steps in LBM,to the transportation of the non-equilibrium distribution.Furthermore,1D dam-break problem is performed and the numerical results agree well with the analytic solutions.

  3. Lattice Boltzmann Numerical Simulation of a Circular Cylinder

    Institute of Scientific and Technical Information of China (English)

    冯士德; 赵颖; 郜宪林; 季仲贞

    2002-01-01

    The lattice Boltzmann equation (LBE) model based on the Boltzmann equation is suitable for the numerical simulation of various flow fields. The fluid dynamics equation can be recovered from the LBE model. However,compared to the Navier-Stokes transport equation, the fluid dynamics equation derived from the LBE model is somewhat different in the viscosity transport term, which contains not only the Navier-Stokes transport equation but also nonsteady pressure and momentum flux terms. The two nonsteady terms can produce the same function as the random stirring force term introduced in the direct numerical or large-eddy vortex simulation of turbulence.Through computation of a circular cylinder, it is verified that the influence of the two nonsteady terms on flow field stability cannot be ignored, which is helpful for the study of turbulence.

  4. A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models

    Science.gov (United States)

    Luo, Li-Shi

    1998-01-01

    A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.

  5. Velocity slip and temperature jump simulations by the three-dimensional thermal finite-difference lattice Boltzmann method.

    Science.gov (United States)

    Watari, Minoru

    2009-06-01

    Two problems exist in the current studies on the application of the lattice Boltzmann method (LBM) to rarefied gas dynamics. First, most studies so far are applications of two-dimensional models. The numbers of velocity particles are small. Consequently, the boundary-condition methods of these studies are not directly applicable to a multispeed finite-difference lattice Boltzmann method (FDLBM) that has many velocity particles. Second, the LBM and FDLBM share their origins with the Boltzmann equation. Therefore, the results of LBM and FDLBM studies should be verified by the results of the continuous Boltzmann equation. In my review to date on the LBM studies, it appears that such verifications were seldom done. In this study, velocity slip and temperature jump simulations in the slip-flow regime were conducted using a three-dimensional FDLBM model. The results were compared with preceding theoretical studies based on the continuous Boltzmann equation. The results agreed with the theory with errors of a few percent. To further improve the accuracy of the FDLBM, it seems necessary to increase the number of velocity particles.

  6. Three-dimensional lattice Boltzmann model for electrodynamics.

    Science.gov (United States)

    Mendoza, M; Muñoz, J D

    2010-11-01

    In this paper we introduce a three-dimensional Lattice-Boltzmann model that recovers in the continuous limit the Maxwell equations in materials. In order to build conservation equations with antisymmetric tensors, like the Faraday law, the model assigns four auxiliary vectors to each velocity vector. These auxiliary vectors, when combined with the distribution functions, give the electromagnetic fields. The evolution is driven by the usual Bhatnager-Gross-Krook (BGK) collision rule, but with a different form for the equilibrium distribution functions. This lattice Bhatnager-Gross-Krook (LBGK) model allows us to consider for both dielectrics and conductors with realistic parameters, and therefore it is adequate to simulate the most diverse electromagnetic problems, like the propagation of electromagnetic waves (both in dielectric media and in waveguides), the skin effect, the radiation pattern of a small dipole antenna and the natural frequencies of a resonant cavity, all with 2% accuracy. Actually, it shows to be one order of magnitude faster than the original Finite-difference time-domain (FDTD) formulation by Yee to reach the same accuracy. It is, therefore, a valuable alternative to simulate electromagnetic fields and opens lattice Boltzmann for a broad spectrum of new applications in electrodynamics.

  7. Element Free Lattice Boltzmann Method for Fluid-Flow Problems

    Energy Technology Data Exchange (ETDEWEB)

    Jo, Jong Chull; Roh, Kyung Wan; Yune, Young Gill; Kim, Hho Jhung [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of); Kwon, Young Kwon [US Naval Postgraduate School, New York (United States)

    2007-10-15

    The Lattice Boltzmann Method (LBM) has been developed for application to thermal-fluid problems. Most of the those studies considered a regular shape of lattice or mesh like square and cubic grids. In order to apply the LBM to more practical cases, it is necessary to be able to solve complex or irregular shapes of problem domains. Some techniques were based on the finite element method. Generally, the finite element method is very powerful for solving two or three-dimensional complex or irregular shapes of domains using the iso-parametric element formulation which is based on a mathematical mapping from a regular shape of element in an imaginary domain to a more general and irregular shape of element in the physical domain. In addition, the element free technique is also quite useful to analyze a complex shape of domain because there is no need to divide a domain by a compatible finite element mesh. This paper presents a new finite element and element free formulations for the lattice Boltzmann equation using the general weighted residual technique. Then, a series of validation examples are presented.

  8. Lattice Boltzmann method for the fractional advection-diffusion equation.

    Science.gov (United States)

    Zhou, J G; Haygarth, P M; Withers, P J A; Macleod, C J A; Falloon, P D; Beven, K J; Ockenden, M C; Forber, K J; Hollaway, M J; Evans, R; Collins, A L; Hiscock, K M; Wearing, C; Kahana, R; Villamizar Velez, M L

    2016-04-01

    Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β, the fractional order α, and the single relaxation time τ, the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.

  9. Lattice Boltzmann method for the fractional advection-diffusion equation

    Science.gov (United States)

    Zhou, J. G.; Haygarth, P. M.; Withers, P. J. A.; Macleod, C. J. A.; Falloon, P. D.; Beven, K. J.; Ockenden, M. C.; Forber, K. J.; Hollaway, M. J.; Evans, R.; Collins, A. L.; Hiscock, K. M.; Wearing, C.; Kahana, R.; Villamizar Velez, M. L.

    2016-04-01

    Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β , the fractional order α , and the single relaxation time τ , the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.

  10. Robustness and breakup of the spiral wave in a two-dimensional lattice network of neurons

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    The robustness and breakup of spiral wave in a two-dimensional lattice networks of neurons are investigated. The effect of small- world type connection is often simplified with local regular connection and the long-range connection with certain probability. The network effect on the development of spiral wave can be better described by local regular connection and changeable long-range connection probability than fixed long-range connection probability because the long-range probability could be changeable in realistic biological system. The effect from the changeable probability for long-range connection is simplified by multiplicative noise. At first, a stable rotating spiral wave is developed by using appropriate initial values, parameters and no-flux boundary conditions, and then the effect of networks is investigated. Extensive numerical studies show that spiral wave keeps its alive and robust when the intensity of multiplicative noise is below a certain threshold, otherwise, the breakup of spiral wave occurs. A statistical factor of synchronization in two-dimensional array is defined to study the phase transition of spiral wave by checking the membrane potentials of all neurons corresponding to the critical parameters(the intensity of noise or forcing current)in the curve for factor of synchronization. The Hindmarsh-Rose model is investigated, the Hodgkin-Huxley neuron model in the presence of the channel noise is also studied to check the model independence of our conclusions. And it is found that breakup of spiral wave is easier to be induced by the multiplicative noise in presence of channel noise.

  11. Coupling lattice Boltzmann and molecular dynamics models for dense fluids

    Science.gov (United States)

    Dupuis, A.; Kotsalis, E. M.; Koumoutsakos, P.

    2007-04-01

    We propose a hybrid model, coupling lattice Boltzmann (LB) and molecular dynamics (MD) models, for the simulation of dense fluids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The MD and LB formulations communicate via the exchange of velocities and velocity gradients at the interface. We validate the present LB-MD model in simulations of two- and three-dimensional flows of liquid argon past and through a carbon nanotube. Comparisons with existing hybrid algorithms and with reference MD solutions demonstrate the validity of the present approach.

  12. Lattice Boltzmann model for nonlinear convection-diffusion equations.

    Science.gov (United States)

    Shi, Baochang; Guo, Zhaoli

    2009-01-01

    A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.

  13. Lattice-Boltzmann Method for Geophysical Plastic Flows

    CERN Document Server

    Leonardi, Alessandro; Mendoza, Miller; Herrmann, Hans J

    2015-01-01

    We explore possible applications of the Lattice-Boltzmann Method for the simulation of geophysical flows. This fluid solver, while successful in other fields, is still rarely used for geotechnical applications. We show how the standard method can be modified to represent free-surface realization of mudflows, debris flows, and in general any plastic flow, through the implementation of a Bingham constitutive model. The chapter is completed by an example of a full-scale simulation of a plastic fluid flowing down an inclined channel and depositing on a flat surface. An application is given, where the fluid interacts with a vertical obstacle in the channel.

  14. Diffusion dominated evaporation in multicomponent lattice Boltzmann simulations

    Science.gov (United States)

    Hessling, Dennis; Xie, Qingguang; Harting, Jens

    2017-02-01

    We present a diffusion dominated evaporation model using the popular pseudopotential multicomponent lattice Boltzmann method introduced by Shan and Chen. With an analytical computation of the diffusion coefficients, we demonstrate that Fick's law is obeyed. We then validate the applicability of our model by demonstrating the agreement of the time evolution of the interface position of an evaporating planar film to the analytical prediction. Furthermore, we study the evaporation of a freely floating droplet and confirm that the effect of Laplace pressure is significant for predicting the time evolution of small droplet radii.

  15. Thrombosis modeling in intracranial aneurysms: a lattice Boltzmann numerical algorithm

    Science.gov (United States)

    Ouared, R.; Chopard, B.; Stahl, B.; Rüfenacht, D. A.; Yilmaz, H.; Courbebaisse, G.

    2008-07-01

    The lattice Boltzmann numerical method is applied to model blood flow (plasma and platelets) and clotting in intracranial aneurysms at a mesoscopic level. The dynamics of blood clotting (thrombosis) is governed by mechanical variations of shear stress near wall that influence platelets-wall interactions. Thrombosis starts and grows below a shear rate threshold, and stops above it. Within this assumption, it is possible to account qualitatively well for partial, full or no occlusion of the aneurysm, and to explain why spontaneous thrombosis is more likely to occur in giant aneurysms than in small or medium sized aneurysms.

  16. Static contact angle in lattice Boltzmann models of immiscible fluids.

    Science.gov (United States)

    Latva-Kokko, M; Rothman, Daniel H

    2005-10-01

    We study numerically the capillary rise between two horizontal plates and in a rectangular tube, using a lattice Boltzmann (LB) method. We derive an equation for the static fluid-solid contact angle as a function of the wetting tendency of the walls and test its validity. We show that the generalized Laplace law with two independent radii of curvature is followed in capillary rise in rectangular tubes. Our method removes the history dependence of the fluid-solid contact angle that had been present in earlier LB schemes.

  17. LATTICE BOLTZMANN EQUATION MODEL IN THE CORIOLIS FIELD

    Institute of Scientific and Technical Information of China (English)

    FENG SHI-DE; MAO JIANG-YU; ZHANG QIONG

    2001-01-01

    In a large-scale field of rotational fluid, various unintelligible and surprising dynamic phenomena are produced due to the effect of the Coriolis force. The lattice Boltzmann equation (LBE) model in the Coriolis field is developed based on previous works.[1-4] Geophysical fluid dynamics equations are derived from the model. Numerical simulations have been made on an ideal atmospheric circulation of the Northern Hemisphere by using the model and they reproduce the Rossby wave motion well. Hence the applicability of the model is verified in both theory and experiment.

  18. Entropic lattice Boltzmann model for gas dynamics: Theory, boundary conditions, and implementation.

    Science.gov (United States)

    Frapolli, N; Chikatamarla, S S; Karlin, I V

    2016-06-01

    We present in detail the recently introduced entropic lattice Boltzmann model for compressible flows [N. Frapolli et al., Phys. Rev. E 92, 061301(R) (2015)PLEEE81539-375510.1103/PhysRevE.92.061301]. The model is capable of simulating a wide range of laminar and turbulent flows, from thermal and weakly compressible flows to transonic and supersonic flows. The theory behind the construction of the model is laid out and its thermohydrodynamic limit is discussed. Based on this theory and the hydrodynamic limit thereof, we also construct the boundary conditions necessary for the simulation of solid walls. We present the inlet and outlet boundary conditions as well as no-slip and free-slip boundary conditions. Details necessary for the implementation of the compressible lattice Boltzmann model are also reported. Finally, simulations of compressible flows are presented, including two-dimensional supersonic and transonic flows around a diamond and a NACA airfoil, the simulation of the Schardin problem, and the three-dimensional simulation of the supersonic flow around a conical geometry.

  19. Periodic, Quasiperiodic and Chaotic Discrete Breathers in a Parametrical Driven Two-Dimensional Discrete Klein-Gordon Lattice

    Institute of Scientific and Technical Information of China (English)

    XU Quan; TIAN Qiang; LUO Jun

    2009-01-01

    @@ We study a two-dimensional lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the two-dimensional Klein-Gordon lattice with hard on-site potential. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver.

  20. High-order hydrodynamics via lattice Boltzmann methods.

    Science.gov (United States)

    Colosqui, Carlos E

    2010-02-01

    In this work, closure of the Boltzmann-Bhatnagar-Gross-Krook (Boltzmann-BGK) moment hierarchy is accomplished via projection of the distribution function f onto a space H(N) spanned by N-order Hermite polynomials. While successive order approximations retain an increasing number of leading-order moments of f , the presented procedure produces a hierarchy of (single) N-order partial-differential equations providing exact analytical description of the hydrodynamics rendered by ( N-order) lattice Boltzmann-BGK (LBBGK) simulation. Numerical analysis is performed with LBBGK models and direct simulation Monte Carlo for the case of a sinusoidal shear wave (Kolmogorov flow) in a wide range of Weissenberg number Wi=taunuk(2) (i.e., Knudsen number Kn=lambdak=square root Wi); k is the wave number, [corrected] tau is the relaxation time of the system, and lambda approximately tauc(s) is the mean-free path, where c(s) is the speed of sound. The present results elucidate the applicability of LBBGK simulation under general nonequilibrium conditions.

  1. Multiple-component lattice Boltzmann equation for fluid-filled vesicles in flow.

    Science.gov (United States)

    Halliday, I; Lishchuk, S V; Spencer, T J; Pontrelli, G; Care, C M

    2013-02-01

    We document the derivation and implementation of extensions to a two-dimensional, multicomponent lattice Boltzmann equation model, with Laplace law interfacial tension. The extended model behaves in such a way that the boundary between its immiscible drop and embedding fluid components can be shown to describe a vesicle of constant volume bounded by a membrane with conserved length, specified interface compressibility, bending rigidity, preferred curvature, and interfacial tension. We describe how to apply this result to several, independent vesicles. The extended scheme is completely Eulerian, and it represents a two-way coupled vesicle membrane and flow within a single framework. Unlike previous methods, our approach dispenses entirely with the need explicitly to track the membrane, or boundary, and makes no use whatsoever of computationally expensive and intricate interface tracking and remeshing. Validation data are presented, which demonstrate the utility of the method in the simulation of the flow of high volume fraction suspensions of deformable objects.

  2. A new multiple-relaxation-time lattice Boltzmann model for incompressible flows in porous media

    CERN Document Server

    Liu, Qing; He, Chao

    2013-01-01

    In this paper, a two-dimensional eight-velocity (D2Q8) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for incompressible porous flows at the representative elementary volume scale based on the Brinkman-Forchheimer-extended Darcy formulation. In the MRT-LB model, newly defined equilibrium moments are employed to account for the porosity of the porous media, and the linear and nonlinear drag forces of the media are incorporated into the model by adding a forcing term to the MRT-LB equation in the moment space. The model is validated by simulating the 2D Poiseuille flow, Couette flow and lid-driven cavity flow in porous media. The numerical results are in excellent agreement with the analytical solutions and/or the well-documented data available in the literature.

  3. Simulation of Rayleigh-Bénard convection using lattice Boltzmann method

    CERN Document Server

    Shan, X

    1996-01-01

    Rayleigh-Bénard convection is numerically simulated in two- and three-dimensions using a recently developed two-component lattice Boltzmann equation (LBE) method. The density field of the second component, which evolves according to the advection-diffusion equation of a passive-scalar, is used to simulate the temperature field. A body force proportional to the temperature is applied, and the system satisfies the Boussinesq equation except for a slight compressibility. A no-slip, isothermal boundary condition is imposed in the vertical direction, and periodic boundary conditions are used in horizontal directions. The critical Rayleigh number for the onset of the Rayleigh-Bénard convection agrees with the theoretical prediction. As the Rayleigh number is increased higher, the steady two-dimensional convection rolls become unstable. The wavy instability and aperiodic motion observed, as well as the Nusselt number as a function of the Rayleigh number, are in good agreement with experimental observations and the...

  4. Phase-field-lattice Boltzmann studies for dendritic growth with natural convection

    Science.gov (United States)

    Takaki, Tomohiro; Rojas, Roberto; Sakane, Shinji; Ohno, Munekazu; Shibuta, Yasushi; Shimokawabe, Takashi; Aoki, Takayuki

    2017-09-01

    Simulating dendritic growth with natural convection is challenging because of the size of the computational domain required when compared to the dendrite scale. In this study, a phase-field-lattice Boltzmann model was used to simulate dendritic growth in the presence of natural convection due to a difference in solute concentration. To facilitate and accelerate the large-scale simulation, a parallel computing code with multiple graphics processing units was developed. The effects of the computational domain size as well as those of gravity on the dendritic morphologies were examined by performing two-dimensional free dendritic growth simulations with natural convection. The effects of the gravity direction on the dendrite spacing and morphology were also investigated by simulating unidirectional solidification from multiple seeds.

  5. Estimation of Reynolds number for flows around cylinders with lattice Boltzmann methods and artificial neural networks

    Science.gov (United States)

    Carrillo, Mauricio; Que, Ulices; González, José A.

    2016-12-01

    The present work investigates the application of artificial neural networks (ANNs) to estimate the Reynolds (Re) number for flows around a cylinder. The data required to train the ANN was generated with our own implementation of a lattice Boltzmann method (LBM) code performing simulations of a two-dimensional flow around a cylinder. As results of the simulations, we obtain the velocity field (v ⃗) and the vorticity (∇ ⃗×v ⃗ ) of the fluid for 120 different values of Re measured at different distances from the obstacle and use them to teach the ANN to predict the Re. The results predicted by the networks show good accuracy with errors of less than 4 % in all the studied cases. One of the possible applications of this method is the development of an efficient tool to characterize a blocked flowing pipe.

  6. Using Digital Imaging to Characterize Threshold Dynamic Parameters in Porous Media Based on Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    XU You-Sheng; LIU Yang; HUANG Guo-Xiang

    2004-01-01

    @@ Digital images (DI) and lattice Boltzmann method (LBM) are used to characterize the threshold dynamic parameters of porous media. Two-dimensional representations of the porous structure are reconstructed from segmentation of digital images obtained from a series of tiny samples. The threshold pressure gradients and threshold Péclet numbers are researched on seven test samples by using LBM. Numerical results are in agreement with that obtained by integrating Darcy's law. The results also indicate that fluids can flow through porous media only if the fluid force is large enough to overcome threshold pressure gradient in porous media. One synthetic case is used to further illustrate the applicability of the proposed technique. In addition, the dynamical rules in our model are local, therefore it can be run on parallel computers with well computational efficiency.

  7. Lattice Boltzmann Method for Diffusion-Reaction-Transport Processes in Heterogeneous Porous Media

    Institute of Scientific and Technical Information of China (English)

    XU You-Sheng; ZHONG Yi-Jun; HUANG Guo-Xiang

    2004-01-01

    Based on the lattice Boltzmann method and general theory of fluids flowing in porous media, a numerical model is presented for the diffusion-reaction-transport (DRT) processes in porous media. As a test, we simulate a DRT process in a two-dimensional horizontal heterogeneous porous medium. The influence of gravitation in this case can be neglected, and the DRT process can be described by a strongly heterogeneous diagnostic test strip or a thin confined piece of soil with stochastically distributing property in horizontal directions. The results obtained for the relations between reduced fluid saturation S, concentration c1, and concentration c2 are shown by using the visualization computing technique. The computational efficiency and stability of the model are satisfactory.

  8. Moving Charged Particles in Lattice Boltzmann-Based Electrokinetics

    CERN Document Server

    Kuron, Michael; Schornbaum, Florian; Bauer, Martin; Godenschwager, Christian; Holm, Christian; de Graaf, Joost

    2016-01-01

    The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann (LB) algorithm for the simulation of hydrodynamic flow and exploits computational locality. However, thus far, a description of how to incorporate moving boundary conditions, which are needed to simulate moving colloids, into the Capuani scheme has been lacking. In this paper, we detail how to introduce such moving boundaries, based on an analogue to the moving boundary method for the pure LB solver. The key ingredients in our method are mass and charge conservation for the solute spec...

  9. Interpolated lattice Boltzmann boundary conditions for surface reaction kinetics.

    Science.gov (United States)

    Walsh, S D C; Saar, M O

    2010-12-01

    This paper describes a method for implementing surface reaction kinetics in lattice Boltzmann simulations. The interpolated boundary conditions are capable of simulating surface reactions and dissolution at both stationary and moving solid-fluid and fluid-fluid interfaces. Results obtained with the boundary conditions are compared to analytical solutions for first-order and constant-flux kinetic surface reactions in a one-dimensional half space, as well as to the analytical solution for evaporation from the surface of a cylinder. Excellent agreement between analytical and simulated results is obtained for a wide range of diffusivities, lattice velocities, and surface reaction rates. The boundary model's ability to represent dissolution in binary fluid mixtures is demonstrated by modeling diffusion from a rising bubble and dissolution of a droplet near a flat plate.

  10. Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator

    CERN Document Server

    Kumar, Manish

    2016-01-01

    We propose a simple and straightforward method to generate a spatially variant lattice structures by optical interference lithography method. Using this method, it is possible to independently vary the orientation and period of the two-dimensional lattice. The method consists of two steps which are: numerical synthesis of corresponding phase mask by employing a two-dimensional integrated gradient calculations and experimental implementation of synthesized phase mask by making use of a phase only spatial light modulator in an optical 4f Fourier filtering setup. As a working example, we provide the experimental fabrication of a spatially variant square lattice structure which has the possibility to guide a Gaussian beam through a 90{\\deg} bend by photonic crystal self-collimation phenomena. The method is digitally reconfigurable, is completely scalable and could be extended to other kind of lattices as well.

  11. Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator

    Energy Technology Data Exchange (ETDEWEB)

    Kumar, Manish, E-mail: manishk@physics.iitd.ac.in; Joseph, Joby, E-mail: joby@physics.iitd.ac.in [Photonics Research Laboratory, Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016 (India)

    2014-08-04

    We propose a simple and straightforward method to generate spatially variant lattice structures by optical interference lithography method. Using this method, it is possible to independently vary the orientation and period of the two-dimensional lattice. The method consists of two steps which are: numerical synthesis of corresponding phase mask by employing a two-dimensional integrated gradient calculations and experimental implementation of synthesized phase mask by making use of a phase only spatial light modulator in an optical 4f Fourier filtering setup. As a working example, we provide the experimental fabrication of a spatially variant square lattice structure which has the possibility to guide a Gaussian beam through a 90° bend by photonic crystal self-collimation phenomena. The method is digitally reconfigurable, is completely scalable, and could be extended to other kind of lattices as well.

  12. Negative refraction and imaging of acoustic waves in a two-dimensional square chiral lattice structure

    Science.gov (United States)

    Zhao, Sheng-Dong; Wang, Yue-Sheng

    2016-05-01

    The negative refraction behavior and imaging effect for acoustic waves in a kind of two-dimensional square chiral lattice structure are studied in this paper. The unit cell of the proposed structure consists of four zigzag arms connected through a thin circular ring at the central part. The relation of the symmetry of the unit cell and the negative refraction phenomenon is investigated. Using the finite element method, we calculate the band structures and the equi-frequency surfaces of the system, and confirm the frequency range where the negative refraction is present. Due to the rotational symmetry of the unit cell, a phase difference is induced to the waves propagating from a point source through the structure to the other side. The phase difference is related to the width of the structure and the frequency of the source, so we can get a tunable deviated imaging. This kind of phenomenon is also demonstrated by the numerical simulation of two Gaussian beams that are symmetrical about the interface normal with the same incident angle, and the different negative refractive indexes are presented. Based on this special performance, a double-functional mirror-symmetrical slab is proposed for realizing acoustic focusing and beam separation.

  13. The sequence d(CGGCGGCCGC) self-assembles into a two dimensional rhombic DNA lattice

    Energy Technology Data Exchange (ETDEWEB)

    Venkadesh, S.; Mandal, P.K. [CAS in Crystallography and Biophysics, University of Madras, Chennai 600 025 (India); Gautham, N., E-mail: n_gautham@hotmail.com [CAS in Crystallography and Biophysics, University of Madras, Chennai 600 025 (India)

    2011-04-15

    Highlights: {yields} This is the first crystal structure of a four-way junction with sticky ends. {yields} Four junction structures bind to each other and form a rhombic cavity. {yields} Each rhombus binds to others to form 'infinite' 2D tiles. {yields} This is an example of bottom-up fabrication of a DNA nano-lattice. -- Abstract: We report here the crystal structure of the partially self-complementary decameric sequence d(CGGCGGCCGC), which self assembles to form a four-way junction with sticky ends. Each junction binds to four others through Watson-Crick base pairing at the sticky ends to form a rhombic structure. The rhombuses bind to each other and form two dimensional tiles. The tiles stack to form the crystal. The crystal diffracted in the space group P1 to a resolution of 2.5 A. The junction has the anti-parallel stacked-X conformation like other junction structures, though the formation of the rhombic net noticeably alters the details of the junction geometry.

  14. High applicability of two-dimensional phosphorous in Kagome lattice predicted from first-principles calculations.

    Science.gov (United States)

    Chen, Peng-Jen; Jeng, Horng-Tay

    2016-03-16

    A new semiconducting phase of two-dimensional phosphorous in the Kagome lattice is proposed from first-principles calculations. The band gaps of the monolayer (ML) and bulk Kagome phosphorous (Kagome-P) are 2.00 and 1.11 eV, respectively. The magnitude of the band gap is tunable by applying the in-plane strain and/or changing the number of stacking layers. High optical absorption coefficients at the visible light region are predicted for multilayer Kagome-P, indicating potential applications for solar cell devices. The nearly dispersionless top valence band of the ML Kagome-P with high density of states at the Fermi level leads to superconductivity with Tc of ~9 K under the optimal hole doping concentration. We also propose that the Kagome-P can be fabricated through the manipulation of the substrate-induced strain during the process of the sample growth. Our work demonstrates the high applicability of the Kagome-P in the fields of electronics, photovoltaics, and superconductivity.

  15. Non-equilibrium relaxation in a two-dimensional stochastic lattice Lotka-Volterra model

    Science.gov (United States)

    Chen, Sheng; Täuber, Uwe C.

    We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. There are stable states when the predators and prey coexist. If the local prey carrying capacity is finite, there emerges an extinction threshold for the predator population at a critical value of the predation rate. We investigate the non-equilibrium relaxation of the predator density in the vicinity of this critical point. The expected power law dependence between the relaxation time and predation rate is observed (critical slowing down). The numerically determined associated critical exponents are in accord with the directed percolation universality class. Following a sudden predation rate change to its critical value, one observes critical aging for the predator density autocorrelation function with a universal scaling exponent. This aging scaling signature of the absorbing state phase transition emerges at significantly earlier times than stationary critical power laws, and could thus serve as an advanced indicator of the population's proximity to its extinction threshold. This research is supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-FG02-09ER46613.

  16. Application of the lattice-Boltzmann method to study flow and dispersion in channels with and without expansion and contraction geometry

    Science.gov (United States)

    Kumar, Rajinder; Nivarthi, Sriram S.; Davis, H. Ted; Kroll, D. M.; Maier, Robert S.

    1999-11-01

    The lattice-Boltzmann (LB) method, derived from lattice gas automata, is a relatively new technique for studying transport problems. The LB method is investigated for its accuracy to study fluid dynamics and dispersion problems. Two problems of relevance to flow and dispersion in porous media are addressed: (i) Poiseuille flow between parallel plates (which is analogous to flow in pore throats in two-dimensional porous networks), and (ii) flow through an expansion-contraction geometry (which is analogous to flow in pore bodies in two-dimensional porous networks). The results obtained from the LB simulations are compared with analytical solutions when available, and with solutions obtained from a finite element code (FIDAP) when analytical results are not available. Excellent agreement is found between the LB results and the analytical/FIDAP solutions in most cases, indicating the utility of the lattice-Boltzmann method for solving fluid dynamics and dispersion problems. Copyright

  17. Contact angles in the pseudopotential lattice Boltzmann modeling of wetting

    Science.gov (United States)

    Li, Qing; Luo, K. H.; Kang, Q. J.; Chen, Q.

    2014-11-01

    In this paper we investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio ρL/ρV=500 . The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994), 10.1103/PhysRevE.49.2941] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions, the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction formulated in the present paper are numerically investigated and compared in terms of the achievable contact angles, the maximum and the minimum densities, and the spurious currents. It is found that the pseudopotential-based interaction works well for simulating small static (liquid) contact angles θ static contact angles close to 180∘. Meanwhile, it is found that the proposed modified pseudopotential-based interaction performs better in light of the maximum and the minimum densities and is overall more suitable for simulating large contact angles θ >90∘ as compared with the two other types of fluid-solid interactions. Furthermore, the spurious currents are found to be enlarged when the fluid-solid interaction force is introduced. Increasing the kinematic viscosity ratio between the vapor and liquid phases is shown to be capable of reducing the spurious currents caused by the fluid-solid interactions.

  18. High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

    Science.gov (United States)

    Li, Weidong

    2017-09-01

    This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.

  19. Lattice Boltzmann model for a steady radiative transfer equation.

    Science.gov (United States)

    Yi, Hong-Liang; Yao, Feng-Ju; Tan, He-Ping

    2016-08-01

    A complete lattice Boltzmann model (LBM) is proposed for the steady radiative transfer equation (RTE). The RTE can be regarded as a pure convection equation with a source term. To derive the expressions for the equilibrium distribution function and the relaxation time, an artificial isotropic diffusion term is introduced to form a convection-diffusion equation. When the dimensionless relaxation time has a value of 0.5, the lattice Boltzmann equation (LBE) is exactly applicable to the original steady RTE. We also perform a multiscale analysis based on the Chapman-Enskog expansion to recover the macroscopic RTE from the mesoscopic LBE. The D2Q9 model is used to solve the LBE, and the numerical results obtained by the LBM are comparable to the results obtained by other methods or analytical solutions, which demonstrates that the proposed model is highly accurate and stable in simulating multidimensional radiative transfer. In addition, we find that the convergence rate of the LBM depends on the transport properties of RTE: for diffusion-dominated RTE with a large optical thickness, the LBM shows a second-order convergence rate in space, while for convection-dominated RTE with a small optical thickness, a lower convergence rate is observed.

  20. Wall Orientation and Shear Stress in the Lattice Boltzmann Model

    CERN Document Server

    Matyka, Maciej; Mirosław, Łukasz

    2013-01-01

    The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near ...

  1. Lattice Boltzmann Simulation for Complex Flow in a Solar Wall

    Institute of Scientific and Technical Information of China (English)

    CHEN Rou; Shao Jiu-Gu; ZHENG You-Qu; YU Hui-Dan; XU You-Sheng

    2013-01-01

    In this letter,we present a lattice Boltzmann simulation for complex flow in a solar wall system which includes porous media flow and heat transfer,specifically for solar energy utilization through an unglazed transpired solar air collector (UTC).Besides the lattice Boltzmann equation (LBE) for time evolution of particle distribution function for fluid field,we introduce an analogy,LBE for time evolution of distribution function for temperature.Both temperature fields of fluid (air) and solid (porous media) are modeled.We study the effects of fan velocity,solar radiation intensity,porosity,etc.on the thermal performance of the UTC.In general,our simulation results are in good agreement with what in literature.With the current system setting,both fan velocity and solar radiation intensity have significant effect on the thermal performance of the UTC.However,it is shown that the porosity has negligible effect on the heat collector indicating the current system setting might not be realistic.Further examinations of thermal performance in different UTC systems are ongoing.The results are expected to present in near future.

  2. Lattice Boltzmann methods for global linear instability analysis

    Science.gov (United States)

    Pérez, José Miguel; Aguilar, Alfonso; Theofilis, Vassilis

    2016-11-01

    Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.

  3. Surface Reconstruction-Induced Coincidence Lattice Formation Between Two-Dimensionally Bonded Materials and a Three-Dimensionally Bonded Substrate

    NARCIS (Netherlands)

    Boschker, Jos E.; Momand, Jamo; Bragaglia, Valeria; Wang, Ruining; Perumal, Karthick; Giussani, Alessandro; Kooi, Bart J.; Riechert, Henning; Calarco, Raffaella

    2014-01-01

    Sb2Te3 films are used for studying the epitaxial registry between two-dimensionally bonded (2D) materials and three-dimensional bonded (3D) substrates. In contrast to the growth of 3D materials, it is found that the formation of coincidence lattices between Sb2Te3 and Si(111) depends on the geometry

  4. Fabrication of deep-profile Al-doped ZnO one- and two-dimensional lattices as plasmonic elements

    DEFF Research Database (Denmark)

    Jensen, Flemming; Shkondin, Evgeniy; Takayama, Osamu

    2016-01-01

    In this work, we report on fabrication of deep-profile one- and two-dimensional lattices made from Al-doped ZnO (AZO). AZO is considered as an alternative plasmonic material having the real part of the permittivity negative in the near infrared range. The exact position of the plasma frequency...

  5. Energy-Dependent Octagonal Lattice Boltzmann Modeling for Compressible Flows

    Science.gov (United States)

    Pavlo, Pavol; Vahala, Linda; Vahala, George

    2000-10-01

    There has been much interest in thermal lattice Boltzmann modeling (TLBM) for compressible flows because of their inherent parallelizeability. Instead of applying CFD techniques to the nonlinear conservation equations, one instead solves a linear BGK kinetic equation. To reduce storage requirements, the velocity space is discretized and lattice geometries are so chosen to minimize the number of degrees of freedom that must be retained in the Chapman-Enskog recovery of the original macroscopic equations. The simplest (and most efficient) TLBM runs at a CFL=1, so that no numerical diffusion or dissipation is introduced. The algorithm involves Lagrangian streaming (shift operator) and purely local operations. Because of the underlying discrete lattice symmetry, the relaxation distributions cannot be Maxwellian and hence the inherent numerical instability problem in TLBM. We are investigating the use of energy-dependent lattices so as to allow simulation of problems of interest in divertor physics, The appeal of TLBM is that it can provide a unified representation for both strongly collisional (‘fluid’) and weakly collisional (‘Monte Carlo’) regimes. Moreover, our TLBM code is more efficiently solved on mulit-PE platforms than the corresponding CFD codes and is readily extended to 3D. MHD can also be handled by TLBM.

  6. Adjoint Parameter Sensitivity Analysis for the Hydrodynamic Lattice Boltzmann Method with Applications to Design Optimization

    DEFF Research Database (Denmark)

    Pingen, Georg; Evgrafov, Anton; Maute, Kurt

    2009-01-01

    We present an adjoint parameter sensitivity analysis formulation and solution strategy for the lattice Boltzmann method (LBM). The focus is on design optimization applications, in particular topology optimization. The lattice Boltzmann method is briefly described with an in-depth discussion...

  7. High-order weighted essentially nonoscillatory finite-difference formulation of the lattice Boltzmann method in generalized curvilinear coordinates

    Science.gov (United States)

    Hejranfar, Kazem; Saadat, Mohammad Hossein; Taheri, Sina

    2017-02-01

    In this work, a high-order weighted essentially nonoscillatory (WENO) finite-difference lattice Boltzmann method (WENOLBM) is developed and assessed for an accurate simulation of incompressible flows. To handle curved geometries with nonuniform grids, the incompressible form of the discrete Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) approximation is transformed into the generalized curvilinear coordinates and the spatial derivatives of the resulting lattice Boltzmann equation in the computational plane are solved using the fifth-order WENO scheme. The first-order implicit-explicit Runge-Kutta scheme and also the fourth-order Runge-Kutta explicit time integrating scheme are adopted for the discretization of the temporal term. To examine the accuracy and performance of the present solution procedure based on the WENOLBM developed, different benchmark test cases are simulated as follows: unsteady Taylor-Green vortex, unsteady doubly periodic shear layer flow, steady flow in a two-dimensional (2D) cavity, steady cylindrical Couette flow, steady flow over a 2D circular cylinder, and steady and unsteady flows over a NACA0012 hydrofoil at different flow conditions. Results of the present solution are compared with the existing numerical and experimental results which show good agreement. To show the efficiency and accuracy of the solution methodology, the results are also compared with the developed second-order central-difference finite-volume lattice Boltzmann method and the compact finite-difference lattice Boltzmann method. It is shown that the present numerical scheme is robust, efficient, and accurate for solving steady and unsteady incompressible flows even at high Reynolds number flows.

  8. High-order weighted essentially nonoscillatory finite-difference formulation of the lattice Boltzmann method in generalized curvilinear coordinates.

    Science.gov (United States)

    Hejranfar, Kazem; Saadat, Mohammad Hossein; Taheri, Sina

    2017-02-01

    In this work, a high-order weighted essentially nonoscillatory (WENO) finite-difference lattice Boltzmann method (WENOLBM) is developed and assessed for an accurate simulation of incompressible flows. To handle curved geometries with nonuniform grids, the incompressible form of the discrete Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) approximation is transformed into the generalized curvilinear coordinates and the spatial derivatives of the resulting lattice Boltzmann equation in the computational plane are solved using the fifth-order WENO scheme. The first-order implicit-explicit Runge-Kutta scheme and also the fourth-order Runge-Kutta explicit time integrating scheme are adopted for the discretization of the temporal term. To examine the accuracy and performance of the present solution procedure based on the WENOLBM developed, different benchmark test cases are simulated as follows: unsteady Taylor-Green vortex, unsteady doubly periodic shear layer flow, steady flow in a two-dimensional (2D) cavity, steady cylindrical Couette flow, steady flow over a 2D circular cylinder, and steady and unsteady flows over a NACA0012 hydrofoil at different flow conditions. Results of the present solution are compared with the existing numerical and experimental results which show good agreement. To show the efficiency and accuracy of the solution methodology, the results are also compared with the developed second-order central-difference finite-volume lattice Boltzmann method and the compact finite-difference lattice Boltzmann method. It is shown that the present numerical scheme is robust, efficient, and accurate for solving steady and unsteady incompressible flows even at high Reynolds number flows.

  9. Lattice Boltzmann formulation for conjugate heat transfer in heterogeneous media.

    Science.gov (United States)

    Karani, Hamid; Huber, Christian

    2015-02-01

    In this paper, we propose an approach for studying conjugate heat transfer using the lattice Boltzmann method (LBM). The approach is based on reformulating the lattice Boltzmann equation for solving the conservative form of the energy equation. This leads to the appearance of a source term, which introduces the jump conditions at the interface between two phases or components with different thermal properties. The proposed source term formulation conserves conductive and advective heat flux simultaneously, which makes it suitable for modeling conjugate heat transfer in general multiphase or multicomponent systems. The simple implementation of the source term approach avoids any correction of distribution functions neighboring the interface and provides an algorithm that is independent from the topology of the interface. Moreover, our approach is independent of the choice of lattice discretization and can be easily applied to different advection-diffusion LBM solvers. The model is tested against several benchmark problems including steady-state convection-diffusion within two fluid layers with parallel and normal interfaces with respect to the flow direction, unsteady conduction in a three-layer stratified domain, and steady conduction in a two-layer annulus. The LBM results are in excellent agreement with analytical solution. Error analysis shows that our model is first-order accurate in space, but an extension to a second-order scheme is straightforward. We apply our LBM model to heat transfer in a two-component heterogeneous medium with a random microstructure. This example highlights that the method we propose is independent of the topology of interfaces between the different phases and, as such, is ideally suited for complex natural heterogeneous media. We further validate the present LBM formulation with a study of natural convection in a porous enclosure. The results confirm the reliability of the model in simulating complex coupled fluid and thermal dynamics

  10. Numerical Simulation of Isothermal Micro Flows by Lattice Boltzmann Method and Theoretical Analysis of the Diffuse Scattering Boundary Condition

    Science.gov (United States)

    Niu, X. D.; Shu, C.; Chew, Y. T.

    A Lattice Boltzmann model for simulating micro flows has been proposed by us recently (Europhysics Letters, 67(4), 600-606 (2004)). In this paper, we will present a further theoretical and numerical validation of the model. In this regards, a theoretical analysis of the diffuse-scattering boundary condition for a simple flow is carried out and the result is consistent with the conventional slip velocity boundary condition. Numerical validation is highlighted by simulating the two-dimensional isothermal pressure-driven micro-channel flows and the thin-film gas bearing lubrication problems, and comparing the simulation results with available experimental data and analytical predictions.

  11. Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows.

    Science.gov (United States)

    Hejranfar, Kazem; Hajihassanpour, Mahya

    2015-01-01

    In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential

  12. Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

    Science.gov (United States)

    Orr, Jeb S.; Powers, Joseph F.; Yang, Hong Q

    2015-01-01

    A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments is based upon a novel approach that relies on the global momentum conservation of the closed fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. A numerical example illustrates the method's application to prediction of bulk fluid behavior during a spacecraft ullage settling maneuver.

  13. Lattice Boltzmann Simulation of Multiple Bubbles Motion under Gravity

    Directory of Open Access Journals (Sweden)

    Deming Nie

    2015-01-01

    Full Text Available The motion of multiple bubbles under gravity in two dimensions is numerically studied through the lattice Boltzmann method for the Eotvos number ranging from 1 to 12. Two kinds of initial arrangement are taken into account: vertical and horizontal arrangement. In both cases the effects of Eotvos number on the bubble coalescence and rising velocity are investigated. For the vertical arrangement, it has been found that the coalescence pattern is similar. The first coalescence always takes place between the two uppermost bubbles. And the last coalescence always takes place between the coalesced bubble and the bottommost bubble. For four bubbles in a horizontal arrangement, the outermost bubbles travel into the wake of the middle bubbles in all cases, which allows the bubbles to coalesce. The coalescence pattern is more complex for the case of eight bubbles, which strongly depends on the Eotvos number.

  14. Lattice Boltzmann based discrete simulation for gas-solid fluidization

    CERN Document Server

    Wang, Limin; Wang, Xiaowei; Ge, Wei

    2013-01-01

    Discrete particle simulation, a combined approach of computational fluid dynamics and discrete methods such as DEM (Discrete Element Method), SPH (Smoothed Particle Hydrodynamics), PIC (Particle-In-Cell), etc., is becoming a practical tool for exploring lab-scale gas-solid systems owing to the fast development of its parallel computation. However, the gas-solid coupling and the corresponding fluid flow solver remain immature. In this work, we presented a modified lattice Boltzmann approach to consider the effect of both the local solid volume fraction and the local relative velocity between the particles and the fluid, which was different from the traditional volume-averaged Navier-Stokes equations. This approach is combined with a time-driven hard sphere algorithm to simulate the motion of individual particles in which particles interact with each other via hard-sphere collisions but the collision detection and motion of the particle are performed at constant time intervals, and the EMMS (energy minimization...

  15. Lattice Boltzmann method for shape optimization of fluid distributor

    CERN Document Server

    Wang, Limin; Luo, Lingai

    2013-01-01

    This paper presents the shape optimization of a flat-type arborescent fluid distributor for the purpose of process intensification. A shape optimization algorithm based on the lattice Boltzmann method (LBM) is proposed with the objective of decreasing the flow resistance of such distributor at the constraint of constant fluid volume. Prototypes of the initial distributor as well as the optimized one are designed. Fluid distribution and hydraulic characteristics of these distributors are investigated numerically. Results show that the pressure drop of the optimized distributor is between 15.9% and 25.1% lower than that of the initial reference while keeping a uniform flow distribution, demonstrating the process intensification in fluid distributor, and suggesting the interests of the proposed optimization algorithm in engineering optimal design.

  16. Lattice Boltzmann modeling of water-like fluids

    Directory of Open Access Journals (Sweden)

    Sauro eSucci

    2014-04-01

    Full Text Available We review recent advances on the mesoscopic modeling of water-like fluids,based on the lattice Boltzmann (LB methodology.The main idea is to enrich the basic LB (hydro-dynamics with angular degrees of freedom responding to suitable directional potentials between water-like molecules.The model is shown to reproduce some microscopic features of liquid water, such as an average number of hydrogen bonds per molecules (HBs between $3$ and $4$, as well as a qualitatively correctstatistics of the hydrogen bond angle as a function of the temperature.Future developments, based on the coupling the present water-like LB model with the dynamics of suspended bodies,such as biopolymers, may open new angles of attack to the simulation of complex biofluidic problems, such as protein folding and aggregation, and the motion of large biomolecules in complex cellular environments.

  17. A Lattice Boltzmann Model for Oscillating Reaction-Diffusion

    Science.gov (United States)

    Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio

    2016-07-01

    A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.

  18. From bijels to Pickering emulsions: A lattice Boltzmann study

    Science.gov (United States)

    Jansen, Fabian; Harting, Jens

    2011-04-01

    Particle stabilized emulsions are ubiquitous in the food and cosmetics industry, but our understanding of the influence of microscopic fluid-particle and particle-particle interactions on the macroscopic rheology is still limited. In this paper we present a simulation algorithm based on a multicomponent lattice Boltzmann model to describe the solvents combined with a molecular dynamics solver for the description of the solved particles. It is shown that the model allows a wide variation of fluid properties and arbitrary contact angles on the particle surfaces. We demonstrate its applicability by studying the transition from a “bicontinuous interfacially jammed emulsion gel” (bijel) to a “Pickering emulsion” in dependence on the contact angle, the particle concentration, and the ratio of the solvents.

  19. Full Eulerian lattice Boltzmann model for conjugate heat transfer.

    Science.gov (United States)

    Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

    2015-12-01

    In this paper a full Eulerian lattice Boltzmann model is proposed for conjugate heat transfer. A unified governing equation with a source term for the temperature field is derived. By introducing the source term, we prove that the continuity of temperature and its normal flux at the interface is satisfied automatically. The curved interface is assumed to be zigzag lines. All physical quantities are recorded and updated on a Cartesian grid. As a result, any complicated treatment near the interface is avoided, which makes the proposed model suitable to simulate the conjugate heat transfer with complex interfaces efficiently. The present conjugate interface treatment is validated by several steady and unsteady numerical tests, including pure heat conduction, forced convection, and natural convection problems. Both flat and curved interfaces are also involved. The obtained results show good agreement with the analytical and/or finite volume results.

  20. Spreading Dynamics of Nanodrops: A Lattice Boltzmann Study

    CERN Document Server

    Gross, Markus

    2014-01-01

    Spreading of nano-droplets is an interesting and technologically relevant phenomenon where thermal fluctuations lead to unexpected deviations from well-known deterministic laws. Here, we apply the newly developed fluctuating non-ideal lattice Boltzmann method [Gross et al., J. Stat. Mech., P03030 (2011)] for the study of this issue. Confirming the predictions of Davidovich and coworkers [PRL 95, 244905 (2005)], we provide the first independent evidence for the existence of an asymptotic, self-similar noise-driven spreading regime in both two- and three-dimensional geometry. The cross over from the deterministic Tanner's law, where the drop's base radius $b$ grows (in 3D) with time as $b \\sim t^{1/10}$ and the noise dominated regime where $b \\sim t^{1/6}$ is also observed by tuning the strength of thermal noise.

  1. Chemical-potential-based Lattice Boltzmann Method for Nonideal Fluids

    CERN Document Server

    Wen, Binghai; He, Bing; Zhang, Chaoying; Fang, Haiping

    2016-01-01

    Chemical potential is an effective way to drive phase transition or express wettability. In this letter, we present a chemical-potential-based lattice Boltzmann model to simulate multiphase flows. The nonideal force is directly evaluated by a chemical potential. The model theoretically satisfies thermodynamics and Galilean invariance. The computational efficiency is improved owing to avoiding the calculation of pressure tensor. We have derived several chemical potentials of the popular equations of state from the free-energy density function. An effective chemical-potential boundary condition is implemented to investigate the wettability of a solid surface. Remarkably, the numerical results show that the contact angle can be linearly tuned by the surface chemical potential.

  2. Free Surface Lattice Boltzmann with Enhanced Bubble Model

    CERN Document Server

    Anderl, Daniela; Rauh, Cornelia; Rüde, Ulrich; Delgado, Antonio

    2016-01-01

    This paper presents an enhancement to the free surface lattice Boltzmann method (FSLBM) for the simulation of bubbly flows including rupture and breakup of bubbles. The FSLBM uses a volume of fluid approach to reduce the problem of a liquid-gas two-phase flow to a single-phase free surface simulation. In bubbly flows compression effects leading to an increase or decrease of pressure in the suspended bubbles cannot be neglected. Therefore, the free surface simulation is augmented by a bubble model that supplies the missing information by tracking the topological changes of the free surface in the flow. The new model presented here is capable of handling the effects of bubble breakup and coalesce without causing a significant computational overhead. Thus, the enhanced bubble model extends the applicability of the FSLBM to a new range of practically relevant problems, like bubble formation and development in chemical reactors or foaming processes.

  3. Lattice Boltzmann implementation for Fluids Flow Simulation in Porous Media

    Directory of Open Access Journals (Sweden)

    Xinming Zhang

    2011-06-01

    Full Text Available In this paper, the lattice-Boltzmann method is developed to investigate the behavior of isothermal two-phase fluid flow in porous media. The method is based on the Shan–Chen multiphase model of nonideal fluids that allow coexistence of two phases of a single substance. We reproduce some different idealized situations (phase separation, surface tension, contact angle, pipe flow, and fluid droplet motion, et al in which the results are already known from theory or laboratory measurements and show the validity of the implementation for the physical two-phase flow in porous media. Application of the method to fluid intrusion in porous media is discussed and shows the effect of wettability on the fluid flow. The capability of reproducing critical flooding phenomena under strong wettability conditions is also proved.

  4. Boundary Slip and Surface Interaction: A Lattice Boltzmann Simulation

    Institute of Scientific and Technical Information of China (English)

    CHEN Yan-Yan; YI Hou-Hui; LI Hua-Bing

    2008-01-01

    The factors affecting slip length in Couette geometry flows are analysed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactions.The main factors influencing the boundary slip are the strength of interactions between fluid-fluid and fluid-wall particles.Other factors,such as fluid viscosity,bulk pressure may also change the slip length.We find that boundary slip only occurs under a certain density(bulk pressure).If the density is large enough,the slip length will tend to zero.In our simulations,a low density layer near the wall does not need to be postulated a priori but emerges naturally from the underlying non-ideal mesoscopic dynamics.It is the low density layer that induces the boundary slip.The results may be helpful to understand recent experimental observations on the slippage of micro flows.

  5. Convection in multiphase flows using Lattice Boltzmann methods

    CERN Document Server

    Biferale, L; Sbragaglia, M; Toschi, F

    2011-01-01

    We present high resolution numerical simulations of convection in multiphase flows (boiling) using a novel algorithm based on a Lattice Boltzmann method. We first validate the thermodynamical and kinematical properties of the algorithm. Then, we perform a series of 3d numerical simulations at changing the mean properties in the phase diagram and compare convection with and without phase coexistence at $Ra \\sim 10^7$. We show that in presence of nucleating bubbles non-Oberbeck Boussinesq effects develops, mean temperature profile becomes asymmetric, heat-transfer and heat-transfer fluctuations are enhanced. We also show that small-scale properties of velocity and temperature fields are strongly affected by the presence of buoyant bubble leading to high non-Gaussian profiles in the bulk.

  6. Lattice Boltzmann simulations of convection heat transfer in porous media

    Science.gov (United States)

    Liu, Qing; He, Ya-Ling

    2017-01-01

    A non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed to study convection heat transfer in porous media at the representative elementary volume scale based on the generalized non-Darcy model. In the method, two different LB models are constructed: one is constructed in the framework of the double-distribution-function approach, and the other is constructed in the framework of the hybrid approach. In particular, the transformation matrices used in the MRT-LB models are non-orthogonal matrices. The present method is applied to study mixed convection flow in a porous channel and natural convection flow in a porous cavity. It is found that the numerical results are in good agreement with the analytical solutions and/or other results reported in previous studies. Furthermore, the non-orthogonal MRT-LB method shows better numerical stability in comparison with the BGK-LB method.

  7. Lattice Boltzmann modeling an introduction for geoscientists and engineers

    CERN Document Server

    Sukop, Michael C

    2005-01-01

    Lattice Boltzmann models have a remarkable ability to simulate single- and multi-phase fluids and transport processes within them. A rich variety of behaviors, including higher Reynolds numbers flows, phase separation, evaporation, condensation, cavitation, buoyancy, and interactions with surfaces can readily be simulated. This book provides a basic introduction that emphasizes intuition and simplistic conceptualization of processes. It avoids the more difficult mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those with more interest in model application than detailed mathematical foundations will find this a powerful "quick start" guide. Example simulations, exercises, and computer codes are included. Working code is provided on the Internet.

  8. Simulation of a Microfluidic Gradient Generator using Lattice Boltzmann Methods

    CERN Document Server

    Simon, Tanaka

    2013-01-01

    Microfluidics provides a powerful and versatile technology to accurately control spatial and temporal conditions for cell culturing and can therefore be used to study cellular responses to gradients. Here we use Lattice Boltzmann methods (LBM) to solve both the Navier-Stokes equation (NSE) for the fluid and the coupled convection-diffusion equation (CDE) for the compounds that form the diffusion-based gradient. The design of a microfluidic chamber for diffusion-based gradients must avoid flow through the cell chamber. This can be achieved by alternately opening the source and the sink channels. The fast toggling of microfluidic valves requires switching between different boundary conditions. We demonstrate that the LBM is a powerful method for handling complex geometries, high Peclet number conditions, discontinuities in the boundary conditions, and multiphysics coupling.

  9. Using an Interactive Lattice Boltzmann Solver in Fluid Mechanics Instruction

    Directory of Open Access Journals (Sweden)

    Mirjam S. Glessmer

    2017-07-01

    Full Text Available This article gives an overview of the diverse range of teaching applications that can be realized using an interactive lattice Boltzmann simulation tool in fluid mechanics instruction and outreach. In an inquiry-based learning framework, examples are given of learning scenarios that address instruction on scientific results, scientific methods or the scientific process at varying levels of student activity, from consuming to applying to researching. Interactive live demonstrations on portable hardware enable new and innovative teaching concepts for fluid mechanics, also for large audiences and in the early stages of the university education. Moreover, selected examples successfully demonstrate that the integration of high-fidelity CFD methods into fluid mechanics teaching facilitates high-quality student research work within reach of the current state of the art in the respective field of research.

  10. Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier–Maxwell slip boundary conditions

    KAUST Repository

    Reis, Tim

    2012-01-01

    We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity the pressure relative to asymptotic solutions of the compressible Navier-Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier-Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself. © 2012 American Institute of Physics.

  11. Towards Full Aircraft Airframe Noise Prediction: Lattice Boltzmann Simulations

    Science.gov (United States)

    Khorrami, Mehdi R.; Fares, Ehab; Casalino, Damiano

    2014-01-01

    Computational results for an 18%-scale, semi-span Gulfstream aircraft model are presented. Exa Corporation's lattice Boltzmann PowerFLOW(trademark) solver was used to perform time-dependent simulations of the flow field associated with this high-fidelity aircraft model. The simulations were obtained for free-air at a Mach number of 0.2 with the flap deflected at 39 deg (landing configuration). We focused on accurately predicting the prominent noise sources at the flap tips and main landing gear for the two baseline configurations, namely, landing flap setting without and with gear deployed. Capitalizing on the inherently transient nature of the lattice Boltzmann formulation, the complex time-dependent flow features associated with the flap were resolved very accurately and efficiently. To properly simulate the noise sources over a broad frequency range, the tailored grid was very dense near the flap inboard and outboard tips. Extensive comparison of the computed time-averaged and unsteady surface pressures with wind tunnel measurements showed excellent agreement for the global aerodynamic characteristics and the local flow field at the flap inboard and outboard tips and the main landing gear. In particular, the computed fluctuating surface pressure field for the flap agreed well with the measurements in both amplitude and frequency content, indicating that the prominent airframe noise sources at the tips were captured successfully. Gear-flap interaction effects were remarkably well predicted and were shown to affect only the inboard flap tip, altering the steady and unsteady pressure fields in that region. The simulated farfield noise spectra for both baseline configurations, obtained using a Ffowcs-Williams and Hawkings acoustic analogy approach, were shown to be in close agreement with measured values.

  12. Contact angles in the pseudopotential lattice Boltzmann modeling of wetting.

    Science.gov (United States)

    Li, Qing; Luo, K H; Kang, Q J; Chen, Q

    2014-11-01

    In this paper we investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio ρ_{L}/ρ_{V}=500. The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994)10.1103/PhysRevE.49.2941] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions, the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction formulated in the present paper are numerically investigated and compared in terms of the achievable contact angles, the maximum and the minimum densities, and the spurious currents. It is found that the pseudopotential-based interaction works well for simulating small static (liquid) contact angles θstatic contact angles close to 180^{∘}. Meanwhile, it is found that the proposed modified pseudopotential-based interaction performs better in light of the maximum and the minimum densities and is overall more suitable for simulating large contact angles θ>90^{∘} as compared with the two other types of fluid-solid interactions. Furthermore, the spurious currents are found to be enlarged when the fluid-solid interaction force is introduced. Increasing the kinematic viscosity ratio between the vapor and liquid phases is shown to be capable of reducing the spurious currents caused by the fluid-solid interactions.

  13. Mass-conserved volumetric lattice Boltzmann method for complex flows with willfully moving boundaries.

    Science.gov (United States)

    Yu, Huidan; Chen, Xi; Wang, Zhiqiang; Deep, Debanjan; Lima, Everton; Zhao, Ye; Teague, Shawn D

    2014-06-01

    In this paper, we develop a mass-conserved volumetric lattice Boltzmann method (MCVLBM) for numerically solving fluid dynamics with willfully moving arbitrary boundaries. In MCVLBM, fluid particles are uniformly distributed in lattice cells and the lattice Boltzmann equations deal with the time evolution of the particle distribution function. By introducing a volumetric parameter P(x,y,z,t) defined as the occupation of solid volume in the cell, we distinguish three types of lattice cells in the simulation domain: solid cell (pure solid occupation, P=1), fluid cell (pure fluid occupation, P=0), and boundary cell (partial solid and partial fluid, 0Boltzmann equations are self-regularized through P and consist of three parts: (1) collision taking into account the momentum exchange between the willfully moving boundary and the flow; (2) streaming accompanying a volumetric bounce-back procedure in boundary cells; and (3) boundary-induced volumetric fluid migration moving the residual fluid particles into the flow domain when the boundary swipes over a boundary cell toward a solid cell. The MCVLBM strictly satisfies mass conservation and can handle irregular boundary orientation and motion with respect to the mesh. Validation studies are carried out in four cases. The first is to simulate fluid dynamics in syringes focusing on how MCVLBM captures the underlying physics of flow driven by a willfully moving piston. The second and third cases are two-dimensional (2D) peristaltic flow and three-dimensional (3D) pipe flow, respectively. In each case, we compare the MCVLBM simulation result with the analytical solution and achieve quantitatively good agreements. The fourth case is to simulate blood flow in human aortic arteries with a very complicated irregular boundary. We study steady flow in two dimensions and unsteady flow via the pulsation of the cardiac cycle in three dimensions. In the 2D case, both vector (velocity) and scalar (pressure) fields are compared to

  14. Photonic band structures of two-dimensional photonic crystals with deformed lattices

    Institute of Scientific and Technical Information of China (English)

    Cai Xiang-Hua; Zheng Wan-Hua; Ma Xiao-Tao; Ren Gang; Xia Jian-Bai

    2005-01-01

    Using the plane-wave expansion method, we have calculated and analysed the changes of photonic band structures arising from two kinds of deformed lattices, including the stretching and shrinking of lattices. The square lattice with square air holes and the triangular lattice with circular air holes are both studied. Calculated results show that the change of lattice size in some special ranges can enlarge the band gap, which depends strongly on the filling factor of air holes in photonic crystals; and besides, the asymmetric band edges will appear with the broken symmetry of lattices.

  15. Lattice-Boltzmann Simulations of Microswimmer-Tracer Interactions

    CERN Document Server

    de Graaf, Joost

    2016-01-01

    Hydrodynamic interactions in systems comprised of self-propelled particles, such as swimming microorganisms, and passive tracers have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force/counter-force based lattice-Boltzmann (LB) algorithm [J. de Graaf~\\textit{et al.}, J. Chem. Phys.~\\textbf{144}, 134106 (2016)], in order to validate its applicability to study large-scale microswimmer suspensions. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The LB algorithm has an inherent near-field renormalization of the flow field, due to the force interpolation between the swimmers and the lattice. This strongly pe...

  16. The Bargmann type reduction for some Lax integrable two-dimensional generalization of the relativistic Toda lattice

    Directory of Open Access Journals (Sweden)

    O. Ye. Hentosh

    2016-01-01

    Full Text Available The possibility of applying the method of reducing upon finite-dimensional invariant subspaces, generated by the eigenvalues of the associated spectral problem, to some two-dimensional generalization of the relativistic Toda lattice with the triple matrix Lax type linearization is investigated. The Hamiltonian property and Lax-Liouville integrability of the vector fields, given by this system, on the invariant subspace related with the Bargmann type reduction are found out.

  17. Second-Order Phase Transition in the Two-Dimensional Classical Lattice Coulomb Gas of Half-Integer Charges

    Institute of Scientific and Technical Information of China (English)

    罗孟波; 陈庆虎; 许祝安; 焦正宽

    2001-01-01

    The second-order phase transition in the two-dimensional (2D) classical Coulomb gas of half-integer charges on a square lattice is investigated by using Monte Carlo simulations. Based on the finite-size scaling analysis,we estimate the second-order phase transition temperature Tc and the static critical exponents β and v with a new numerical analysis method. More precise critical temperature Tc = 0.1311(2) and critical exponents β/ν = 0.1152(12) and ν = 0.857(15) are obtained. The estimated value of ν indicates that the charge lattice melting transition is different from the pure 2D Ising transition.

  18. Absolute band gaps of a two-dimensional triangular-lattice dielectric photonic crystal with different shapes

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    Absolute band gaps of a two-dimensional triangular-lattice photonic crystal are calculated with the finite-difference time-domain method in this paper.Through calculating the photonic band structures of the triangular-lattice photonic crystal consisting of Ge rods immersed in air with different shapes,it is found that a large absolute band gap of 0.098 (2c/a) can be obtained for the structures with hollow triangular Ge rods immersed in air,corresponding to 19.8% of the middle frequency.The influence of the different factors on the width of the absolute band gaps is also discussed.

  19. Lattice Boltzmann methods for complex micro-flows: applicability and limitations for practical applications

    Science.gov (United States)

    Suga, K.

    2013-06-01

    The extensive evaluation studies of the lattice Boltzmann method for micro-scale flows (μ-flow LBM) by the author's group are summarized. For the two-dimensional test cases, force-driven Poiseuille flows, Couette flows, a combined nanochannel flow, and flows in a nanochannel with a square- or triangular cylinder are discussed. The three-dimensional (3D) test cases are nano-mesh flows and a flow between 3D bumpy walls. The reference data for the complex test flow geometries are from the molecular dynamics simulations of the Lennard-Jones fluid by the author's group. The focused flows are mainly in the slip and a part of the transitional flow regimes at Kn flow LBMs are the lattice Bhatnagar-Gross-Krook and the multiple-relaxation time LBMs with several boundary conditions and discrete velocity models. The effects of the discrete velocity models, the wall boundary conditions, the near-wall correction models of the molecular mean free path and the regularization process are discussed to confirm the applicability and the limitations of the μ-flow LBMs for complex flow geometries.

  20. Lattice Boltzmann methods for complex micro-flows: applicability and limitations for practical applications

    Energy Technology Data Exchange (ETDEWEB)

    Suga, K, E-mail: suga@me.osakafu-u.ac.jp [Department of Mechanical Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 (Japan)

    2013-06-15

    The extensive evaluation studies of the lattice Boltzmann method for micro-scale flows ({mu}-flow LBM) by the author's group are summarized. For the two-dimensional test cases, force-driven Poiseuille flows, Couette flows, a combined nanochannel flow, and flows in a nanochannel with a square- or triangular cylinder are discussed. The three-dimensional (3D) test cases are nano-mesh flows and a flow between 3D bumpy walls. The reference data for the complex test flow geometries are from the molecular dynamics simulations of the Lennard-Jones fluid by the author's group. The focused flows are mainly in the slip and a part of the transitional flow regimes at Kn < 1. The evaluated schemes of the {mu}-flow LBMs are the lattice Bhatnagar-Gross-Krook and the multiple-relaxation time LBMs with several boundary conditions and discrete velocity models. The effects of the discrete velocity models, the wall boundary conditions, the near-wall correction models of the molecular mean free path and the regularization process are discussed to confirm the applicability and the limitations of the {mu}-flow LBMs for complex flow geometries. (invited review)

  1. Comparing Entropic and Multiple Relaxation Times Lattice Boltzmann Methods for blood flow simulations

    NARCIS (Netherlands)

    Geerdink, J.B.W.; Hoekstra, A.G.

    2009-01-01

    We compare the Lattice BGK, the Multiple Relaxation Times and the Entropic Lattice Boltzmann Methods for time harmonic flows. We measure the stability, speed and accuracy of the three models for Reynolds and Womersley numbers that are representative for human arteries. The Lattice BGK shows

  2. Dispersion of guided modes in two-dimensional split ring lattices

    CERN Document Server

    Lunnemann, Per

    2014-01-01

    We present a semi-analytical point-dipole method that uses Ewald lattice summation to find the dispersion relation of guided plasmonic and bianisotropic modes in metasurfaces composed of 2D periodic lattices of arbitrarily strongly scattering magneto-electric dipole scatterers. This method takes into account all retarded electrodynamic interactions as well as radiation damping selfconsistently. As illustration we analyze the dispersion of plasmon nanorod lattices, and of 2D split ring resonator lattices. Plasmon nanorod lattices support transverse and longitudinal in-plane electric modes. Scatterers that have an in-plane electric and out-of-plane magnetic polarizability, but without intrinsic magnetoelectric coupling, result in two bands that are mixtures of the bands of electric-only and magnetic-only lattices. Thereby bianisotropy through mutual coupling, in absence of building-block bianisotropy, is evident. Once strong bi-anisotropy is included in each building block, the Bloch modes become even more stro...

  3. Generation and enumeration of compact conformations on the two-dimensional triangular and three-dimensional fcc lattices

    Science.gov (United States)

    Peto, Myron; Sen, Taner Z.; Jernigan, Robert L.; Kloczkowski, Andrzej

    2007-07-01

    We enumerated all compact conformations within simple geometries on the two-dimensional (2D) triangular and three-dimensional (3D) face centered cubic (fcc) lattice. These compact conformations correspond mathematically to Hamiltonian paths and Hamiltonian circuits and are frequently used as simple models of proteins. The shapes that were studied for the 2D triangular lattice included m ×n parallelograms, regular equilateral triangles, and various hexagons. On the 3D fcc lattice we generated conformations for a limited class of skewed parallelepipeds. Symmetries of the shape were exploited to reduce the number of conformations. We compared surface to volume ratios against protein length for compact conformations on the 3D cubic lattice and for a selected set of real proteins. We also show preliminary work in extending the transfer matrix method, previously developed by us for the 2D square and the 3D cubic lattices, to the 2D triangular lattice. The transfer matrix method offers a superior way of generating all conformations within a given geometry on a lattice by completely avoiding attrition and reducing this highly complicated geometrical problem to a simple algebraic problem of matrix multiplication.

  4. Generation and enumeration of compact conformations on the two-dimensional triangular and three-dimensional fcc lattices.

    Science.gov (United States)

    Peto, Myron; Sen, Taner Z; Jernigan, Robert L; Kloczkowski, Andrzej

    2007-07-28

    We enumerated all compact conformations within simple geometries on the two-dimensional (2D) triangular and three-dimensional (3D) face centered cubic (fcc) lattice. These compact conformations correspond mathematically to Hamiltonian paths and Hamiltonian circuits and are frequently used as simple models of proteins. The shapes that were studied for the 2D triangular lattice included mxn parallelograms, regular equilateral triangles, and various hexagons. On the 3D fcc lattice we generated conformations for a limited class of skewed parallelepipeds. Symmetries of the shape were exploited to reduce the number of conformations. We compared surface to volume ratios against protein length for compact conformations on the 3D cubic lattice and for a selected set of real proteins. We also show preliminary work in extending the transfer matrix method, previously developed by us for the 2D square and the 3D cubic lattices, to the 2D triangular lattice. The transfer matrix method offers a superior way of generating all conformations within a given geometry on a lattice by completely avoiding attrition and reducing this highly complicated geometrical problem to a simple algebraic problem of matrix multiplication.

  5. Cluster algorithm for two-dimensional U(1) lattice gauge theory

    Science.gov (United States)

    Sinclair, R.

    1992-03-01

    We use gauge fixing to rewrite the two-dimensional U(1) pure gauge model with Wilson action and periodic boundary conditions as a nonfrustrated XY model on a closed chain. The Wolff single-cluster algorithm is then applied, eliminating critical slowing down of topological modes and Polyakov loops.

  6. Immiscible multicomponent lattice Boltzmann model for fluids with high relaxation time ratio

    Indian Academy of Sciences (India)

    Tao Jiang; Qiwei Gong; Ruofan Qiu; Anlin Wang

    2014-10-01

    An immiscible multicomponent lattice Boltzmann model is developed for fluids with high relaxation time ratios, which is based on the model proposed by Shan and Chen (SC). In the SC model, an interaction potential between particles is incorporated into the discrete lattice Boltzmann equation through the equilibrium velocity. Compared to the SC model, external forces in our model are discretized directly into the discrete lattice Boltzmann equation, as proposed by Guo et al. We develop it into a new multicomponent lattice Boltzmann (LB) model which has the ability to simulate immiscible multicomponent fluids with relaxation time ratio as large as 29.0 and to reduce `spurious velocity’. In this work, the improved model is validated and studied using the central bubble case and the rising bubble case. It finds good applications in both static and dynamic cases for multicomponent simulations with different relaxation time ratios.

  7. Lattice Boltzmann simulation of transverse wave travelling in Maxwell viscoelastic fluid

    Institute of Scientific and Technical Information of China (English)

    Li Hua-Bing; Fang Hai-Ping

    2004-01-01

    A nine-velocity lattice Boltzmann method for Maxwell viscoelastic fluid is proposed. Travelling of transverse wave in Maxwell viscoelastic fluid is simulated. The instantaneous oscillating velocity, transverse shear speed and decay rate agree with theoretical results very well.

  8. A Stability Notion for the viscous Shallow Water Lattice Boltzmann Equations

    CERN Document Server

    Banda, Mapundi K

    2015-01-01

    The stability of Lattice Boltzmann Equations modelling Shallow Water Equations in the special case of reduced gravity is investigated theoretically. A stability notion is defined as applied in incompressible Navier-Stokes equations in Banda, M. K., Yong, W.- A. and Klar, A: A stability notion for lattice Boltzmann equations. SIAM J. Sci. Comput. {\\bf 27(6)}, 2098-2111 (2006). It is found that to maintain stability a careful choice of the value of the reduced gravity must be made. The stability notion is employed to investigate different shallow water lattice Boltzmann Equations. The effect of the reduced gravity on the mechanism of instability is investigated. Results are tested using the Lattice Boltzmann Method for various values of the governing parameters of the flow. It is observed that even for the discrete model the reduced gravity has a significant effect on the stability.

  9. Design, fabrication, and characterization of lightweight and broadband microwave absorbing structure reinforced by two dimensional composite lattice

    Science.gov (United States)

    Chen, Mingji; Pei, Yongmao; Fang, Daining

    2012-07-01

    Microwave absorbing structures (MASs) reinforced by two dimensional (2D) composite lattice elements have been designed and fabricated. The density of these MASs is lower than 0.5 g/cm3. Experimental measurements show that the sandwich structure with glass fiber reinforced composite (GFRC) lattice core can serve as a broadband MAS with its reflectivity below -10 dB over the frequency range of 4-18 GHz. The low permittivity GFRC is indicated to be the proper material for both the structural element of the core and the transparent face sheet. Calculations by the periodic moment method (PMM) demonstrate that the 2D Kagome lattice performs better for microwave absorbing than the square one at relatively low frequencies. The volume fraction and cell size of the structural element are also revealed to be key factors for microwave absorbing performance.

  10. Note on Invariance of One-Dimensional Lattice-Boltzmann Equation

    Institute of Scientific and Technical Information of China (English)

    RAN Zheng

    2007-01-01

    Invariance of the one-dimensional lattice Boltzmann model is proposed together with its rigorous theoretical background.It is demonstrated that the symmetry inherent in Navier-Stokes equations is not really recovered in the one-dimensional lattice Boltzmann equation (LBE),especially for shock calculation.Symmetry breaking may be the inherent cause for the non-physical oscillations in the vicinity of the shock for LBE calculation.

  11. Lattice Boltzmann model for the perfect gas flows with near-vacuum region

    Institute of Scientific and Technical Information of China (English)

    GuangwuYAN; LiYUAN

    2000-01-01

    It is known that the standard lattice Boltzmann method has near-vacuum limit,i. e., when the density is near zero, this method is invalid. In this letter, we propose a simple lattice Boltzmann model for one-dimensional flows. It possesses the ability of simulating nearvacuum area by setting a limitation of the relaxation factor. Thus, the model overcomes the disadvantage of non-physical pressure and the density. The numerical examples show these results are satisfactory.

  12. A Lattice Boltzmann Model and Simulation of KdV-Burgers Equation

    Institute of Scientific and Technical Information of China (English)

    ZHANGChao-Ying; TANHui-Li; LIUMu-Ren; KONGLing-Jiang

    2004-01-01

    A lattice Boltzmann model of KdV-Burgers equation is derived by using the single-relaxation form of the lattice Boltzmann equation. With the present model, we simulate the traveling-wave solutions, the solitary-wave solutions, and the sock-wave solutions of KdV-Burgers equation, and calculate the decay factor and the wavelength of the sock-wave solution, which has exponential decay. The numerical results agree with the analytical solutions quite well.

  13. A New Lattice Boltzmann Model for KdV-Burgers Equation

    Institute of Scientific and Technical Information of China (English)

    MA Chang-Feng

    2005-01-01

    @@ A new lattice Boltzmann model with amending-function for KdV-Burgers equation, ut +uux - αuxx +βuxxx = 0,is presented by using the single-relaxation form of the lattice Boltzmann equation. Applying the proposed model,we simulate the solutions ofa kind of KdV-Burgers equations, and the numerical results agree with the analytical solutions quite well.

  14. Lattice Boltzmann modeling of three-phase incompressible flows

    Science.gov (United States)

    Liang, H.; Shi, B. C.; Chai, Z. H.

    2016-01-01

    In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems.

  15. Application of Lattice Boltzmann Method to Flows in Microgeometries

    Directory of Open Access Journals (Sweden)

    Anoop K. Dass

    2010-07-01

    Full Text Available In the present investigation, Lattice Boltzmann Method (LBM is used to simulate rarefied gaseous microflows in three microgeometries. These are micro-couette, micro lid-driven cavity and micro-poiseuille flows. The Knudsen number is used to measure the degree of rarefaction in the microflows. First, micro-couette flow is computed with the effects of varying Knudsen number in the slip and threshold of the transition regime and the results compare well with existing results. After having thus established the credibility of the code and the method including boundary conditions, LBM is then used to investigate the micro lid-driven cavity flow with various aspect ratios. Simulation of microflow not only requires an appropriate method, it also requires suitable boundary conditions to provide a well-posed problem and unique solution. In this work, LBM and three slip boundary conditions, namely, diffuse scattering boundary condition, specular reflection and a combination of bounce-back and specular reflection is used to predict the micro lid-driven cavity flow fields. Then the LBM simulation is extended to micro-poiseuille flow. The results are substantiated through comparison with existing results and it is felt that the present methodology is reasonable to be employed in analyzing the flow in micro-systems.

  16. Flow visualisation of downhill skiers using the lattice Boltzmann method

    Science.gov (United States)

    Asai, Takeshi; Hong, Sungchan; Ijuin, Koichi

    2017-03-01

    In downhill alpine skiing, skiers often exceed speeds of 120 km h-1, with air resistance substantially affecting the overall race times. To date, studies on air resistance in alpine skiing have used wind tunnels and actual skiers to examine the relationship between the gliding posture and magnitude of drag and for the design of skiing equipment. However, these studies have not revealed the flow velocity distribution and vortex structure around the skier. In the present study, computational fluid dynamics are employed with the lattice Boltzmann method to derive the relationship between total drag and the flow velocity around a downhill skier in the full-tuck position. Furthermore, the flow around the downhill skier is visualised, and its vortex structure is examined. The results show that the total drag force in the downhill skier model is 27.0 N at a flow velocity of 15 m s-1, increasing to 185.8 N at 40 m s-1. From analysis of the drag distribution and the flow profile, the head, upper arms, lower legs, and thighs (including buttocks) are identified as the major sources of drag on a downhill skier. Based on these results, the design of suits and equipment for reducing the drag from each location should be the focus of research and development in ski equipment. This paper describes a pilot study that introduces undergraduate students of physics or engineering into this research field. The results of this study are easy to understand for undergraduate students.

  17. Lattice Boltzmann Simulations of Evaporating Droplets with Nanoparticles

    Science.gov (United States)

    Zhao, Mingfei; Yong, Xin

    2016-11-01

    Elucidating the nanoparticle dynamics in drying droplets provides fundamental hydrodynamic insight into the evaporation-induced self-assembly, which is of great importance to materials printing and thin film processing. We develop a free-energy-based multiphase lattice Boltzmann model coupled with Lagrangian particle tracking to simulate evaporating particle-laden droplets on a solid substrate with specified wetting behavior. This work focuses on the interplay between the evaporation-driven advection and the self-organization of nanoparticles inside the droplet and at the droplet surface. For static droplets, the different parameters, fluid-particle interaction strength and particle number, governing the nanoparticle-droplet dynamics are systematically investigated, such as particle radial and circumferential distribution. We clarify the effect of nanoparticle presence on the droplet surface tension and wetting behavior. For evaporating droplets, we observe how droplet evaporation modulates the self-assembly of nanoparticles when the droplet has different static contact angles and hysteresis windows. We also confirm that the number of nanoparticles at the liquid-vapor interface influences the evaporation flux at the liquid-vapor interface.

  18. Multiple anisotropic collisions for advection-diffusion Lattice Boltzmann schemes

    Science.gov (United States)

    Ginzburg, Irina

    2013-01-01

    This paper develops a symmetrized framework for the analysis of the anisotropic advection-diffusion Lattice Boltzmann schemes. Two main approaches build the anisotropic diffusion coefficients either from the anisotropic anti-symmetric collision matrix or from the anisotropic symmetric equilibrium distribution. We combine and extend existing approaches for all commonly used velocity sets, prescribe most general equilibrium and build the diffusion and numerical-diffusion forms, then derive and compare solvability conditions, examine available anisotropy and stable velocity magnitudes in the presence of advection. Besides the deterioration of accuracy, the numerical diffusion dictates the stable velocity range. Three techniques are proposed for its elimination: (i) velocity-dependent relaxation entries; (ii) their combination with the coordinate-link equilibrium correction; and (iii) equilibrium correction for all links. Two first techniques are also available for the minimal (coordinate) velocity sets. Even then, the two-relaxation-times model with the isotropic rates often gains in effective stability and accuracy. The key point is that the symmetric collision mode does not modify the modeled diffusion tensor but it controls the effective accuracy and stability, via eigenvalue combinations of the opposite parity eigenmodes. We propose to reduce the eigenvalue spectrum by properly combining different anisotropic collision elements. The stability role of the symmetric, multiple-relaxation-times component, is further investigated with the exact von Neumann stability analysis developed in diffusion-dominant limit.

  19. High-order regularization in lattice-Boltzmann equations

    Science.gov (United States)

    Mattila, Keijo K.; Philippi, Paulo C.; Hegele, Luiz A.

    2017-04-01

    A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.

  20. A Lattice-Boltzmann Method for Partially Saturated Computational Cells

    Science.gov (United States)

    Noble, D. R.; Torczynski, J. R.

    The lattice-Boltzmann (LB) method is applied to complex, moving geometries in which computational cells are partially filled with fluid. The LB algorithm is modified to include a term that depends on the percentage of the cell saturated with fluid. The method is useful for modeling suspended obstacles that do not conform to the grid. Another application is to simulations of flow through reconstructed media that are not easily segmented into solid and liquid regions. A detailed comparison is made with FIDAP simulation results for the flow about a periodic line of cylinders in a channel at a non-zero Reynolds number. Two cases are examined. In the first simulation, the cylinders are given a constant velocity along the axis of the channel, and the steady solution is acquired. The transient behavior of the system is then studied by giving the cylinders an oscillatory velocity. For both steady and oscillatory flows, the method provides excellent agreement with FIDAP simulation results, even at locations close to the surface of a cylinder. In contrast to step-like solutions produced using the "bounce-back" condition, the proposed condition gives close agreement with the smooth FIDAP predictions. Computed drag forces with the proposed condition exhibit apparent quadratic convergence with grid refinement rather than the linear convergence exhibited by other LB boundary conditions.

  1. Treatment of moving boundaries in lattice-Boltzmann simulations.

    Science.gov (United States)

    Indireshkumar, K.; Pal, A.; Brasseur, J. G.

    2000-11-01

    We consider the treatment of moving boundaries with the lattice-Boltzmann (LB) technique, where the treatment of the boundary often does not precisely conserve mass and spurious fluctuations in density/pressure result from boundary motion through fixed grids. First, we applied the extrapolation method proposed by Chen et. al.(S. Y. Chen, D. Martinez, and R Mei, Phys. Fluids) 8, 2527 (1996) to incompressible flow induced by the movement of a piston in a 2D ``cylinder'' with mass flow out of or into the cylinder. In these simulations, the velocity of the boundary nodes is set equal to the (known) velocity of the boundary (piston) in the equilibrium distribution function (Method I). In a second set of simulations, the boundary node velocities are obtained by interpolating between interior nodes and the boundary, thus including the effect of boundary position more precisely (Method II). Comparison of LB predictions with simulations using FIDAP show pressure agreement to witnin 2 %. The total mass is conserved to within 0.1% with Method I and improves to within 0.02 % using method II. Spurious fluctuations in density/pressure due to boundary movement is about 0.9% with Method I, which improves significantly to about 0.3% with Method II. The application of these simple techniques to more complex geometries and wall (and fluid) motions in a stomach during gastric emptying will be presented.

  2. Lattice Boltzmann modeling of directional wetting: Comparing simulations to experiments

    Science.gov (United States)

    Jansen, H. Patrick; Sotthewes, Kai; van Swigchem, Jeroen; Zandvliet, Harold J. W.; Kooij, E. Stefan

    2013-07-01

    Lattice Boltzmann Modeling (LBM) simulations were performed on the dynamic behavior of liquid droplets on chemically striped patterned surfaces, ultimately with the aim to develop a predictive tool enabling reliable design of future experiments. The simulations accurately mimic experimental results, which have shown that water droplets on such surfaces adopt an elongated shape due to anisotropic preferential spreading. Details of the contact line motion such as advancing of the contact line in the direction perpendicular to the stripes exhibit pronounced similarities in experiments and simulations. The opposite of spreading, i.e., evaporation of water droplets, leads to a characteristic receding motion first in the direction parallel to the stripes, while the contact line remains pinned perpendicular to the stripes. Only when the aspect ratio is close to unity, the contact line also starts to recede in the perpendicular direction. Very similar behavior was observed in the LBM simulations. Finally, droplet movement can be induced by a gradient in surface wettability. LBM simulations show good semiquantitative agreement with experimental results of decanol droplets on a well-defined striped gradient, which move from high- to low-contact angle surfaces. Similarities and differences for all systems are described and discussed in terms of the predictive capabilities of LBM simulations to model direction wetting.

  3. Acoustic equations of state for simple lattice Boltzmann velocity sets.

    Science.gov (United States)

    Viggen, Erlend Magnus

    2014-07-01

    The lattice Boltzmann (LB) method typically uses an isothermal equation of state. This is not sufficient to simulate a number of acoustic phenomena where the equation of state cannot be approximated as linear and constant. However, it is possible to implement variable equations of state by altering the LB equilibrium distribution. For simple velocity sets with velocity components ξ(iα)∈(-1,0,1) for all i, these equilibria necessarily cause error terms in the momentum equation. These error terms are shown to be either correctable or negligible at the cost of further weakening the compressibility. For the D1Q3 velocity set, such an equilibrium distribution is found and shown to be unique. Its sound propagation properties are found for both forced and free waves, with some generality beyond D1Q3. Finally, this equilibrium distribution is applied to a nonlinear acoustics simulation where both mechanisms of nonlinearity are simulated with good results. This represents an improvement on previous such simulations and proves that the compressibility of the method is still sufficiently strong even for nonlinear acoustics.

  4. Lattice Boltzmann Simulation Optimization on Leading Multicore Platforms

    Energy Technology Data Exchange (ETDEWEB)

    Williams, Samuel; Carter, Jonathan; Oliker, Leonid; Shalf, John; Yelick, Katherine

    2008-02-01

    We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to a lattice Boltzmann application (LBMHD) that historically has made poor use of scalar microprocessors due to its complex data structures and memory access patterns. We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Clovertown, AMD Opteron X2, Sun Niagara2, STI Cell, as well as the single core Intel Itanium2. Rather than hand-tuning LBMHD for each system, we develop a code generator that allows us identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our auto-tuned LBMHD application achieves up to a 14x improvement compared with the original code. Additionally, we present detailed analysis of each optimization, which reveal surprising hardware bottlenecks and software challenges for future multicore systems and applications.

  5. Analysis of two-dimensional photonic band gap structure with a rhombus lattice

    Institute of Scientific and Technical Information of China (English)

    Limei Qi; Ziqiang Yang; Xi Gao; Zheng Liang

    2008-01-01

    @@ The relative band gap for a rhombus lattice photonic crystal is studied by plane wave expansion method and high frequency structure simulator (HFSS) simulation. General wave vectors in the first Briliouin zone are derived. The relative band gap as a function of air-filling factor and background material is investigated, respectively, and the nature of photonic band gap for different lattice angles is analyzed by the distribution of electric energy. These results would provide theoretical instruction for designing optical integrated devices using photonic crystal with a rhombus lattice.

  6. Properties of the two-dimensional spin-1/2 Heisenberg model on a honeycomb lattice with interlayer coupling

    Directory of Open Access Journals (Sweden)

    U. Löw

    2009-01-01

    Full Text Available The magnetic properties of the two-dimensional S=1/2 (quantum antiferromagnetic Heisenberg model on a honeycomb lattice with and without interlayer coupling are studied by means of a continuous Euclidean time Quantum Monte-Carlo algorithm. The internal energy, the magnetic susceptibility and the staggered magnetization are determined in the full temperature range. For the two-dimensional system the ground-state energy/bond is found to be E0hc=-0.36303(13, and the zero temperature staggered magnetization mst=0.2681(8. For coupled planes of honeycomb systems a phase transition from an ordered phase to a disordered phase is found at T/J=0.695(10.

  7. Two-Dimensional Anharmonic Crystal Lattices: Solitons, Solectrons, and Electric Conduction

    OpenAIRE

    Velarde, Manuel G.; Ebeling, Werner; Chetverikov, Alexander P.

    2011-01-01

    Reported here are salient features of soliton-mediated electron transport in anharmonic crystal lattices.After recalling how an electron-soliton bound state (solectron) can be formed we comment on consequences like electron surfing on a sound wave and balistic transport, possible percolation in 2d lattices, and a novel form of electron pairing with strongly correlated electrons both in real space and momentum space.

  8. Percolation in spatial evolutionary prisoner's dilemma game on two-dimensional lattices

    Science.gov (United States)

    Choi, Woosik; Yook, Soon-Hyung; Kim, Yup

    2015-11-01

    We study the spatial evolutionary prisoner's dilemma game with updates of imitation max on triangular, hexagonal, and square lattices. We use the weak prisoner's dilemma game with a single parameter b . Due to the competition between the temptation value b and the coordination number z of the base lattice, a greater variety of percolation properties is expected to occur on the lattice with the larger z . From the numerical analysis, we find six different regimes on the triangular lattice (z =6 ). Regardless of the initial densities of cooperators and defectors, cooperators always percolate in the steady state in two regimes for small b . In these two regimes, defectors do not percolate. In two regimes for the intermediate value of b , both cooperators and defectors undergo percolation transitions. The defector always percolates in two regimes for large b . On the hexagonal lattice (z =3 ), there exist two distinctive regimes. For small b , both the cooperators and the defectors undergo percolation transitions while only defectors always percolate for large b . On the square lattice (z =4 ), there exist three regimes. Combining with the finite-size scaling analyses, we show that all the observed percolation transitions belong to the universality class of the random percolation. We also show how the detailed growth mechanism of cooperator and defector clusters decides each regime.

  9. Tunable spin wave spectra in two-dimensional Ni{sub 80}Fe{sub 20} antidot lattices with varying lattice symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Mandal, R.; Barman, S.; Saha, S.; Barman, A., E-mail: abarman@bose.res.in [Department of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700 098 (India); Otani, Y. [CEMS-RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581 (Japan)

    2015-08-07

    Ferromagnetic antidot lattices are important systems for magnetic data storage and magnonic devices, and understanding their magnetization dynamics by varying their structural parameters is an important problems in magnetism. Here, we investigate the variation in spin wave spectrum in two-dimensional nanoscale Ni{sub 80}Fe{sub 20} antidot lattices with lattice symmetry. By varying the bias magnetic field values in a broadband ferromagnetic resonance spectrometer, we observed a stark variation in the spin wave spectrum with the variation of lattice symmetry. The simulated mode profiles showed further difference in the spatial nature of the modes between different lattices. While for square and rectangular lattices extended modes are observed in addition to standing spin wave modes, all modes in the hexagonal, honeycomb, and octagonal lattices are either localized or standing waves. In addition, the honeycomb and octagonal lattices showed two different types of modes confined within the honeycomb (octagonal) units and between two such consecutive units. Simulated internal magnetic fields confirm the origin of such a wide variation in the frequency and spatial nature of the spin wave modes. The tunability of spin waves with the variation of lattice symmetry is important for the design of future magnetic data storage and magnonic devices.

  10. The focusing effect of electromagnetic waves in two-dimensional photonic crystals with gradually varying lattice constant

    Directory of Open Access Journals (Sweden)

    F Bakhshi Garmi

    2016-02-01

    Full Text Available In this paper we studied the focusing effect of electromagnetic wave in the two-dimensional graded photonic crystal consisting of Silicon rods in the air background with gradually varying lattice constant. The results showed that graded photonic crystal can focus wide beams on a narrow area at frequencies near the lower edge of the band gap, where equal frequency contours are not concave. For calculation of photonic band structure and equal frequency contours, we have used plane wave expansion method and revised plane wave expansion method, respectively. The calculation of the electric and magnetic fields was performed by finite difference time domain method.

  11. Bloch waves in an arbitrary two-dimensional lattice of subwavelength Dirichlet scatterers

    CERN Document Server

    Schnitzer, Ory

    2016-01-01

    We study waves governed by the planar Helmholtz equation, propagating in an infinite lattice of subwavelength Dirichlet scatterers, the periodicity being comparable to the wavelength. Applying the method of matched asymptotic expansions, the scatterers are effectively replaced by asymptotic point constraints. The resulting coarse-grained Bloch-wave dispersion problem is solved by a generalised Fourier series, whose singular asymptotics in the vicinities of scatterers yield the dispersion relation governing modes that are strongly perturbed from plane-wave solutions existing in the absence of the scatterers; there are also empty-lattice waves that are only weakly perturbed. Characterising the latter is useful in interpreting and potentially designing the dispersion diagrams of such lattices. The method presented, that simplifies and expands on Krynkin & McIver [Waves Random Complex, 19 347 2009], could be applied in the future to study more sophisticated designs entailing resonant subwavelength elements di...

  12. Auxetic two-dimensional lattice with Poisson's Ratio arbitrarily close to -1

    CERN Document Server

    Cabras, L

    2014-01-01

    In this paper we propose a new lattice structure having macroscopic Poisson's ratio arbitrarily close to the stability limit -1. We tested experimentally the effective Poisson's ratio of the micro-structured medium; the uniaxial test has been performed on a thermoplastic lattice produced with a 3d printing technology. A theoretical analysis of the effective properties has been performed and the expression of the macroscopic constitutive properties is given in full analytical form as a function of the constitutive properties of the elements of the lattice and on the geometry of the microstructure. The analysis has been performed on three micro-geometry leading to an isotropic behaviour for the cases of three-fold and six-fold symmetry and to a cubic behaviour for the case of four-fold symmetry.

  13. Average site perimeter of directed animals on the two-dimensional lattices

    CERN Document Server

    Bacher, Axel

    2009-01-01

    We introduce new combinatorial (bijective) methods that enable us to compute the average value of three parameters of directed animals of a given area, including the site perimeter. Our results cover directed animals of any one-line source on the square lattice and its bounded variants, and we give counterparts for most of them in the triangular lattices. We thus prove conjectures by Conway and Le Borgne. The techniques used are based on Viennot's correspondence between directed animals and heaps of pieces (or elements of a partially commutative monoid).

  14. Guide modes in photonic crystal heterostructures composed of rotating non-circular air cylinders in two-dimensional lattices

    CERN Document Server

    Zhou Yun Song; Wang Fu He

    2003-01-01

    We investigate the properties of guide modes localized at the interfaces of photonic crystal (PC) heterostructures which are composed of two semi-infinite two-dimensional PCs consisting of non-circular air cylinders with different rotating angles embedded in a homogeneous host dielectric. Photonic band gap structures are calculated with the use of the plane-wave expansion method in combination with a supercell technique. We consider various configurations, for instance, rectangular (square) lattice-rectangular (square) air cylinders, and different rotating angles of the cylinders in the lattices on either side of the interface of a heterostructure. We find that the absolute gap width and the number of guide modes strongly depend on geometric and physical parameters of the heterostructures. It is anticipated that the guide modes in such heterostructures can be engineered by adjusting parameters.

  15. Normally attracting manifolds and periodic behavior in one-dimensional and two-dimensional coupled map lattices

    Science.gov (United States)

    Giberti, Claudio; Vernia, Cecilia

    1994-12-01

    We consider diffusively coupled logistic maps in one- and two-dimensional lattices. We investigate periodic behaviors as the coupling parameter varies, i.e., existence and bifurcations of some periodic orbits with the largest domain of attraction. Similarity and differences between the two lattices are shown. For small coupling the periodic behavior appears to be characterized by a number of periodic orbits structured in such a way to give rise to distinct, reverse period-doubling sequences. For intermediate values of the coupling a prominent role in the dynamics is played by the presence of normally attracting manifolds that contain periodic orbits. The dynamics on these manifolds is very weakly hyperbolic, which implies long transients. A detailed investigation allows the understanding of the mechanism of their formation. A complex bifurcation is found which causes an attracting manifold to become unstable.

  16. Periodic, quasiperiodic and chaotic discrete breathers in a parametrical driven two-dimensional discrete diatomic Klein-Gordon lattice

    Institute of Scientific and Technical Information of China (English)

    Xu Quan; Tian Qiang

    2009-01-01

    We study a two-dimensional (2D) diatomic lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers (DBs) can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein-Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers (QDBs) and chaotic discrete breathers (CDBs) by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.

  17. Lattice Boltzmann simulations of multiple-droplet interaction dynamics

    Science.gov (United States)

    Zhou, Wenchao; Loney, Drew; Fedorov, Andrei G.; Degertekin, F. Levent; Rosen, David W.

    2014-03-01

    A lattice Boltzmann (LB) formulation, which is consistent with the phase-field model for two-phase incompressible fluid, is proposed to model the interface dynamics of droplet impingement. The interparticle force is derived by comparing the macroscopic transport equations recovered from LB equations with the governing equations of the continuous phase-field model. The inconsistency between the existing LB implementations and the phase-field model in calculating the relaxation time at the phase interface is identified and an approximation is proposed to ensure the consistency with the phase-field model. It is also shown that the commonly used equilibrium velocity boundary for the binary fluid LB scheme does not conserve momentum at the wall boundary and a modified scheme is developed to ensure the momentum conservation at the boundary. In addition, a geometric formulation of the wetting boundary condition is proposed to replace the popular surface energy formulation and results show that the geometric approach enforces the prescribed contact angle better than the surface energy formulation in both static and dynamic wetting. The proposed LB formulation is applied to simulating droplet impingement dynamics in three dimensions and results are compared to those obtained with the continuous phase-field model, the LB simulations reported in the literature, and experimental data from the literature. The results show that the proposed LB simulation approach yields not only a significant speed improvement over the phase-field model in simulating droplet impingement dynamics on a submillimeter length scale, but also better accuracy than both the phase-field model and the previously reported LB techniques when compared to experimental data. Upon validation, the proposed LB modeling methodology is applied to the study of multiple-droplet impingement and interactions in three dimensions, which demonstrates its powerful capability of simulating extremely complex interface

  18. Noise Threshold for a Fault-Tolerant Two-Dimensional Lattice Architecture

    CERN Document Server

    Svore, K M; Terhal, B M; Svore, Krysta M.; Vincenzo, David P. Di; Terhal, Barbara M.

    2006-01-01

    We consider a model of quantum computation in which the set of operations is limited to nearest-neighbor interactions on a 2D lattice. We model movement of qubits with noisy SWAP operations. For this architecture we design a fault-tolerant coding scheme using the concatenated [[7,1,3

  19. Programming Self-Assembly of DNA Origami Honeycomb Two-Dimensional Lattices and Plasmonic Metamaterials.

    Science.gov (United States)

    Wang, Pengfei; Gaitanaros, Stavros; Lee, Seungwoo; Bathe, Mark; Shih, William M; Ke, Yonggang

    2016-06-22

    Scaffolded DNA origami has proven to be a versatile method for generating functional nanostructures with prescribed sub-100 nm shapes. Programming DNA-origami tiles to form large-scale 2D lattices that span hundreds of nanometers to the micrometer scale could provide an enabling platform for diverse applications ranging from metamaterials to surface-based biophysical assays. Toward this end, here we design a family of hexagonal DNA-origami tiles using computer-aided design and demonstrate successful self-assembly of micrometer-scale 2D honeycomb lattices and tubes by controlling their geometric and mechanical properties including their interconnecting strands. Our results offer insight into programmed self-assembly of low-defect supra-molecular DNA-origami 2D lattices and tubes. In addition, we demonstrate that these DNA-origami hexagon tiles and honeycomb lattices are versatile platforms for assembling optical metamaterials via programmable spatial arrangement of gold nanoparticles (AuNPs) into cluster and superlattice geometries.

  20. Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh.

    Science.gov (United States)

    Li, Yusong; LeBoeuf, Eugene J; Basu, P K

    2005-10-01

    A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility.

  1. Mixing and Transport in the Small Intestine: A Lattice-Boltzmann Model

    Science.gov (United States)

    Banco, Gino; Brasseur, James; Wang, Yanxing; Aliani, Amit; Webb, Andrew

    2007-11-01

    The two primary functions of the small intestine are absorption of nutrients into the blood stream and transport of material along the gut for eventual evacuation. The primary transport mechanism is peristalsis. The time scales for absorption, however, rely on mixing and transport of molecules between the bulk flow and epithelial surface. Two basic motions contribute to mixing: peristalsis and repetitive segmental contraction of short segments of the gut. In this study we evaluate the relative roles of peristalsis vs. segmental contraction on the degree of mixing and time scales of nutrient transport to the epithelium using a two-dimensional model of flow and mixing in the small intestine. The model uses the lattice-Boltzmann framework with second-order moving boundary conditions and passive scalar (Sc = 10). Segmental and peristaltic contractions were parameterized using magnetic resonance imaging data from rat models. The Reynolds numbers (1.9), segment lengths (33 mm), max radii (2.75 mm) and occlusion ratios (0.33) were matched for direct comparison. Mixing is quantified by the rate of dispersion of scalar from an initial concentration in the center of the segment. We find that radial mixing is more rapid with segmental than peristaltic motion, that radial dispersion is much more rapid than axial, and that axial is comparable between the motions.

  2. Extraction of macroscopic and microscopic adjoint concepts using a lattice Boltzmann method and discrete adjoint approach

    Science.gov (United States)

    Hekmat, Mohamad Hamed; Mirzaei, Masoud

    2015-01-01

    In the present research, we tried to improve the performance of the lattice Boltzmann (LB) -based adjoint approach by utilizing the mesoscopic inherent of the LB method. In this regard, two macroscopic discrete adjoint (MADA) and microscopic discrete adjoint (MIDA) approaches are used to answer the following two challenging questions. Is it possible to extend the concept of the macroscopic and microscopic variables of the flow field to the corresponding adjoint ones? Further, similar to the conservative laws in the LB method, is it possible to find the comparable conservation equations in the adjoint approach? If so, then a definite framework, similar to that used in the flow solution by the LB method, can be employed in the flow sensitivity analysis by the MIDA approach. This achievement can decrease the implementation cost and coding efforts of the MIDA method in complicated sensitivity analysis problems. First, the MADA and MIDA equations are extracted based on the LB method using the duality viewpoint. Meanwhile, using an elementary case, inverse design of a two-dimensional unsteady Poiseuille flow in a periodic channel with constant body forces, the procedure of analytical evaluation of the adjoint variables is described. The numerical results show that similar correlations between the distribution functions can be seen between the corresponding adjoint ones. Besides, the results are promising, emphasizing the flow field adjoint variables can be evaluated via the adjoint distribution functions. Finally, the adjoint conservative laws are introduced.

  3. An immersed boundary-lattice Boltzmann model for biofilm growth in porous media

    Science.gov (United States)

    Benioug, M.; Golfier, F.; Oltéan, C.; Buès, M. A.; Bahar, T.; Cuny, J.

    2017-09-01

    In this paper, we present a two-dimensional pore-scale numerical model to investigate the main mechanisms governing biofilm growth in porous media. The fluid flow and solute transport equations are coupled with a biofilm evolution model. Fluid flow is simulated with an immersed boundary-lattice Boltzmann model while solute transport is described with a volume-of-fluid-type approach. A cellular automaton algorithm combined with immersed boundary methods was developed to describe the spreading and distribution of biomass. Bacterial attachment and detachment mechanisms are also taken into account. The capability of this model to describe correctly the couplings involved between fluid circulation, nutrient transport and bacterial growth is tested under different hydrostatic and hydrodynamic conditions (i) on a flat medium and (ii) for a complex porous medium. For the second case, different regimes of biofilm growth are identified and are found to be related to the dimensionless parameters of the model, Damköhler and Péclet numbers and dimensionless shear stress. Finally, the impact of biofilm growth on the macroscopic properties of the porous medium is investigated and we discuss the unicity of the relationships between hydraulic conductivity and biofilm volume fraction.

  4. Design of a Photonic-Crystal Channel-Drop Filter Based on the Two-Dimensional Triangular-Lattice Hole Structure

    Institute of Scientific and Technical Information of China (English)

    Kyu; Hwan; Hwang; G.; Hugh; Song; Chanmook; Lim; Soan; Kim; Kyung-Won; Chun; Mahn; Yong; Park

    2003-01-01

    A channel-drop filter has been designed based on the two-dimensional triangular-lattice hole photonic-crystal structure, which consists of two line defects and two point defects, by a two-dimensional finite-difference time-domain simulation.

  5. A lattice based solution of the collisional Boltzmann equation with applications to microchannel flows

    Science.gov (United States)

    Green, B. I.; Vedula, Prakash

    2013-07-01

    An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework.

  6. Two-dimensional lattice solitons in polariton condensates with spin-orbit coupling

    CERN Document Server

    Kartashov, Yaroslav V

    2016-01-01

    We study two-dimensional fundamental and vortex solitons in polariton condensates with spin-orbit coupling and Zeeman splitting evolving in square arrays of microcavity pillars. Due to repulsive excitonic nonlinearity such states are encountered in finite gaps in the spectrum of the periodic array. Spin-orbit coupling between two polarization components stemming from TE-TM energy splitting of the cavity photons acting together with Zeeman splitting lifts the degeneracy between vortex solitons with opposite topological charges and makes their density profiles different for a fixed energy. This results in formation of four distinct families of vortex solitons with topological charges m=+-1, all of which can be stable. At the same time, only two stable families of fundamental gap solitons characterized by domination of different polarization components are encountered.

  7. Phase diagram of the two-dimensional O(3) model from dual lattice simulations

    CERN Document Server

    Bruckmann, Falk; Kloiber, Thomas; Sulejmanpasic, Tin

    2016-01-01

    We have simulated the asymptotically free two-dimensional O(3) model at nonzero chemical potential using the model's dual representation. We first demonstrate how the latter solves the sign (complex action) problem. The system displays a crossover at nonzero temperature, while at zero temperature it undergoes a quantum phase transition when mu reaches the particle mass (generated dynamically similar to QCD). The density follows a square root behavior universal for repulsive bosons in one spatial dimension. We have also measured the spin stiffness, known to be sensitive to the spatial correlation length, using different scaling trajectories to zero temperature and infinite size. It points to a dynamical critical exponent z=2. Comparisons to thermodynamic Bethe ansaetze are shown as well.

  8. Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension

    Science.gov (United States)

    Lin, Qian; Xiao, Meng; Yuan, Luqi; Fan, Shanhui

    2016-12-01

    Weyl points, as a signature of 3D topological states, have been extensively studied in condensed matter systems. Recently, the physics of Weyl points has also been explored in electromagnetic structures such as photonic crystals and metamaterials. These structures typically have complex three-dimensional geometries, which limits the potential for exploring Weyl point physics in on-chip integrated systems. Here we show that Weyl point physics emerges in a system of two-dimensional arrays of resonators undergoing dynamic modulation of refractive index. In addition, the phase of modulation can be controlled to explore Weyl points under different symmetries. Furthermore, unlike static structures, in this system the non-trivial topology of the Weyl point manifests in terms of surface state arcs in the synthetic space that exhibit one-way frequency conversion. Our system therefore provides a versatile platform to explore and exploit Weyl point physics on chip.

  9. Unconventional phases in quantum spin and pseudospin systems in two dimensional and three dimensional lattices

    Science.gov (United States)

    Xu, Cenke

    Several examples of quantum spin systems and pseudo spin systems have been studied, and unconventional states of matters and phase transitions have been realized in all these systems under consideration. In the p +/- ip superconductor Josephson lattice and the p--band cold atomic system trapped in optical lattices, novel phases which behave similarly to 1+1 dimensional systems are realized, despite the fact that the real physical systems are in two or three dimensional spaces. For instance, by employing a spin-wave analysis together with a new duality transformation, we establish the existence and stability of a novel gapless "critical phase", which we refer to as a "bond algebraic liquid". This novel critical phase is analogous to the 1+1 dimensional algebraic boson liquid phase. The reason for the novel physics is that there is a quasilocal gauge symmetry in the effective low energy Hamiltonian. In a spin-1 system on the kagome lattice, and a hard-core boson system on the honeycomb lattice, the low energy physics is controlled by two components of compact U(1) gauge symmetries that emerge at low energy. Making use of the confinement nature of the 2+1 dimensional compact gauge theories and the powerful duality between gauge theories and height field theories, the crystalline phase diagrams are studied for both systems, and the transitions to other phases are also considered. These phase diagrams might be accessible in strongly correlated materials, or atomic systems in optical lattices. A novel quantum ground state of matter is realized in a bosonic model on three dimensional fcc lattice with emergent low energy excitations. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the

  10. Fabrication of deep-profile Al-doped ZnO one- and two-dimensional lattices as plasmonic elements

    Science.gov (United States)

    Jensen, Flemming; Shkondin, Evgeniy; Takayama, Osamu; Larsen, Pernille V.; Mar, Mikkel D.; Malureanu, Radu; Lavrinenko, Andrei V.

    2016-09-01

    In this work, we report on fabrication of deep-profile one- and two-dimensional lattices made from Al-doped ZnO (AZO). AZO is considered as an alternative plasmonic material having the real part of the permittivity negative in the near infrared range. The exact position of the plasma frequency of AZO is doping concentration dependent, allowing for tuning possibilities. In addition, the thickness of the AZO film also affects its material properties. Physical vapor deposition techniques typically applied for AZO coating do not enable deep profiling of a plasmonic structure. Using the atomic layer deposition technique, a highly conformal deposition method, allows us to fabricate high-aspect ratio structures such as one-dimensional lattices with a period of 400 nm and size of the lamina of 200 nm in width and 3 μm in depth. Thus, our structures have an aspect ratio of 1:15 and are homogeneous on areas of 2×2 cm2 and more. We also produce two-dimensional arrays of circular nanopillars with similar dimensions. Instead of nanopillars hollow tubes with a wall thickness on demand from 20 nm up to a complete fill can be fabricated.

  11. General model for a entanglement-enhanced composed quantum game on a two-dimensional lattice

    CERN Document Server

    Miszczak, Jarosław Adam; Sładkowski, Jan

    2013-01-01

    We introduce a method of analyzing entanglement enhanced quantum games on regular lattices of agents. Our method is valid for setups with periodic and non-periodic boundary conditions. To demonstrate our approach we study two different types games, namely the prisoner's dilemma game and a cooperative Parrondo's game. In both cases we obtain results showing, that entanglement is a crucial resource necessary for the agents to achieve positive capital gain.

  12. Three-dimensional vortex solitons in quasi-two-dimensional lattices.

    Science.gov (United States)

    Leblond, Hervé; Malomed, Boris A; Mihalache, Dumitru

    2007-08-01

    We consider the three-dimensional (3D) Gross-Pitaevskii or nonlinear Schrödinger equation with a quasi-2D square-lattice potential (which corresponds to the optical lattice trapping a self-attractive Bose-Einstein condensate, or, in some approximation, to a photonic-crystal fiber, in terms of nonlinear optics). Stable 3D solitons, with embedded vorticity S=1 and 2, are found by means of the variational approximation and in a numerical form. They are built, basically, as sets of four fundamental solitons forming a rhombus, with phase shifts piS2 between adjacent sites, and an empty site in the middle. The results demonstrate two species of stable 3D solitons, which were not studied before, viz., localized vortices ("spinning light bullets," in terms of optics) with S>1 , and vortex solitons (with any S not equal 0 ) supported by a lattice in the 3D space. Typical scenarios of instability development (collapse or decay) of unstable localized vortices are identified too.

  13. Dispersion of guided modes in two-dimensional split ring lattices

    DEFF Research Database (Denmark)

    Hansen, Per Lunnemann; Koenderink, A. Femius

    2014-01-01

    -plane electric modes. Scatterers that have an in-plane electric and out-of-plane magnetic polarizability, but without intrinsic magnetoelectric coupling, result in two bands that are mixtures of the bands of electric-only and magnetic-only lattices. Thereby, bianisotropy through mutual coupling, in absence...... of building-block bianisotropy, is evident. Once strong bianisotropy is included in each building block, the Bloch modes become even more strongly magnetoelectric. Our results are important to understand spatial dispersion and bianisotropy of metasurface and metamaterial designs....

  14. Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities

    Science.gov (United States)

    El-Jallal, Said; Oudich, Mourad; Pennec, Yan; Djafari-Rouhani, Bahram; Laude, Vincent; Beugnot, Jean-Charles; Martínez, Alejandro; Escalante, José María; Makhoute, Abdelkader

    2013-11-01

    We theoretically investigate phonon-photon interaction in cavities created in a phoxonic crystal slab constituted by a two-dimensional (2D) square array of holes in a silicon membrane. The structure without defects provides 2D band gaps for both electromagnetic and elastic waves. We consider two types of cavities, namely, an L3 cavity (a row of three holes is removed) and a cross-shape cavity, which both possess highly confined phononic and photonic localized modes suitable for enhancing their interaction. In our theoretical study, we take into account two mechanisms that contribute to optomechanical interaction, namely, the photoelastic and the interface motion effects. We show that, depending on the considered pair of photonic and phononic modes, the two mechanisms can have similar or very different magnitudes, and their contributions can be either in or out of phase. We find out that only acoustic modes with a specific symmetry are allowed to couple with photonic cavity modes. The coupling strength is quantified by two different methods. In the first method, we compute a direct estimation of coupling rates by overlap integrals, while in the second one, we analyze the temporal modulation of the resonant photonic frequency by the phonon-induced acoustic vibrational motion during one acoustic period. Interestingly, we obtain high optomechanical interaction, with the coupling rate reaching more than 2.4 MHz for some specific phonon-photon pairs.

  15. Critical Behavior of Spatial Evolutionary Game with Altruistic to Spiteful Preferences on Two-Dimensional Lattices

    Science.gov (United States)

    Yang, Bo; Li, Xiao-Teng; Chen, Wei; Liu, Jian; Chen, Xiao-Song

    2016-10-01

    Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents v, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model. Supported by the National Natural Science Foundation of China under Grant Nos. 11121403 and 11504384

  16. First-order phase transitions in repulsive rigid k-mers on two-dimensional lattices

    Science.gov (United States)

    Pasinetti, P. M.; Romá, F.; Ramirez-Pastor, A. J.

    2012-02-01

    In a previous paper [F. Romá, A. J. Ramirez-Pastor, and J. L. Riccardo, Phys. Rev. B 72, 035444 (2005)], the critical behavior of repulsive rigid rods of length k (k-mers) on a square lattice at half coverage has been studied by using Monte Carlo (MC) simulations. The obtained results indicated that (1) the phase transition occurring in the system is a second-order phase transition for all adsorbate sizes k; and (2) the universality class of the transition changes from 2D Ising-type for monomers (k = 1) to an unknown universality class for k ≥ 2. In the present work, we revisit our previous results together with further numerical evidences, resulting from new extensive MC simulations based on an efficient exchange algorithm and using high-performance computational capabilities. In contrast to our previous conclusions (1) and (2), the new numerical calculations clearly support the occurrence of a first-order phase transition for k ≥ 2. In addition, a similar scenario was found for k-mers adsorbed on the triangular lattice at coverage k/(2k+1).

  17. From Discreteness to Continuity: Dislocation Equation for Two-Dimensional Triangular Lattice

    Institute of Scientific and Technical Information of China (English)

    WANG Shao-Feng

    2007-01-01

    @@ A systematic method from the discreteness to the continuity is presented for the dislocation equation of the triangular lattice. A modification of the Peierls equation has been derived strictly. The modified equation includes the higher order corrections of the discrete effect which are important for the core structure of dislocation. It is observed that the modified equation possesses a universal form which is model-independent except the factors.The factors, which depend on the detail of the model, are related to the derivatives of the kernel at its zero point in the wave-vector space. The results open a way to deal with the complicated models because what one needs to do is to investigate the behaviour near the zero point of the kernel in the wave-vector space instead of calculating the kernel completely.

  18. Spectroscopy of Dipolar Fermions in Layered Two-Dimensional and Three-Dimensional Lattices

    Science.gov (United States)

    2011-09-06

    term. We approximate Vαβ(j,ρ) by Vαβ(j,ρ) ≈ γαβU(j,ρ) (8) and Vsf by Vsf(j,ρ) ≈ ηU(j,ρ), (9) with U(j,ρ) = δ0j 1 ρ3 + A + (1 − δ0j ) 1 − 3( ( jdl )2 ρ2... jdl )2 ) [ρ2 + ( jdl )2]3/2 , (10) where γαβ = dααdββ/(4π 0), η = | ∫ dzw∗1(z)w2(z)|2d212/(4π 0), and dl is the lattice spacing, where A ∼ 3, with...3( ( jdl )2 ρ2+( jdl )2 ) [ρ2 + ( jdl )2]3/2 ] = 2π3/2 √ m β n (γ12 − γ11 + η) (thermal), (28) 033608-5 HAZZARD, GORSHKOV, AND REY PHYSICAL REVIEW A 84

  19. Numerical simulation of fluid flow of two rotating side-by-side circular cylinders by Lattice Boltzmann method

    Science.gov (United States)

    Nemati, Hasan; Sedighi, Kurosh; Farhadi, Mousa; Pirouz, Mohammad Mohammadi; Fattahi, Ehsan

    2010-03-01

    A numerical investigation of the two-dimensional laminar flow around side-by-side rotating circular cylinders using Lattice Boltzmann method is conducted. The effects of variation of rotational speed ratio β and different gap spacings g* at Reynolds number of 100 are studied. A various range of rotational speed ratio 0 ≤ β ≤ 2 for four different gap spacings of 3, 1.5, 0.7 and 0.2 are investigated. Flow conditions and its characteristics, such as lift and drag coefficients and Strouhal number, is studied. The results indicated that as β increases, the flow changes its condition from periodic to steady after a critical rotational speed. Results also indicated that variation of the gap spacing and rotational speed has significant effect on wake pattern. Wake pattern in turn has significant effect on the Strouhal number. Finally, the result is compared with experimental and other numerical data.

  20. Two-dimensional transition metal dichalcogenides with a hexagonal lattice: Room-temperature quantum spin Hall insulators

    Science.gov (United States)

    Ma, Yandong; Kou, Liangzhi; Li, Xiao; Dai, Ying; Heine, Thomas

    2016-01-01

    So far, several transition metal dichalcogenide (TMDC)-based two-dimensional (2D) topological insulators (TIs) have been discovered, all of them based on a tetragonal lattice. However, in 2D crystals, the hexagonal rather than the tetragonal symmetry is the most common motif. Here, based on first principles calculations, we propose a class of stable 2D TMDCs of composition MX2(M =Mo ,W ;X =S ,Se ,Te ) with a hexagonal lattice. They are all in the same stability range as other 2D TMDC allotropes that have been demonstrated experimentally, and they are identified to be practical 2D TIs with large band gaps ranging from 41 to 198 meV, making them suitable for applications at room temperature. Besides, in contrast to tetragonal 2D TMDCs, their hexagonal lattice will greatly facilitate the integration of theses novel TI state van der Waals crystals with other hexagonal or honeycomb materials and thus provide a route for 2D material-based devices for wider nanoelectronic and spintronic applications. The nontrivial band gaps of both WS e2 and WT e2 2D crystals are 198 meV, which are larger than that in any previously reported TMDC-based TIs. These large band gaps entirely stem from the strong spin orbit coupling strength within the d orbitals of Mo/W atoms near the Fermi level. Our findings broaden the scientific and technological impact of both 2D TIs and TMDCs.

  1. Second order bounce back boundary condition for the lattice Boltzmann fluid simulation

    Energy Technology Data Exchange (ETDEWEB)

    Kim, In Chan [Kunsan National Univ., Kunsan (Korea, Republic of)

    2000-01-01

    A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method.

  2. Application of Lattice Boltzmann Methods in Complex Mass Transfer Systems

    Science.gov (United States)

    Sun, Ning

    Lattice Boltzmann Method (LBM) is a novel computational fluid dynamics method that can easily handle complex and dynamic boundaries, couple local or interfacial interactions/reactions, and be easily parallelized allowing for simulation of large systems. While most of the current studies in LBM mainly focus on fluid dynamics, however, the inherent power of this method makes it an ideal candidate for the study of mass transfer systems involving complex/dynamic microstructures and local reactions. In this thesis, LBM is introduced to be an alternative computational method for the study of electrochemical energy storage systems (Li-ion batteries (LIBs) and electric double layer capacitors (EDLCs)) and transdermal drug design on mesoscopic scale. Based on traditional LBM, the following in-depth studies have been carried out: (1) For EDLCs, the simulation of diffuse charge dynamics is carried out for both the charge and the discharge processes on 2D systems of complex random electrode geometries (pure random, random spheres and random fibers). Steric effect of concentrated solutions is considered by using modified Poisson-Nernst-Plank (MPNP) equations and compared with regular Poisson-Nernst-Plank (PNP) systems. The effects of electrode microstructures (electrode density, electrode filler morphology, filler size, etc.) on the net charge distribution and charge/discharge time are studied in detail. The influence of applied potential during discharging process is also discussed. (2) For the study of dendrite formation on the anode of LIBs, it is shown that the Lattice Boltzmann model can capture all the experimentally observed features of microstructure evolution at the anode, from smooth to mossy to dendritic. The mechanism of dendrite formation process in mesoscopic scale is discussed in detail and compared with the traditional Sand's time theories. It shows that dendrite formation is closely related to the inhomogeneous reactively at the electrode-electrolyte interface

  3. Simulation of swimming of a flexible filament using the generalized lattice-spring lattice-Boltzmann method.

    Science.gov (United States)

    Wu, Tai-Hsien; Guo, Rurng-Sheng; He, Guo-Wei; Liu, Ying-Ming; Qi, Dewei

    2014-05-21

    A generalized lattice-spring lattice-Boltzmann model (GLLM) is introduced by adding a three-body force in the traditional lattice-spring model. This method is able to deal with bending deformation of flexible biological bodies in fluids. The interactions between elastic solids and fluid are treated with the immersed boundary-lattice Boltzmann method. GLLM is validated by comparing the present results with the existing theoretical and simulation results. As an application of GLLM, swimming of flagellum in fluid is simulated and propulsive force as a function of driven frequency and fluid structures at various Reynolds numbers 0.15-5.1 are presented in this paper. Copyright © 2014 Elsevier Ltd. All rights reserved.

  4. Lattice Boltzmann method for three-dimensional moving particles in a Newtonian fluid

    Institute of Scientific and Technical Information of China (English)

    Fang Hai-Ping; Chen Shi-Yi

    2004-01-01

    @@ A lattice Boltzmann method is developed to simulate three-dimensional solid particle motions in fluids. In the present model, a uniform grid is used and the exact spatial location of the physical boundary of the suspended particles is determined using an interpolation scheme. The numerical accuracy and efficiency of the proposed lattice Boltzmann method is demonstrated by simulating the sedimentation of a single sphere in a square cylinder. Highly accurate simulation results can be achieved with few meshes, compared with the previous lattice Boltzmann methods. The present method is expected to find applications on the flow systems with moving boundaries, such as the blood flow in distensible vessels, the particle-flow interaction and the solidification of alloys.

  5. Flow Simulation Around Cambered Airfoil by Using Conformal Mapping and Intermediate Domain in Lattice Boltzmann Method

    Science.gov (United States)

    Poozesh, Amin; Mirzaei, Masoud

    2017-01-01

    In this paper the developed interpolation lattice Boltzmann method is used for simulation of unsteady fluid flow. It combines the desirable features of the lattice Boltzmann and the Joukowski transformation methods. This approach has capability to simulate flow around curved boundary geometries such as airfoils in a body fitted grid system. Simulation of unsteady flow around a cambered airfoil in a non-uniform grid for the first time is considered to show the capability of this method for modeling of fluid flow around complex geometries and complicated long-term periodic flow phenomena. The developed solver is also coupled with a fast adaptive grid generator. In addition, the new approach retains all the advantages of the standard lattice Boltzmann method. The Strouhal number, the pressure, the drag and the lift coefficients obtained from the simulations agree well with classical computational fluid dynamics simulations. Numerical studies for various test cases illustrate the strength of this new approach.

  6. Simulation of Magnetorheological Fluids Based on Lattice Boltzmann Method with Double Meshes

    Directory of Open Access Journals (Sweden)

    Xinhua Liu

    2012-01-01

    Full Text Available In order to study the rheological characteristics of magnetorheological fluids, a novel approach based on the two-component Lattice Boltzmann method with double meshes was proposed, and the micro-scale structures of magnetorheological fluids in different strength magnetic fields were simulated. The framework composed of three steps for the simulation of magnetorheological fluids was addressed, and the double meshes method was elaborated. Moreover, the various internal and external forces acting on the magnetic particles were analyzed and calculated. The two-component Lattice Boltzmann model was set up, and the flowchart for the simulation of magnetorheological fluids based on the two-component Lattice Boltzmann method with double meshes was designed. Finally, a physics experiment was carried out, and the simulation examples were provided. The comparison results indicated that the proposed approach was feasible, efficient, and outperforming others.

  7. Entropic Lattice Boltzmann Method for Moving and Deforming Geometries in Three Dimensions

    CERN Document Server

    Dorschner, B; Karlin, I V

    2016-01-01

    Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work Dorschner et al. [11] as well as for three dimensional one-way coupled simulations of engine-type geometries in Dorschner et al. [12] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases including two-way coupling between fluid and structure, turbulence and deformable meshes. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil at a Reynolds number of Re = 40000 an...

  8. Pythagoras's theorem on a two-dimensional lattice from a 'natural' Dirac operator and Connes's distance formula

    Energy Technology Data Exchange (ETDEWEB)

    Dai Jian [Theory Group, Department of Physics, Peking University, Beijing (China)]. E-mail: jdai@mail.phy.pku.edu.cn; Song Xingchang [Theory Group, Department of Physics, Peking University, Beijing (China)]. E-mail: songxc@ibm320h.phy.pku.edu.cn

    2001-07-13

    One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as 'natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices. (author)

  9. Magnon Breakdown in a Two Dimensional Triangular Lattice Heisenberg Antiferromagnet of Multiferroic LuMnO3

    Science.gov (United States)

    Oh, Joosung; Le, Manh Duc; Jeong, Jaehong; Lee, Jung-hyun; Woo, Hyungje; Song, Wan-Young; Perring, T. G.; Buyers, W. J. L.; Cheong, S.-W.; Park, Je-Geun

    2013-12-01

    The breakdown of magnons, the quasiparticles of magnetic systems, has rarely been seen. By using an inelastic neutron scattering technique, we report the observation of spontaneous magnon decay in multiferroic LuMnO3, a simple two dimensional Heisenberg triangular lattice antiferromagnet, with large spin S=2. The origin of this rare phenomenon lies in the nonvanishing cubic interaction between magnons in the spin Hamiltonian arising from the noncollinear 120° spin structure. We observed all three key features of the nonlinear effects as theoretically predicted: a rotonlike minimum, a flat mode, and a linewidth broadening, in our inelastic neutron scattering measurements of single crystal LuMnO3. Our results show that quasiparticles in a system hitherto thought of as “classical” can indeed break down.

  10. Magnon breakdown in a two dimensional triangular lattice Heisenberg antiferromagnet of multiferroic LuMnO3.

    Science.gov (United States)

    Oh, Joosung; Le, Manh Duc; Jeong, Jaehong; Lee, Jung-hyun; Woo, Hyungje; Song, Wan-Young; Perring, T G; Buyers, W J L; Cheong, S-W; Park, Je-Geun

    2013-12-20

    The breakdown of magnons, the quasiparticles of magnetic systems, has rarely been seen. By using an inelastic neutron scattering technique, we report the observation of spontaneous magnon decay in multiferroic LuMnO3, a simple two dimensional Heisenberg triangular lattice antiferromagnet, with large spin S=2. The origin of this rare phenomenon lies in the nonvanishing cubic interaction between magnons in the spin Hamiltonian arising from the noncollinear 120° spin structure. We observed all three key features of the nonlinear effects as theoretically predicted: a rotonlike minimum, a flat mode, and a linewidth broadening, in our inelastic neutron scattering measurements of single crystal LuMnO3. Our results show that quasiparticles in a system hitherto thought of as "classical" can indeed break down.

  11. Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice

    CERN Document Server

    Ochiai, Tetsuyuki

    2016-01-01

    We show the presence of Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice. The Weyl points in the three-dimensional Brillouin zone and Fermi-arc surface states are clearly demonstrated in the quasienergy spectrum of the system in the Weyl phase. In addition, chiral surface states coexist in this phase. The Floquet-topological-insulator phase is characterized by the winding number of two in the reflection matrices of the semi-infinite system and resulting two gapless surface states in the quasienergy g ap of the bulk. The phase diagram of the system is derived in the two-parameter space of hopping S-matrices among the rings. We also discuss a possible optical realization of the system together with the introduction of synthetic gauge fields.

  12. Localization of a two-component Bose–Einstein condensate in a two-dimensional bichromatic optical lattice

    Energy Technology Data Exchange (ETDEWEB)

    Xi, Kui-Tian, E-mail: kuitianxi@gmail.com; Li, Jinbin, E-mail: jinbin@nuaa.edu.cn; Shi, Da-Ning, E-mail: shi@nuaa.edu.cn

    2014-03-01

    We consider a weakly interacting two-component Bose–Einstein condensate (BEC) in a two-dimensional (2D) quasi-periodic bichromatic optical lattice (BOL). The problem is studied by means of split-step Crank–Nicolson method. The effects of weak intra- and inter-component interactions on localization of a two-component BEC are investigated. It is shown that in the quasi-2D regime, due to the enhanced disorder, there is no symmetry breaking like that in the one-dimensional (1D) case under a sine-typed potential, while configurations of density profiles are also quite different from that in the 1D case. By modulating interactions, the interplay of disorder and weak repulsive or attractive interactions is studied in detail. The cases with sine- and cosine-typed potentials acting on components 1 and 2 respectively are also discussed.

  13. Identification of the dynamics of a two-dimensional grid structure using least square lattice filters. [for large space structures

    Science.gov (United States)

    Montgomery, R. C.; Sundararajan, N.

    1984-01-01

    It is doubtful whether the dynamics of large space structures (LSS) can be predicted well enough for control system design applications. Hence, dynamic modeling from on-orbit measurements followed by a modification of the control system is of interest, taking into account the utilization of adaptive control concepts. The present paper is concerned with the model determination phase of the adaptive control problem. Using spectral decoupling to determine mode shapes, mode frequency and damping data can be obtained with the aid of an equation error parameter identification method. This method employs a second-order auto-regressive moving average (ARMA) model to represent the natural mode amplitudes. The discussed procedure involves an extension of the application of the least square lattice filter in system identification to a nonintegral, two-dimensional grid structure made of overlapping bars.

  14. Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice

    Science.gov (United States)

    Ochiai, Tetsuyuki

    2016-10-01

    We show the presence of Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice. The Weyl points in the three-dimensional Brillouin zone and Fermi-arc surface states are clearly demonstrated in the quasienergy spectrum of the system in the Floquet-Weyl phase. In addition, chiral surface states coexist in this phase. The Floquet-topological-insulator phase is characterized by the winding number of two in the reflection matrices of the semi-infinite system and resulting two gapless surface states in the quasienergy gap of the bulk. The phase diagram of the system is derived in the two-parameter space of hopping S-matrices among the rings. We also discuss a possible optical realization of the system together with the introduction of synthetic gauge fields.

  15. A novel two-dimensional MgB6 crystal: metal-layer stabilized boron kagome lattice.

    Science.gov (United States)

    Xie, Sheng-Yi; Li, Xian-Bin; Tian, Wei Quan; Chen, Nian-Ke; Wang, Yeliang; Zhang, Shengbai; Sun, Hong-Bo

    2015-01-14

    Based on first-principles calculations, we designed for the first time a boron-kagome-based two-dimensional MgB6 crystal, in which two boron kagome layers sandwich a triangular magnesium layer. The two-dimensional lattice is metallic with several bands across the Fermi level, and among them a Dirac point appears at the K point of the first Brillouin zone. This metal-stabilized boron kagome system displays electron-phonon coupling, with a superconductivity critical transition temperature of 4.7 K, and thus it is another possible superconducting Mg-B compound besides MgB2. Furthermore, the proposed 2D MgB6 can also be used for hydrogen storage after decoration with Ca. Up to five H2 molecules can be attracted by one Ca with an average binding energy of 0.225 eV. The unique properties of 2D MgB6 will spur broad interest in nanoscience and technology.

  16. Numerical study of active control of mixing in electro-osmotic flows by temperature difference using lattice Boltzmann methods.

    Science.gov (United States)

    Alizadeh, A; Wang, J K; Pooyan, S; Mirbozorgi, S A; Wang, M

    2013-10-01

    In this paper, the effect of temperature difference between inlet flow and walls on the electro-osmotic flow through a two-dimensional microchannel is investigated. The main objective is to study the effect of temperature variations on the distribution of ions and consequently internal electric potential field, electric body force, and velocity fields in an electro-osmotic flow. We assume constant temperature and zeta potential on walls and use the mean temperature of each cross section to characterize the Boltzmann ion distribution across the channel. Based on these assumptions, the multiphysical transports are still able to be described by the classical Poisson-Boltzmann model. In this work, the Navier-Stokes equation for fluid flow, the Poisson-Boltzmann equation for ion distribution, and the energy equation for heat transfer are solved by a couple lattice Boltzmann method. The modeling results indicate that the temperature difference between walls and the inlet solution may lead to two symmetrical vortices at the entrance region of the microchannel which is appropriate for mixing enhancements. The advantage of this phenomenon for active control of mixing in electro-osmotic flow is the manageability of the vortex scale without extra efforts. For instance, the effective domain of this pattern could broaden by the following modulations: decreasing the external electric potential field, decreasing the electric double layer thickness, or increasing the temperature difference between inlet flow and walls. This work may provide a novel strategy for design or optimization of microsystems. Copyright © 2013 Elsevier Inc. All rights reserved.

  17. From Pore Scale to Turbulent Flow with the Unstructured Lattice Boltzmann Method

    DEFF Research Database (Denmark)

    Matin, Rastin

    Abstract: The lattice Boltzmann method is a class of methods in computational fluid dynamics for simulating fluid flow. Implementations on unstructured grids are particularly relevant for various engineering applications, where geometric flexibility or high resolution near a body or a wall...... is required. The main topic of this thesis is to further develop unstructured lattice Boltzmann methods for simulations of Newtonian fluid flow in three dimensions, in particular porous flow. Two methods are considered in this thesis based on the finite volume method and finite element method, respectively...

  18. A Lattice Boltzmann Model for Fluid-Solid Coupling Heat Transfer in Fractal Porous Media

    Institute of Scientific and Technical Information of China (English)

    CAI Jun; HUAI Xiu-Lan

    2009-01-01

    We report a lattice Boltzmann model that can be used to simulate fluid-solid coupling heat transfer in fractal porous media.A numerical simulation is conducted to investigate the temperature evolution under different ratios of thermal conductivity of solid matrix of porous media to that of fluid.The accordance of our simulation results with the solutions from the conventional CFD method indicates the feasibility and the reliability for the developed lattice Boltzmann model to reveal the phenomena and rules of fluid-solid coupling heat transfer in complex porous structures.

  19. Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method

    Science.gov (United States)

    Kang, Xiu-Ying; Liu, Da-He; Zhou, Jing; Jin, Yong-Juan

    2005-11-01

    The application of the lattice Boltzmann method to the large vessel bifurcation blood flow is investigated in a wide range of Reynolds numbers. The velocity, shear stress and pressure distributions at the bifurcation are presented in detail. The flow separation zones revealed with increase of Reynolds number are located in the areas of the daughter branches distal to the outer corners of the bifurcation where some deposition of particular blood components might occur to form arteriosclerosis. The results also demonstrate that the lattice Boltzmann method is adaptive to simulating the flow in larger vessels under a high Reynolds number.

  20. Lattice Boltzmann Model for The Volume-Averaged Navier-Stokes Equations

    CERN Document Server

    Zhang, Jingfeng; Ouyang, Jie

    2014-01-01

    A numerical method, based on discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged Navier-Stokes equations can be recovered from the lattice Boltzmann equation in the limit of small Mach number by the Chapman-Enskog analysis and Taylor expansion. Due to its advantages such as explicit solver and inherent parallelism, the method appears to be more competitive with traditional numerical techniques. Numerical simulations show that the proposed model can accurately reproduce both the linear and nonlinear drag effects of porosity in the fluid flow through porous media.

  1. A lattice Boltzmann method based on generalized polynomials and its application for electrons in metals

    Science.gov (United States)

    Coelho, Rodrigo C. V.; Ilha, Anderson S.; Doria, Mauro M.

    2016-10-01

    A lattice Boltzmann method is proposed based on the expansion of the equilibrium distribution function in powers of a new set of generalized orthonormal polynomials which are here presented. The new polynomials are orthonormal under the weight defined by the equilibrium distribution function itself. The D-dimensional Hermite polynomials is a sub-case of the present ones, associated to the particular weight of a Gaussian function. The proposed lattice Boltzmann method allows for the treatment of semi-classical fluids, such as electrons in metals under the Drude-Sommerfeld model, which is a particular case that we develop and validate by the Riemann problem.

  2. Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids.

    Science.gov (United States)

    Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping

    2016-02-01

    In this paper, we developed a unified lattice Boltzmann model (LBM) to simulate electroconvection in a dielectric liquid induced by unipolar charge injection. Instead of solving the complex set of coupled Navier-Stokes equations, the charge conservation equation, and the Poisson equation of electric potential, three consistent lattice Boltzmann equations are formulated. Numerical results are presented for both strong and weak injection regimes, and different scenarios for the onset and evolution of instability, bifurcation, and chaos are tracked. All LBM results are found to be highly consistent with the analytical solutions and other numerical work.

  3. A lattice Boltzmann coupled to finite volumes method for solving phase change problems

    Directory of Open Access Journals (Sweden)

    El Ganaoui Mohammed

    2009-01-01

    Full Text Available A numerical scheme coupling lattice Boltzmann and finite volumes approaches has been developed and qualified for test cases of phase change problems. In this work, the coupled partial differential equations of momentum conservation equations are solved with a non uniform lattice Boltzmann method. The energy equation is discretized by using a finite volume method. Simulations show the ability of this developed hybrid method to model the effects of convection, and to predict transfers. Benchmarking is operated both for conductive and convective situation dominating solid/liquid transition. Comparisons are achieved with respect to available analytical solutions and experimental results.

  4. Lattice Boltzmann equation calculation of internal, pressure-driven turbulent flow

    CERN Document Server

    Hammond, L A; Care, C M; Stevens, A

    2002-01-01

    We describe a mixing-length extension of the lattice Boltzmann approach to the simulation of an incompressible liquid in turbulent flow. The method uses a simple, adaptable, closure algorithm to bound the lattice Boltzmann fluid incorporating a law-of-the-wall. The test application, of an internal, pressure-driven and smooth duct flow, recovers correct velocity profiles for Reynolds number to 1.25 x 10 sup 5. In addition, the Reynolds number dependence of the friction factor in the smooth-wall branch of the Moody chart is correctly recovered. The method promises a straightforward extension to other curves of the Moody chart and to cylindrical pipe flow.

  5. Simple Navier’s slip boundary condition for the non-Newtonian Lattice Boltzmann fluid dynamics solver

    DEFF Research Database (Denmark)

    Svec, Oldrich; Skoček, Jan

    2013-01-01

    The ability of the Lattice Boltzmann method, as the fluid dynamics solver, to properly simulate macroscopic Navier’s slip boundary condition is investigated. An approximate equation relating the Lattice Boltzmann variable slip boundary condition with the macroscopic Navier’s slip boundary condition...

  6. Two-dimensional intra-band solitons in lattice potentials with local defects and self-focusing nonlinearity

    CERN Document Server

    Zeng, Jianhua

    2013-01-01

    It is commonly known that stable bright solitons in periodic potentials, which represent gratings in photonics/plasmonics, or optical lattices in quantum gases, exist either in the spectral semi-infinite gap (SIG) or in finite bandgaps. Using numerical methods, we demonstrate that, under the action of the cubic self-focusing nonlinearity, defects in the form of "holes" in two-dimensional (2D) lattices support continuous families of 2D solitons \\textit{embedded} into the first two Bloch bands of the respective linear spectrum, where solitons normally do not exist. The two families of the \\textit{embedded defect solitons} (EDSs) are found to be continuously linked by the branch of \\textit{gap defect solitons} (GDSs) populating the first finite bandgap. Further, the EDS branch traversing the first band links the GDS family with the branch of regular defect-supported solitons populating the SIG. Thus, we construct a continuous chain of regular, embedded, and gap-mode solitons ("superfamily") threading the entire ...

  7. Fluctuations in an ordered c (2×2) two-dimensional lattice-gas system with repulsive interactions

    Science.gov (United States)

    Argyrakis, P.; Chumak, A. A.; Maragakis, M.

    2005-06-01

    Fluctuations of the particle density in an ordered c(2×2) two-dimensional lattice-gas system are studied both analytically and by means of Monte Carlo simulations. The ordering is caused by a strong interparticle repulsive interaction resulting in the second order phase transition. The lattice of adsorption sites is divided into two sublattices (almost filled and almost empty sublattices) each of which contains a small number of structural “defects,” i.e., vacancies and excess particles. The relaxation of the correlation function of fluctuations turns out to be governed by two different functions. This peculiarity is to be contrasted with the traditional fluctuation theory which predicts the existence of a single damping constant, determined by the collective diffusion coefficient. A specific thesis of the proposed approach is that transport phenomena in ordered systems may be described in terms of both displacements and generation-recombination of structural defects. Accordingly, the correlation function of fluctuations depends on diffusion coefficients of two defect species as well as on the generation-recombination frequency. Our theory reduces to the usual one when fluctuations occur under local equilibrium conditions, i.e., for a sufficiently large size of probe areas and not too great values of interaction parameter. The analytical results agree well with those obtained in the Monte Carlo framework.

  8. Characterization of oscillatory instability in lid driven cavity flows using lattice Boltzmann method

    Science.gov (United States)

    Anupindi, Kameswararao; Lai, Weichen; Frankel, Steven

    2014-01-01

    In the present work, lattice Boltzmann method (LBM) is applied for simulating flow in a three-dimensional lid driven cubic and deep cavities. The developed code is first validated by simulating flow in a cubic lid driven cavity at 1000 and 12000 Reynolds numbers following which we study the effect of cavity depth on the steady-oscillatory transition Reynolds number in cavities with depth aspect ratio equal to 1, 2 and 3. Turbulence modeling is performed through large eddy simulation (LES) using the classical Smagorinsky sub-grid scale model to arrive at an optimum mesh size for all the simulations. The simulation results indicate that the first Hopf bifurcation Reynolds number correlates negatively with the cavity depth which is consistent with the observations from two-dimensional deep cavity flow data available in the literature. Cubic cavity displays a steady flow field up to a Reynolds number of 2100, a delayed anti-symmetry breaking oscillatory field at a Reynolds number of 2300, which further gets restored to a symmetry preserving oscillatory flow field at 2350. Deep cavities on the other hand only attain an anti-symmetry breaking flow field from a steady flow field upon increase of the Reynolds number in the range explored. As the present work involved performing a set of time-dependent calculations for several Reynolds numbers and cavity depths, the parallel performance of the code is evaluated a priori by running the code on up to 4096 cores. The computational time required for these runs shows a close to linear speed up over a wide range of processor counts depending on the problem size, which establishes the feasibility of performing a thorough search process such as the one presently undertaken. PMID:24587561

  9. Implementation of the Lattice Boltzmann Method on Heterogeneous Hardware and Platforms using OpenCL

    Directory of Open Access Journals (Sweden)

    TEKIC, P. M.

    2012-02-01

    Full Text Available The Lattice Boltzmann method (LBM has become an alternative method for computational fluid dynamics with a wide range of applications. Besides its numerical stability and accuracy, one of the major advantages of LBM is its relatively easy parallelization and, hence, it is especially well fitted to many-core hardware as graphics processing units (GPU. The majority of work concerning LBM implementation on GPU's has used the CUDA programming model, supported exclusively by NVIDIA. Recently, the open standard for parallel programming of heterogeneous systems (OpenCL has been introduced. OpenCL standard matures and is supported on processors from most vendors. In this paper, we make use of the OpenCL framework for the lattice Boltzmann method simulation, using hardware accelerators - AMD ATI Radeon GPU, AMD Dual-Core CPU and NVIDIA GeForce GPU's. Application has been developed using a combination of Java and OpenCL programming languages. Java bindings for OpenCL have been utilized. This approach offers the benefits of hardware and operating system independence, as well as speeding up of lattice Boltzmann algorithm. It has been showed that the developed lattice Boltzmann source code can be executed without modification on all of the used hardware accelerators. Performance results have been presented and compared for the hardware accelerators that have been utilized.

  10. Pseudopotential multi-relaxation-time lattice Boltzmann model for cavitation bubble collapse with high density ratio

    Science.gov (United States)

    Shan, Ming-Lei; Zhu, Chang-Ping; Yao, Cheng; Yin, Cheng; Jiang, Xiao-Yan

    2016-10-01

    The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In the present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q et al. [Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity. By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multi-relaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling. Project supported by the National Natural Science Foundation of China (Grant Nos. 11274092 and 1140040119) and the Natural Science Foundation of Jiangsu Province, China (Grant No. SBK2014043338).

  11. Parallel-plate rheometer calibration using oil and lattice Boltzmann simulation

    DEFF Research Database (Denmark)

    Ferraris, Chiara F; Geiker, Mette Rica; Martys, Nicos S.

    2007-01-01

    compute the viscosity. This paper presents a modified parallel plate rheometer, and proposes means of calibration using standard oils and numerical simulation of the flow. A lattice Boltzmann method was used to simulate the flow in the modified rheometer, thus using an accurate numerical solution in place...

  12. Calibrating the Shan-Chen lattice Boltzmann model for immiscible displacement in porous media

    DEFF Research Database (Denmark)

    Christensen, Britt Stenhøj Baun; Schaap, M.G.; Wildenschild, D.

    2006-01-01

    The lattice Boltzmann (LB) modeling technique is increasingly being applied in a variety of fields where computational fluid dynamics are investigated. In our field of interest, environmentally related flow processes in porous media, the use of the LB method is still not common. For the LB...

  13. Topology optimization of unsteady flow problems using the lattice Boltzmann method

    DEFF Research Database (Denmark)

    Nørgaard, Sebastian Arlund; Sigmund, Ole; Lazarov, Boyan Stefanov

    2016-01-01

    This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems...

  14. Calibration of modified parallel-plate rheometer through calibrated oil and lattice Boltzmann simulation

    DEFF Research Database (Denmark)

    Ferraris, Chiara F; Geiker, Mette Rica; Martys, Nicos S

    2007-01-01

    inapplicable here. This paper presents the analysis of a modified parallel plate rheometer for measuring cement mortar and propose a methodology for calibration using standard oils and numerical simulation of the flow. A lattice Boltzmann method was used to simulate the flow in the modified rheometer, thus...

  15. A note on the Lattice Boltzmann Method Beyond the Chapman Enskog Limits

    NARCIS (Netherlands)

    Sbragaglia, M.; Succi, S.

    2006-01-01

    A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the lattice Boltzmann method, can provide semi-quantitative results also

  16. Lattice Boltzmann simulation for the spiral waves in the excitable medium

    Institute of Scientific and Technical Information of China (English)

    GuangwuYAN; LiYUAN

    2000-01-01

    We propose lattice Boltzmann method for the spiral waves. Using Chapman-Enskog expansion and multiscales technique, we obtain equilibrium distribution functions of the model. As an example, we simulate the Selkov reactions with scratching mark, i. e. using a scratching mark pacemaker, obtained one classical spiral waves.

  17. A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects

    NARCIS (Netherlands)

    Kamali, M.R.

    2013-01-01

    The aim of the present research was to explore the promises and shift the limits of the numerical framework of lattice Boltzmann (LB) for studying the physics behind multi-component two-phase heterogeneous non-isothermal reactive flows under industrial conditions. An example of such an industrially

  18. Aerodynamic simulation of high-speed trains based on the Lattice Boltzmann Method (LBM)

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Aerodynamic simulation of high-speed trains has been carried out by using Lattice Boltzmann Method (LBM). Non-simplified train model was used and the number of space grids reached tens of millions. All results under different working conditions reflected the actual situation.

  19. A Lattice Boltzmann Approach to Multi-Phase Surface Reactions with Heat Effects

    NARCIS (Netherlands)

    Kamali, M.R.

    2013-01-01

    The aim of the present research was to explore the promises and shift the limits of the numerical framework of lattice Boltzmann (LB) for studying the physics behind multi-component two-phase heterogeneous non-isothermal reactive flows under industrial conditions. An example of such an industrially

  20. Modeling of flow of particles in a non-Newtonian fluid using lattice Boltzmann method

    DEFF Research Database (Denmark)

    Skocek, Jan; Svec, Oldrich; Spangenberg, Jon

    2011-01-01

    is necessary. In this contribution, the model at the scale of aggregates is introduced. The conventional lattice Boltzmann method for fluid flow is enriched with the immersed boundary method with direct forcing to simulate the flow of rigid particles in a non- Newtonian liquid. Basic ingredients of the model...

  1. Lattice-Boltzmann-based two-phase thermal model for simulating phase change

    NARCIS (Netherlands)

    Kamali, M.R.; Gillissen, J.J.J.; Van den Akker, H.E.A.; Sundaresan, S.

    2013-01-01

    A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A

  2. Alternative formulation to incorporate forcing terms in a lattice Boltzmann scheme with central moments

    Science.gov (United States)

    De Rosis, Alessandro

    2017-02-01

    Within the framework of the central-moment-based lattice Boltzmann method, we propose a strategy to account for external forces in two and three dimensions. Its numerical properties are evaluated against consolidated benchmark problems, highlighting very high accuracy and optimal convergence. Moreover, our derivations are light and intelligible.

  3. Lattice Boltzmann based multicomponent reactive transport model coupled with geochemical solver for scale simulations

    NARCIS (Netherlands)

    Patel, R.A.; Perko, J.; Jaques, D.; De Schutter, G.; Ye, G.; Van Breugel, K.

    2013-01-01

    A Lattice Boltzmann (LB) based reactive transport model intended to capture reactions and solid phase changes occurring at the pore scale is presented. The proposed approach uses LB method to compute multi component mass transport. The LB multi-component transport model is then coupled with the well

  4. Lattice-Boltzmann-based two-phase thermal model for simulating phase change

    NARCIS (Netherlands)

    Kamali, M.R.; Gillissen, J.J.J.; Van den Akker, H.E.A.; Sundaresan, S.

    2013-01-01

    A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A

  5. Elastic wave band gaps tuned by configuring radii of rods in two-dimensional phononic crystals with a hybrid square-like lattice

    Science.gov (United States)

    Liu, Rongqiang; Zhao, Haojiang; Zhang, Yingying; Guo, Honghwei; Deng, Zongquan

    2015-12-01

    The plane wave expansion (PWE) method is used to calculate the band gaps of two-dimensional (2D) phononic crystals (PCs) with a hybrid square-like (HSL) lattice. Band structures of both XY-mode and Z-mode are calculated. Numerical results show that the band gaps between any two bands could be maximized by altering the radius ratio of the inclusions at different positions. By comparing with square lattice and bathroom lattice, the HSL lattice is more efficient in creating larger gaps.

  6. Tunable spin wave dynamics in two-dimensional Ni{sub 80}Fe{sub 20} nanodot lattices by varying dot shape

    Energy Technology Data Exchange (ETDEWEB)

    Mahato, Bipul Kumar; Rana, Bivas; Kumar, Dheeraj; Barman, Saswati; Barman, Anjan, E-mail: abarman@bose.res.in [Thematic Unit of Excellence on Nanodevice Technology, Department of Condensed Matter Physics and Material Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098 (India); Sugimoto, Satoshi [Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581 (Japan); Otani, YoshiChika [Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581 (Japan); CEMS-RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan)

    2014-07-07

    We demonstrate tunable spin wave spectrum in two-dimensional Ni{sub 80}Fe{sub 20} nanodot lattices by varying dot shape. A single collective mode in elliptical dot lattices transforms into three distinct modes for the half-elliptical, rectangular, and diamond dot lattices, albeit with different peak frequencies and intensities. A drastic change is observed for the triangular dots, where eight modes covering a broad band are observed. Using micromagnetic simulations, we characterized the modes as different localized, extended, and quantized modes, whose frequencies and spatial profiles are determined by a combination of internal field profiles within the nanodots and the stray magnetic field within the lattice.

  7. A Stochastic Sharpening Method for the Propagation of Phase Boundaries in Multiphase Lattice Boltzmann Simulations

    KAUST Repository

    Reis, T.

    2010-09-06

    Existing lattice Boltzmann models that have been designed to recover a macroscopic description of immiscible liquids are only able to make predictions that are quantitatively correct when the interface that exists between the fluids is smeared over several nodal points. Attempts to minimise the thickness of this interface generally leads to a phenomenon known as lattice pinning, the precise cause of which is not well understood. This spurious behaviour is remarkably similar to that associated with the numerical simulation of hyperbolic partial differential equations coupled with a stiff source term. Inspired by the seminal work in this field, we derive a lattice Boltzmann implementation of a model equation used to investigate such peculiarities. This implementation is extended to different spacial discretisations in one and two dimensions. We shown that the inclusion of a quasi-random threshold dramatically delays the onset of pinning and facetting.

  8. Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

    CERN Document Server

    Farhat, Hassan; Kondaraju, Sasidhar

    2014-01-01

    Colloids are ubiquitous in the food, medical, cosmetics, polymers, water purification, and pharmaceutical industries. The thermal, mechanical, and storage properties of colloids are highly dependent on their interface morphology and their rheological behavior. Numerical methods provide a convenient and reliable tool for the study of colloids. Accelerated Lattice Boltzmann Model for Colloidal Suspensions introduce the main building-blocks for an improved lattice Boltzmann–based numerical tool designed for the study of colloidal rheology and interface morphology. This book also covers the migrating multi-block used to simulate single component, multi-component, multiphase, and single component multiphase flows and their validation by experimental, numerical, and analytical solutions.   Among other topics discussed are the hybrid lattice Boltzmann method (LBM) for surfactant-covered droplets; biological suspensions such as blood; used in conjunction with the suppression of coalescence for investigating the...

  9. Synthetic gauge field and pseudospin-orbit interaction in a stacked two-dimensional ring-network lattice

    Science.gov (United States)

    Ochiai, Tetsuyuki

    2017-02-01

    We study the effects of a synthetic gauge field and pseudospin-orbit interaction in a stacked two-dimensional ring-network model. The model was introduced to simulate light propagation in the corresponding ring-resonator lattice, and is thus completely bosonic. Without these two items, the model exhibits Floquet-Weyl and Floquet-topological-insulator phases with topologically gapless and gapped band structures, respectively. The synthetic magnetic field implemented in the model results in a three-dimensional Hofstadter-butterfly-type spectrum in a photonic platform. The resulting gaps are characterized by the winding number of relevant S-matrices together with the Chern number of the bulk bands. The pseudospin-orbit interaction is defined as the mixing term between two pseudospin degrees of freedom in the rings, namely, the clockwise and counter-clockwise modes. It destroys the Floquet-topological-insulator phases, while the Floquet-Weyl phase with multiple Weyl points can be preserved by breaking the space-inversion symmetry. Implementing both the synthetic gauge field and pseudospin-orbit interaction requires a certain nonreciprocity.

  10. Phase transitions in a two-dimensional antiferromagnetic Potts model on a triangular lattice with next-nearest neighbor interactions

    Energy Technology Data Exchange (ETDEWEB)

    Babaev, A. B., E-mail: b-albert78@mail.ru; Magomedov, M. A.; Murtazaev, A. K. [Russian Academy of Sciences, Amirkhanov Institute of Physics, Dagestan Scientific Center (Russian Federation); Kassan-Ogly, F. A.; Proshkin, A. I. [Russian Academy of Sciences, Institute of Metal Physics, Ural Branch (Russian Federation)

    2016-02-15

    Phase transitions (PTs) and frustrations in two-dimensional structures described by a three-vertex antiferromagnetic Potts model on a triangular lattice are investigated by the Monte Carlo method with regard to nearest and next-nearest neighbors with interaction constants J{sub 1} and J{sub 2}, respectively. PTs in these models are analyzed for the ratio r = J{sub 2}/J{sub 1} of next-nearest to nearest exchange interaction constants in the interval |r| = 0–1.0. On the basis of the analysis of the low-temperature entropy, the density of states function of the system, and the fourth-order Binder cumulants, it is shown that a Potts model with interaction constants J{sub 1} < 0 and J{sub 2} < 0 exhibits a first-order PT in the range of 0 ⩽ r < 0.2, whereas, in the interval 0.2 ⩽ r ⩽ 1.0, frustrations arise in the system. At the same time, for J{sub 1} > 0 and J{sub 2} < 0, frustrations arise in the range 0.5 < |r| < 1.0, while, in the interval 0 ⩽ |r| ⩽ 1/3, the model exhibits a second-order PT.

  11. Lattice-Boltzmann simulation of laser interaction with weakly ionized helium plasmas.

    Science.gov (United States)

    Li, Huayu; Ki, Hyungson

    2010-07-01

    This paper presents a lattice Boltzmann method for laser interaction with weakly ionized plasmas considering electron impact ionization and three-body recombination. To simulate with physical properties of plasmas, the authors' previous work on the rescaling of variables is employed and the electromagnetic fields are calculated from the Maxwell equations by using the finite-difference time-domain method. To calculate temperature fields, energy equations are derived separately from the Boltzmann equations. In this way, we attempt to solve the full governing equations for plasma dynamics. With the developed model, the continuous-wave CO2 laser interaction with helium is simulated successfully.

  12. Partition function for the two-dimensional square lattice Ising model in a non-zero magnetic field-A heuristic analysis

    OpenAIRE

    2008-01-01

    The exact partition function of the two-dimensional nearest neighbour Ising model pertaining to square lattices is derived for N sites in the case of a non-vanishing magnetic field.When the magnetic field is zero,the partition functions estimated from the present analysis are identical with those arising from Onsager's exact solution.

  13. Soliton assisted control of source to drain electron transport along natural channels - crystallographic axes - in two-dimensional triangular crystal lattices

    Science.gov (United States)

    Chetverikov, A. P.; Ebeling, W.; Velarde, M. G.

    2016-09-01

    We present computational evidence of the possibility of fast, supersonic or subsonic, nearly loss-free ballistic-like transport of electrons bound to lattice solitons (a form of electron surfing on acoustic waves) along crystallographic axes in two-dimensional anharmonic crystal lattices. First we study the structural changes a soliton creates in the lattice and the time lapse of recovery of the lattice. Then we study the behavior of one electron in the polarization field of one and two solitons with crossing pathways with suitably monitored delay. We show how an electron surfing on a lattice soliton may switch to surf on the second soliton and hence changing accordingly the direction of its path. Finally we discuss the possibility to control the way an excess electron proceeds from a source at a border of the lattice to a selected drain at another border by following appropriate straight pathways on crystallographic axes.

  14. Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

    Science.gov (United States)

    Li, Q; He, Y L; Wang, Y; Tao, W Q

    2007-11-01

    A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

  15. Quantum and thermal phase transitions in a bosonic atom-molecule mixture in a two-dimensional optical lattice

    Science.gov (United States)

    de Forges de Parny, L.; Rousseau, V. G.

    2017-01-01

    We study the ground state and the thermal phase diagram of a two-species Bose-Hubbard model, with U(1 ) ×Z2 symmetry, describing atoms and molecules on a two-dimensional optical lattice interacting via a Feshbach resonance. Using quantum Monte Carlo simulations and mean-field theory, we show that the conversion between the two species, coherently coupling the atomic and molecular states, has a crucial impact on the Mott-superfluid transition and stabilizes an insulating phase with a gap controlled by the conversion term—the Feshbach insulator—instead of a standard Mott-insulating phase. Depending on the detuning between atoms and molecules, this model exhibits three phases: the Feshbach insulator, a molecular condensate coexisting with noncondensed atoms, and a mixed atomic-molecular condensate. Employing finite-size scaling analysis, we observe three-dimensional (3D) X Y (3D Ising) transition when U(1 ) (Z2) symmetry is broken, whereas the transition is first order when both U(1 ) and Z2 symmetries are spontaneously broken. The finite-temperature phase diagram is also discussed. The thermal disappearance of the molecular superfluid leads to a Berezinskii-Kosterlitz-Thouless transition with unusual universal jump in the superfluid density. The loss of the quasi-long-range coherence of the mixed atomic and molecular superfluid is more subtle since only atoms exhibit conventional Berezinskii-Kosterlitz-Thouless criticality. We also observe a signal compatible with a classical first-order transition between the mixed superfluid and the normal Bose liquid at low temperature.

  16. Lattice-Boltzmann simulation methods for chemically reactive systems in the micro area; Lattice Boltzmann Simulationsmethoden fuer chemisch reaktive Systeme im Microbereich - Schlussbericht

    Energy Technology Data Exchange (ETDEWEB)

    Karlin, I.; Frouzakis, Ch.; Boulouchos, K.

    2007-07-01

    This final report for the Swiss Federal Office of Energy (SFOE) reports on work done in 2007 at the Swiss Federal Institute of Technology ETH in Zurich on simulation methods for chemically reactive systems at the micrometer scale. The Lattice-Boltzmann method using lattice models is examined and the results obtained are discussed. A three-dimensional thermal model was developed and used to analyse flows with considerable temperature and density variations. The model was also used for the analysis of flows in diluted gases. A method for the reduction of complex reaction mechanisms was developed and tested for future combustion applications. 30 publications are noted and new possibilities for the analysis of flows in micro-channels and porous media - as used in reformers, catalyzers and fuel cells - are discussed.

  17. Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework

    KAUST Repository

    Neumann, Philipp

    2012-01-01

    We present simulation results of flows in the finite Knudsen range, which is in the slip and transition flow regime. Our implementations are based on the Lattice Boltzmann method and are accomplished within the Peano framework. We validate our code by solving two- and three-dimensional channel flow problems and compare our results with respective experiments from other research groups. We further apply our Lattice Boltzmann solver to the geometrical setup of a microreactor consisting of differently sized channels and a reactor chamber. Here, we apply static adaptive grids to fur-ther reduce computational costs. We further investigate the influence of using a simple BGK collision kernel in coarse grid regions which are further away from the slip boundaries. Our results are in good agreement with theory and non-adaptive simulations, demonstrating the validity and the capabilities of our adaptive simulation software for flow problems at finite Knudsen numbers.

  18. Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers

    KAUST Repository

    Atanasov, Atanas

    2016-10-17

    We present an Anderson acceleration-based approach to spatially couple three-dimensional Lattice Boltzmann and Navier–Stokes (LBNS) flow simulations. This allows to locally exploit the computational features of both fluid flow solver approaches to the fullest extent and yields enhanced control to match the LB and NS degrees of freedom within the LBNS overlap layer. Designed for parallel Schwarz coupling, the Anderson acceleration allows for the simultaneous execution of both Lattice Boltzmann and Navier–Stokes solver. We detail our coupling methodology, validate it, and study convergence and accuracy of the Anderson accelerated coupling, considering three steady-state scenarios: plane channel flow, flow around a sphere and channel flow across a porous structure. We find that the Anderson accelerated coupling yields a speed-up (in terms of iteration steps) of up to 40% in the considered scenarios, compared to strictly sequential Schwarz coupling.

  19. Lattice Boltzmann model for collisionless electrostatic drift wave turbulence obeying Charney-Hasegawa-Mima dynamics

    CERN Document Server

    Held, M

    2015-01-01

    A lattice Boltzmann method (LBM) approach to the Charney-Hasegawa-Mima (CHM) model for adiabatic drift wave turbulence in magnetised plasmas, is implemented. The CHM-LBM model contains a barotropic equation of state for the potential, a force term including a cross-product analogous to the Coriolis force in quasigeostrophic models, and a density gradient source term. Expansion of the resulting lattice Boltzmann model equations leads to cold-ion fluid continuity and momentum equations, which resemble CHM dynamics under drift ordering. The resulting numerical solutions of standard test cases (monopole propagation, stable drift modes and decaying turbulence) are compared to results obtained by a conventional finite difference scheme that directly discretizes the CHM equation. The LB scheme resembles characteristic CHM dynamics apart from an additional shear in the density gradient direction. The occuring shear reduces with the drift ratio and is ascribed to the compressible limit of the underlying LBM.

  20. Evaluation of the Finite Element Lattice Boltzmann Method for Binary Fluid Flows

    CERN Document Server

    Matin, Rastin; Hernandez-Garcia, Anier; Mathiesen, Joachim

    2016-01-01

    In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex boundaries. The current work combines characteristic-based integration of the streaming step with the free-energy based multiphase model by Lee et. al. [Journal of Computational Physics, 206 (1), 2005 ]. This allows for simulation time steps more than an order of magnitude larger than the relaxation time. Unlike previous work by Wardle et. al. [Computers and Mathematics with Applications, 65 (2), 2013 ] that integrated intermolecular forcing terms in the advection term, the current scheme applies collision and forcing terms locally for a simpler finite element formulation. A series of thorough benchmark studies reveal that this does not compromise stability and that the scheme is able to accurately simulate flows at large density and viscosity contrasts.

  1. Lattice boltzmann study on the contact angle and contact line dynamics of liquid-vapor interfaces.

    Science.gov (United States)

    Zhang, Junfeng; Kwok, Daniel Y

    2004-09-14

    The moving contact line problem of liquid-vapor interfaces was studied using a mean-field free-energy lattice Boltzmann method recently proposed [Phys. Rev. E 2004, 69, 032602]. We have examined the static and dynamic interfacial behaviors by means of the bubble and capillary wave tests and found that both the Laplace equation of capillarity and the dispersion relation were satisfied. Dynamic contact angles followed the general trend of contact line velocity observed experimentally and can be described by Blake's theory. The velocity fields near the interface were also obtained and are in good agreement with fluid mechanics and molecular dynamics studies. Our simulations demonstrated that incorporating interfacial effects into the lattice Boltzmann model can be a valuable and powerful alternative in interfacial studies.

  2. Thermal Lattice Boltzmann Simulations for Vapor-Liquid Two-Phase Flows in Two Dimensions

    Science.gov (United States)

    Wei, Yikun; Qian, Yuehong

    2011-11-01

    A lattice Boltzmann model with double distribution functions is developed to simulate thermal vapor-liquid two-phase flows. In this model, the so-called mesoscopic inter-particle pseudo-potential for the single component multi-phase lattice Boltzmann model is used to simulate the fluid dynamics and the internal energy field is simulated by using a energy distribution function. Theoretical results for large-scale dynamics including the internal energy equation can be derived and numerical results for the coexistence curve of vapor-liquid systems are in good agreement with the theoretical predictions. It is shown from numerical simulations that the model has the ability to mimic phase transitions, bubbly flows and slugging flows. This research is support in part by the grant of Education Ministry of China IRT0844 and the grant of Shanghai CST 11XD1402300.

  3. Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9*

    Directory of Open Access Journals (Sweden)

    Graille Benjamin

    2012-04-01

    Full Text Available In this paper, we recall the linear version of the lattice Boltzmann schemes in the framework proposed by d’Humières. According to the equivalent equations we introduce a definition for a scheme to be isotropic at some order. This definition is chosen such that the equivalent equations are preserved by orthogonal transformations of the frame. The property of isotropy can be read through a group operation and then implies a sequence of relations on relaxation times and equilibrium states that characterizes a lattice Boltzmann scheme. We propose a method to select the parameters of the scheme according to the desired order of isotropy. Applying it to the D2Q9 scheme yields the classical constraints for the first and second orders and some non classical for the third and fourth orders.

  4. Lattice Boltzmann model for incompressible axisymmetric thermal flows through porous media.

    Science.gov (United States)

    Grissa, Kods; Chaabane, Raoudha; Lataoui, Zied; Benselama, Adel; Bertin, Yves; Jemni, Abdelmajid

    2016-10-01

    The present work proposes a simple lattice Boltzmann model for incompressible axisymmetric thermal flows through porous media. By incorporating forces and source terms into the lattice Boltzmann equation, the incompressible Navier-Stokes equations are recovered through the Chapman-Enskog expansion. It is found that the added terms are just the extra terms in the governing equations for the axisymmetric thermal flows through porous media compared with the Navier-Stokes equations. Four numerical simulations are performed to validate this model. Good agreement is obtained between the present work and the analytic solutions and/or the results of previous studies. This proves its efficacy and simplicity regarding other methods. Also, this approach provides guidance for problems with more physical phenomena and complicated force forms.

  5. Comparison of lattice-Boltzmann and brownian-dynamics simulations of polymer migration in confined flows.

    Science.gov (United States)

    Kekre, Rahul; Butler, Jason E; Ladd, Anthony J C

    2010-07-01

    This paper compares results from lattice-Boltzmann and brownian-dynamics simulations of polymer migration in confined flows bounded by planar walls. We have considered both a uniform shear rate and a constant pressure gradient. Lattice-Boltzmann simulations of the center-of-mass distribution agree quantitatively with brownian-dynamics results, contradicting previously published results. The mean end-to-end distance of the extended polymer is more sensitive to grid resolution Δx and time-step Δt. Nevertheless, for sufficiently small Δx and Δt, convergent results for the polymer stretch are obtained which agree with brownian dynamics within statistical uncertainties. The brownian-dynamics simulations incorporate a mobility matrix for a confined polymer that is both symmetric and positive definite for all physically accessible configurations.

  6. Magnetic nanoparticles in fluid environment: combining molecular dynamics and Lattice-Boltzmann

    Science.gov (United States)

    Melenev, Petr

    2017-06-01

    Hydrodynamic interactions between magnetic nanoparticles suspended in the Newtonian liquid are accounted for using a combination of the lattice Boltzmann method and molecular dynamics simulations. Nanoparticle is modelled by the system of molecular dynamics material points (which form structure resembles raspberry) coupled to the lattice Boltzmann fluid. The hydrodynamic coupling between the colloids is studied by simulations of the thermo-induced rotational diffusion of two raspberry objects. It was found that for the considered range of model parameters the approaching of the raspberries leads to slight retard of the relaxation process. The presence of the weak magnetic dipolar interaction between the objects leads to modest decrease of the relaxation time and the extent of the acceleration of the diffusion is intensified along with magnetic forces.

  7. Simulation of Rarefied Gas Flow in Slip and Transitional Regimes by the Lattice Boltzmann Method

    Directory of Open Access Journals (Sweden)

    S Abdullah

    2010-07-01

    Full Text Available In this paper, a lattice Boltzmann method (LBM based simulation of microscale flow has been carried out, for various values of Knudsen number. The details in determining the parameters critical for LBM applications in microscale flow are provided. Pressure distributions in the slip flow regime are compared with the analytical solution based on the Navier-Stokes equationwith slip-velocity boundary condition. Satisfactory agreements have been achieved. Simulations are then extended to transition regime (Kn = 0.15 and compared with the same analytical solution. The results show some deviation from the analytical solution due to the breakdown of continuum assumption. From this study, we may conclude that the lattice Boltzmann method is an efficient approach for simulation of microscale flow.

  8. Study of acoustic bubble cluster dynamics using a lattice Boltzmann model

    Institute of Scientific and Technical Information of China (English)

    Mahdi Daemi; Mohammad Taeibi-Rahni; Hamidreza Massah

    2015-01-01

    Search for the development of a reliable mathematical model for understanding bubble dynamics behavior is an ongoing endeavor. A long list of complex phenomena underlies physics of this problem. In the past decades, the lattice Boltzmann (LB) method has emerged as a promising tool to address such complexities. In this regard, we have applied a 121-velocity multiphase lattice Boltzmann model (LBM) to an asymmetric cluster of bubbles in an acoustic field. A problem as a benchmark is studied to check the consistency and applicability of the model. The problem of interest is to study the deformation and coalescence phenomena in bubble cluster dynamics, and the screening effect on an acoustic multi-bubble medium. It has been observed that the LB model is able to simulate the combination of the three aforementioned phenomena for a bubble cluster as a whole and for every individual bubble in the cluster.

  9. Investigation of Resistivity of Saturated Porous Media with Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    YUE Wen-Zheng; TAO Guo; ZHU Ke-Qin

    2004-01-01

    The lattice Boltzmann method is employed to study the electrical transport properties of saturated porous media.Electrical current flow through the porous media is simulated and the relationship between resistivity index and water saturation is derived. It is found that this kind of relation is not a straight line as described by the Archie equation with the parameter n being a constant in a log-log scale. A new equation is thus developed to formulate this relation with n being a function of porosity and water saturation. The comparisons between the results by lattice Boltzmann and by the laboratory experiments on rock samples demonstrate that this numerical method can provide an alternative way for the expensive laboratory experiments to investigate the electrical transport properties of saturated porous media and can be used to explore micro mechanisms more conveniently.

  10. Numerical modeling of microchannel gas flows in the transition flow regime via cascaded lattice Boltzmann method

    CERN Document Server

    Liu, Qing

    2016-01-01

    As a numerically accurate and computationally efficient mesoscopic numerical method, the lattice Boltzmann (LB) method has achieved great success in simulating microscale rarefied gas flows. In this paper, an LB method based on the cascaded collision operator is presented to simulate microchannel gas flows in the transition flow regime. The Bosanquet-type effective viscosity is incorporated into the cascaded lattice Boltzmann (CLB) method to account for the rarefaction effects. In order to gain accurate simulations and match the Bosanquet-type effective viscosity, the combined bounce-back/specular-reflection scheme with a modified second-order slip boundary condition is employed in the CLB method. The present method is applied to study gas flow in a microchannel with periodic boundary condition and gas flow in a long microchannel with pressure boundary condition over a wide range of Knudsen numbers. The predicted results, including the velocity profile, the mass flow rate, and the non-linear pressure deviatio...

  11. Momentum-exchange method in lattice Boltzmann simulations of particle-fluid interactions.

    Science.gov (United States)

    Chen, Yu; Cai, Qingdong; Xia, Zhenhua; Wang, Moran; Chen, Shiyi

    2013-07-01

    The momentum exchange method has been widely used in lattice Boltzmann simulations for particle-fluid interactions. Although proved accurate for still walls, it will result in inaccurate particle dynamics without corrections. In this work, we reveal the physical cause of this problem and find that the initial momentum of the net mass transfer through boundaries in the moving-boundary treatment is not counted in the conventional momentum exchange method. A corrected momentum exchange method is then proposed by taking into account the initial momentum of the net mass transfer at each time step. The method is easy to implement with negligible extra computation cost. Direct numerical simulations of a single elliptical particle sedimentation are carried out to evaluate the accuracy for our method as well as other lattice Boltzmann-based methods by comparisons with the results of the finite element method. A shear flow test shows that our method is Galilean invariant.

  12. Steady State Convergence Acceleration of the Generalized Lattice Boltzmann Equation with Forcing Term through Preconditioning

    CERN Document Server

    Premnath, Kannan N; Banerjee, Sanjoy

    2008-01-01

    Several applications exist in which lattice Boltzmann methods (LBM) are used to compute stationary states of fluid motions, particularly those driven or modulated by external forces. Standard LBM, being explicit time-marching in nature, requires a long time to attain steady state convergence, particularly at low Mach numbers due to the disparity in characteristic speeds of propagation of different quantities. In this paper, we present a preconditioned generalized lattice Boltzmann equation (GLBE) with forcing term to accelerate steady state convergence to flows driven by external forces. The use of multiple relaxation times in the GLBE allows enhancement of the numerical stability. Particular focus is given in preconditioning external forces, which can be spatially and temporally dependent. In particular, correct forms of moment-projections of source/forcing terms are derived such that they recover preconditioned Navier-Stokes equations with non-uniform external forces. As an illustration, we solve an extende...

  13. Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

    Science.gov (United States)

    Rubinstein, Robert; Luo, Li-Shi

    2007-01-01

    In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

  14. Dynamically adaptive Lattice Boltzmann simulation of shallow water flows with the Peano framework

    KAUST Repository

    Neumann, Philipp

    2015-09-01

    © 2014 Elsevier Inc. All rights reserved. We present a dynamically adaptive Lattice Boltzmann (LB) implementation for solving the shallow water equations (SWEs). Our implementation extends an existing LB component of the Peano framework. We revise the modular design with respect to the incorporation of new simulation aspects and LB models. The basic SWE-LB implementation is validated in different breaking dam scenarios. We further provide a numerical study on stability of the MRT collision operator used in our simulations.

  15. Entropic multirelaxation-time lattice Boltzmann method for moving and deforming geometries in three dimensions.

    Science.gov (United States)

    Dorschner, B; Chikatamarla, S S; Karlin, I V

    2017-06-01

    Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work [B. Dorschner, S. Chikatamarla, F. Bösch, and I. Karlin, J. Comput. Phys. 295, 340 (2015)JCTPAH0021-999110.1016/j.jcp.2015.04.017] as well as for three-dimensional one-way coupled simulations of engine-type geometries in B. Dorschner, F. Bösch, S. Chikatamarla, K. Boulouchos, and I. Karlin [J. Fluid Mech. 801, 623 (2016)JFLSA70022-112010.1017/jfm.2016.448] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases, including two-way coupling between fluid and structure and then turbulence and deforming geometries. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil in the transitional regime at a Reynolds number of Re=40000 and, finally, to access the model's performance for deforming geometries, we conduct a two-way coupled simulation of a self-propelled anguilliform swimmer. These simulations confirm the viability of the new fluid-structure interaction lattice Boltzmann algorithm to simulate flows of engineering relevance.

  16. Lattice-Boltzmann-based two-phase thermal model for simulating phase change

    OpenAIRE

    Kamali, M.R.; Gillissen, J.J.J.; Van den Akker, H.E.A.; Sundaresan, S.

    2013-01-01

    A lattice Boltzmann (LB) method is presented for solving the energy conservation equation in two phases when the phase change effects are included in the model. This approach employs multiple distribution functions, one for a pseudotemperature scalar variable and the rest for the various species. A nonideal equation of state (EOS) is introduced by using a pseudopotential LB model. The evolution equation for the pseudotemperature variable is constructed in such a manner that in the continuum l...

  17. Entropic multirelaxation-time lattice Boltzmann method for moving and deforming geometries in three dimensions

    Science.gov (United States)

    Dorschner, B.; Chikatamarla, S. S.; Karlin, I. V.

    2017-06-01

    Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work [B. Dorschner, S. Chikatamarla, F. Bösch, and I. Karlin, J. Comput. Phys. 295, 340 (2015), 10.1016/j.jcp.2015.04.017] as well as for three-dimensional one-way coupled simulations of engine-type geometries in B . Dorschner, F. Bösch, S. Chikatamarla, K. Boulouchos, and I. Karlin [J. Fluid Mech. 801, 623 (2016), 10.1017/jfm.2016.448] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases, including two-way coupling between fluid and structure and then turbulence and deforming geometries. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil in the transitional regime at a Reynolds number of Re =40 000 and, finally, to access the model's performance for deforming geometries, we conduct a two-way coupled simulation of a self-propelled anguilliform swimmer. These simulations confirm the viability of the new fluid-structure interaction lattice Boltzmann algorithm to simulate flows of engineering relevance.

  18. A unified lattice Boltzmann model for some nonlinear partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Chai Zhenhua [State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074 (China); Shi Baochang [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)], E-mail: sbchust@126.com; Zheng Lin [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)

    2008-05-15

    In this paper, a unified and novel lattice Boltzmann model is proposed for solving nonlinear partial differential equation that has the form DU{sub t} + {alpha}UU{sub x} + {beta}U{sup n}U{sub x} - {gamma}U{sub xx} + {delta} U{sub xxx} = F(x,t). Numerical results agree well with the analytical solutions and results derived by existing literature, which indicates the present model is satisfactory and efficient on solving nonlinear partial differential equations.

  19. LATTICE BOLTZMANN METHOD SIMULATION ON THE FLOW OF TWO IMMISCIBLE FLUIDS IN COMPLEX GEOMETRY

    Institute of Scientific and Technical Information of China (English)

    Fang Hai-ping; Wan Rong-zheng; Fan Le-wen

    2000-01-01

    The multicomponent nonideal gas lattice Boltzmann model byShan and Chen (S-C) can be used to simulate the immiscible fluidflow. In this paper, weshow that the relaxation constant 1 is a necessarycondition for the immiscible fluid flow in the S-C model. In asystem with very complex boundary geometry, for 0.8 1, the S-C model describes the immiscible flow quite well, and=1 is the best.

  20. Numerical simulation of laminar jet-forced flow using lattice Boltzmann method

    Institute of Scientific and Technical Information of China (English)

    Yuan LI; Ya-li DUAN; Yan GUO; Ru-xun LIU

    2009-01-01

    In the paper, a numerical study on symmetrical and asymmetrical laminar jet-forced flows is carried out by using a lattice Boltzmann method (LBM) with a special boundary treatment. The simulation results are in very good agreement with the available numerical prediction. It is shown that the LBM is a competitive method for the laminar jet-forced flow in terms of computational efficiency and stability.

  1. Modeling flue pipes: Subsonic flow, lattice Boltzmann, and parallel distributed computers

    Science.gov (United States)

    Skordos, Panayotis A.

    1995-01-01

    The problem of simulating the hydrodynamics and the acoustic waves inside wind musical instruments such as the recorder the organ, and the flute is considered. The problem is attacked by developing suitable local-interaction algorithms and a parallel simulation system on a cluster of non-dedicated workstations. Physical measurements of the acoustic signal of various flue pipes show good agreement with the simulations. Previous attempts at this problem have been frustrated because the modeling of acoustic waves requires small integration time steps which make the simulation very compute-intensive. In addition, the simulation of subsonic viscous compressible flow at high Reynolds numbers is susceptible to slow-growing numerical instabilities which are triggered by high-frequency acoustic modes. The numerical instabilities are mitigated by employing suitable explicit algorithms: lattice Boltzmann method, compressible finite differences, and fourth-order artificial-viscosity filter. Further, a technique for accurate initial and boundary conditions for the lattice Boltzmann method is developed, and the second-order accuracy of the lattice Boltzmann method is demonstrated. The compute-intensive requirements are handled by developing a parallel simulation system on a cluster of non-dedicated workstations. The system achieves 80 percent parallel efficiency (speedup/processors) using 20 HP-Apollo workstations. The system is built on UNIX and TCP/IP communication routines, and includes automatic process migration from busy hosts to free hosts.

  2. Entropic Lattice Boltzmann Methods for Fluid Mechanics: Thermal, Multi-phase and Turbulence

    Science.gov (United States)

    Chikatamarla, Shyam; Boesch, F.; Frapolli, N.; Mazloomi, A.; Karlin, I.

    2014-11-01

    With its roots in statistical mechanics and kinetic theory, the lattice Boltzmann method (LBM) is a paradigm-changing innovation, offering for the first time an intrinsically parallel CFD algorithm. Over the past two decades, LBM has achieved numerous results in the field of CFD and is now in a position to challenge state-of-the art CFD techniques. Major restyling of LBM resulted in an unconditionally stable entropic LBM which restored Second Law (Boltzmann H theorem) in the LBM kinetics and thus enabled affordable direct simulations of fluid turbulence. In this talk, we shall review recent advances in ELBM as a practical, modeling-free tool for simulation of complex flow phenomenon. We shall present recent simulations of fluid turbulence including turbulent channel flow, flow past a circular cylinder, creation and dynamics of vortex tubes, and flow past a surface mounted cube. Apart from its achievements in turbulent flow simulations, ELBM has also presented us the opportunity to extend lattice Boltzmann method to higher order lattices which shall be employed for turbulent, multi-phase and thermal flow simulations. A new class of entropy functions are proposed to handle non-ideal equation of state and surface tension terms in multi-phase flows. It is shown the entropy principle brings unconditional stability and thermodynamic consistency to all the three flow regimes considered here. Acknowledgements: ERC Advanced Grant ``ELBM'' and CSCS grant s437 are deeply acknowledged. References:

  3. An exact energy conservation property of the quantum lattice Boltzmann algorithm

    Energy Technology Data Exchange (ETDEWEB)

    Dellar, Paul J., E-mail: dellar@maths.ox.ac.uk [OCIAM, Mathematical Institute, 24-29 St Giles' , Oxford OX1 3LB (United Kingdom)

    2011-11-28

    The quantum lattice Boltzmann algorithm offers a unitary and readily parallelisable discretisation of the Dirac equation that is free of the fermion-doubling problem. The expectation of the discrete time-advance operator is an exact invariant of the algorithm. Its imaginary part determines the expectation of the Hamiltonian operator, the energy of the solution, with an accuracy that is consistent with the overall accuracy of the algorithm. In the one-dimensional case, this accuracy may be increased from first to second order using a variable transformation. The three-dimensional quantum lattice Boltzmann algorithm uses operator splitting to approximate evolution under the three-dimensional Dirac equation by a sequence of solutions of one-dimensional Dirac equations. The three-dimensional algorithm thus inherits the energy conservation property of the one-dimensional algorithm, although the implementation shown remains only first-order accurate due to the splitting error. -- Highlights: ► The quantum lattice Boltzmann algorithm approximates the Dirac equation. ► It has an exact invariant: the expectation of the discrete time-advance operator. ► The invariant consistently approximates the energy of the continuous system. ► We achieve second-order accuracy through a variable transformation.

  4. A pseudopotential-based multiple-relaxation-time lattice Boltzmann model for multicomponent/multiphase flows

    Institute of Scientific and Technical Information of China (English)

    Zhen-Hua Chai; Tian-Shou Zhao

    2012-01-01

    In this paper,a pseudopotential-based multiplerelaxation-time lattice Boltzmann model is proposed for multicomponent/multiphase flow systems.Unlike previous models in the literature,the present model not only enables the study of multicomponent flows with different molecular weights,different viscosities and different Schmidt numbers,but also ensures that the distribution function of each component evolves on the same square lattice without invoking additional interpolations.Furthermore,the Chapman-Enskog analysis shows that the present model results in the correct hydrodynamic equations,and satisfies the indifferentiability principle.The numerical validation exercises further demonstrate that the favorable performance of the present model.

  5. Simulation of Blood Flow at Vessel Bifurcation by Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    KANG Xiu-Ying; LIU Da-He; ZHOU Jing; JIN Yong-Juan

    2005-01-01

    @@ The application of the lattice Boltzmann method to the large vessel bifurcation blood flow is investigated in awide range of Reynolds numbers. The velocity, shear stress and pressure distributions at the bifurcation arepresented in detail. The flow separation zones revealed with increase of Reynolds number are located in theareas of the daughter branches distal to the outer corners of the bifurcation where some deposition of particularblood components might occur to form arteriosclerosis. The results also demonstrate that the lattice Boltzmannmethod is adaptive to simulating the flow in larger vessels under a high Reynolds number.

  6. Effect of a Two-Dimensional Periodic Dielectric Background on Complete Photonic Band Gap in Complex Square Lattices

    Institute of Scientific and Technical Information of China (English)

    ZHANG Yan; SHI Jun-Jie

    2008-01-01

    A two-dimensional photonic crystal model with a periodic square dielectric background is proposed.The photonic band modulation effects due to the two-dimensional periodic background are investigated jn detail.It is found that periodic modulation of the dielectric background greatly alters photonic band structures,especially for the Epolarization modes.The number,width and position of the photonic band gaps sensitively depend on the dielectric constants of the two-dimensional periodic background.Complete band gaps are found,and the dependence of the widths of these gaps on the structural and material parameters of the two alternating rods/holes is studied.

  7. Partition Function for Two-Dimensional Nearest Neighbour Ising Model in a Non-Zero Magnetic Field for a Square Lattice of 16 Sites

    OpenAIRE

    2007-01-01

    An explicit expression for the partition function of two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived by a systematic enumeration of all the spin configurations pertaining to a square lattice of sixteen sites. The critical temperature is shown to be in excellent agreement with the reported values while the corresponding dimensionless magnetic field is obtained as 0.004.

  8. Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer.

    Science.gov (United States)

    Shi, Yong; Yap, Ying Wan; Sader, John E

    2015-07-01

    Ability to characterize the heat transfer in flowing gases is important for a wide range of applications involving micro- and nanoscale devices. Gas flows away from the continuum limit can be captured using the Boltzmann equation, whose analytical solution poses a formidable challenge. An efficient and accurate numerical simulation of the Boltzmann equation is thus highly desirable. In this article, the linearized Boltzmann Bhatnagar-Gross-Krook equation is used to develop a hierarchy of thermal lattice Boltzmann (LB) models based on half-space Gaussian-Hermite (GH) quadrature ranging from low to high algebraic precision, using double distribution functions. Simplified versions of the LB models in the continuum limit are also derived, and are shown to be consistent with existing thermal LB models for noncontinuum heat transfer reported in the literature. Accuracy of the proposed LB hierarchy is assessed by simulating thermal Couette flows for a wide range of Knudsen numbers. Effects of the underlying quadrature schemes (half-space GH vs full-space GH) and continuum-limit simplifications on computational accuracy are also elaborated. The numerical findings in this article provide direct evidence of improved computational capability of the proposed LB models for modeling noncontinuum flows and heat transfer at small length scales.

  9. Kinetic lattice Boltzmann method for microscale gas flows: issues on boundary condition, relaxation time, and regularization.

    Science.gov (United States)

    Niu, Xiao-Dong; Hyodo, Shi-Aki; Munekata, Toshihisa; Suga, Kazuhiko

    2007-09-01

    It is well known that the Navier-Stokes equations cannot adequately describe gas flows in the transition and free-molecular regimes. In these regimes, the Boltzmann equation (BE) of kinetic theory is invoked to govern the flows. However, this equation cannot be solved easily, either by analytical techniques or by numerical methods. Hence, in order to efficiently maneuver around this equation for modeling microscale gas flows, a kinetic lattice Boltzmann method (LBM) has been introduced in recent years. This method is regarded as a numerical approach for solving the BE in discrete velocity space with Gauss-Hermite quadrature. In this paper, a systematic description of the kinetic LBM, including the lattice Boltzmann equation, the diffuse-scattering boundary condition for gas-surface interactions, and definition of the relaxation time, is provided. To capture the nonlinear effects due to the high-order moments and wall boundaries, an effective relaxation time and a modified regularization procedure of the nonequilibrium part of the distribution function are further presented based on previous work [Guo et al., J. Appl. Phys. 99, 074903 (2006); Shan et al., J. Fluid Mech. 550, 413 (2006)]. The capability of the kinetic LBM of simulating microscale gas flows is illustrated based on the numerical investigations of micro Couette and force-driven Poiseuille flows.

  10. Development of an Innovative Algorithm for Aerodynamics-Structure Interaction Using Lattice Boltzmann Method

    Science.gov (United States)

    Mei, Ren-Wei; Shyy, Wei; Yu, Da-Zhi; Luo, Li-Shi; Rudy, David (Technical Monitor)

    2001-01-01

    The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is

  11. Heat transfer and fluid flow in microchannels and nanochannels at high Knudsen number using thermal lattice-Boltzmann method.

    Science.gov (United States)

    Ghazanfarian, J; Abbassi, A

    2010-08-01

    The present paper deals with the two-dimensional numerical simulation of gaseous flow and heat transfer in planar microchannel and nanochannel with different wall temperatures in transitional regime 0.1≤Kn≤1 . An atomistic molecular simulation method is used known as thermal lattice-Boltzmann method. The results of simulation are presented in four cases corresponding to the Fourier flow, shear-driven flow (Couette flow), pressure-driven flow (Poiseuille flow), and mixed shear-pressure-driven flow in the developing and fully developed regions. The mixed shear-pressure-driven flow is divided into two subcases with shear stress and pressure gradient acting in the same and the opposite directions. Normalized temperature and velocity profiles across the channel, distribution of local wall Nusselt number, and friction coefficient are illustrated. Using this method, nonlinear pressure distribution in the streamwise direction, reduction in mass flow rate, C(f) Re, and Nu by increasing the Knudsen number are studied. It is seen that for Couette flow, Nu over the hotter plate is greater than the cooler plate, but for the pressure-driven flow with stationary wall temperature dependency of viscosity and thermal conductivity causes this trend to be reversed. The reversed flow appearance in the velocity profile is captured in the case of opposite shear-pressure-driven flow.

  12. Numerical simulation of gas flow and heat transfer in a rough microchannel using the lattice Boltzmann method.

    Science.gov (United States)

    Dorari, Elaheh; Saffar-Avval, Majid; Mansoori, Zohreh

    2015-12-01

    In microfluidics, two important factors responsible for the differences between the characteristics of the flow and heat transfer in microchannels and conventional channels are rarefaction and surface roughness which are studied in the present work. An incompressible gas flow in a microchannel is simulated two dimensionally using the lattice Boltzmann method. The flow is in the slip regime and surface roughness is modeled by both regular and Gaussian random distribution of rectangular modules. The effects of relative surface roughness height and Knudsen number on gaseous flow and heat transfer are studied. It was shown that as the relative roughness height increases, the Poiseuille number increases and the Nusselt number has a decreasing or increasing trend, depending on the degree of rarefaction. A comparison between the flow and heat transfer characteristics in regular and random distribution of surface roughness demonstrates that in regular roughness, circular flows are more pronounced; Poiseuille number is higher and Nusselt number is lower than that of its equivalent random roughness.

  13. Kinetic theory of correlated fluids: from dynamic density functional to Lattice Boltzmann methods.

    Science.gov (United States)

    Marconi, Umberto Marini Bettolo; Melchionna, Simone

    2009-07-07

    Using methods of kinetic theory and liquid state theory we propose a description of the nonequilibrium behavior of molecular fluids, which takes into account their microscopic structure and thermodynamic properties. The present work represents an alternative to the recent dynamic density functional theory, which can only deal with colloidal fluids and is not apt to describe the hydrodynamic behavior of a molecular fluid. The method is based on a suitable modification of the Boltzmann transport equation for the phase space distribution and provides a detailed description of the local structure of the fluid and its transport coefficients. Finally, we propose a practical scheme to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method.

  14. Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities

    KAUST Repository

    Allen, Rebecca

    2016-06-29

    We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.

  15. A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide

    KAUST Repository

    Allen, Rebecca

    2013-01-01

    The storage of CO2 in fluid-filled geological formations has been carried out for more than a decade in locations around the world. After CO2 has been injected into the aquifer and has moved laterally under the aquifer\\'s cap-rock, density-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE) to formulate a model for a similar scenario when a solute diffuses into a fluid and density differences lead to convective mixing. The LBE is a promising alternative to the traditional methods of computational fluid dynamics. Rather than discretizing the system of partial differential equations of classical continuum mechanics directly, the LBE is derived from a velocity-space truncation of the Boltzmann equation of classical kinetic theory. We propose an extension to the LBE, which can accurately predict the transport of dissolved CO2 in water, as a step towards fluid-filled porous media simulations. This is achieved by coupling two LBEs, one for the fluid flow and one for the convection and diffusion of CO2. Unlike existing lattice Boltzmann equations for porous media flow, our model is derived from a system of moment equations and a Crank-Nicolson discretization of the velocity-truncated Boltzmann equation. The forcing terms are updated locally without the need for additional central difference approximation. Therefore our model preserves all the computational advantages of the single-phase lattice Boltzmann equation and is formally second-order accurate in both space and time. Our new model also features a novel implementation of boundary conditions, which is simple to implement and does not suffer from the grid-dependent error that is present in the standard "bounce-back" condition. The significance of using the LBE in this work lies in the ability to efficiently

  16. Gray free-energy multiphase lattice Boltzmann model with effective transport and wetting properties.

    Science.gov (United States)

    Zalzale, Mohamad; Ramaioli, M; Scrivener, K L; McDonald, P J

    2016-11-01

    The paper shows that it is possible to combine the free-energy lattice Boltzmann approach to multiphase modeling of fluids involving both liquid and vapor with the partial bounce back lattice Boltzmann approach to modeling effective media. Effective media models are designed to mimic the properties of porous materials with porosity much finer than the scale of the simulation lattice. In the partial bounce-back approach, an effective media parameter or bounce-back fraction controls fluid transport. In the combined model, a wetting potential is additionally introduced that controls the wetting properties of the fluid with respect to interfaces between free space (white nodes), effective media (gray nodes), and solids (black nodes). The use of the wetting potential combined with the bounce-back parameter gives the model the ability to simulate transport and sorption of a wide range of fluid in material systems. Results for phase separation, permeability, contact angle, and wicking in gray media are shown. Sorption is explored in small sections of model multiscale porous systems to demonstrate two-step desorption, sorption hysteresis, and the ink-bottle effect.

  17. Study on an antagonist differentiated heated lid driven-cavity enclosing a tube: lattice Boltzmann method

    Science.gov (United States)

    Ma, Xiaoyan; Pellerin, Nicolas; Reggio, Marcelo; Bennacer, Rachid

    2017-05-01

    The method of lattice-Boltzmann multiple relaxation time (MRT) is commonly applied to study the conversion system consisting in a combination of forced convection and natural convection occurred in a cavity. Moving the top surface horizontally at a fixed speed, while two vertical walls are applied with constant different temperatures, assuming adiabatic case on both bottom and top walls. We consider a "non-cooperating" situation, where dynamics and buoyancy forces counterbalance. The cavity contains a circular cylinder placed at various positions. Boundary conditions for velocity and temperature have been applied to handle the non-Cartesian boundary of the cylinder. In lattice Boltzmann methods we adopt the double distribution model for calculating both the thermal and hydrodynamic fields. The D2Q5 and D2Q9 lattice are chosen to perform the simulations for a wide range of Reynolds and Rayleigh numbers. By calculating the average Nusselt number, we also investigated the influence of different obstacle positions on characteristics of flow and heat transfer. The results show the influence of the obstacle position on the dimensionless numbers, so as to effect the heat transfer behaviors inside the cavity. It is also indicates that the governing parameters are also related to driven power for the upper surface sliding. Contribution to the topical issue "Materials for Energy harvesting, conversion and storage II (ICOME 2016)", edited by Jean-Michel Nunzi, Rachid Bennacer and Mohammed El Ganaoui

  18. Gray free-energy multiphase lattice Boltzmann model with effective transport and wetting properties

    Science.gov (United States)

    Zalzale, Mohamad; Ramaioli, M.; Scrivener, K. L.; McDonald, P. J.

    2016-11-01

    The paper shows that it is possible to combine the free-energy lattice Boltzmann approach to multiphase modeling of fluids involving both liquid and vapor with the partial bounce back lattice Boltzmann approach to modeling effective media. Effective media models are designed to mimic the properties of porous materials with porosity much finer than the scale of the simulation lattice. In the partial bounce-back approach, an effective media parameter or bounce-back fraction controls fluid transport. In the combined model, a wetting potential is additionally introduced that controls the wetting properties of the fluid with respect to interfaces between free space (white nodes), effective media (gray nodes), and solids (black nodes). The use of the wetting potential combined with the bounce-back parameter gives the model the ability to simulate transport and sorption of a wide range of fluid in material systems. Results for phase separation, permeability, contact angle, and wicking in gray media are shown. Sorption is explored in small sections of model multiscale porous systems to demonstrate two-step desorption, sorption hysteresis, and the ink-bottle effect.

  19. Effects of Nanoparticles on Melting Process with Phase-Change Using the Lattice Boltzmann Method

    KAUST Repository

    Ibrahem, Ahmed M.

    2017-05-04

    In this work, the problem of nanoparticles dispersion effects on coupled heat transfer and solid-liquid phase change has been studied. The lattice Boltzmann method (LBM) enthalpy-based is employed. The collision model of lattice Bhatangar-Gross-Krook (LBGK) is used to solve the problem of 1D melting by conduction. On the other hand, we use the model of multi-distribution functions (MDF) to calculate the density, the velocity and the temperature for the problem of 2D melting by free convection, associated with different boundary conditions. In these simulations, the volume fractions of copper nanoparticles (0-2%) added to water-base fluid and Rayleigh numbers of 103to105. We use the Chapman-Enskog expansion to derive the governing macroscopic quantities from the mesoscopic lattice Boltzmann equation. The results obtained by these models have been compared to an analytical solution or other numerical methods. The effects of nanoparticles on conduction and natural convection during the melting process have been investigated. Moreover, the influences of nanoparticles on moving of the phase change front, the thermal conductivity and the latent heat of fusion are also studied.

  20. Lattice Boltzmann Methods to Address Fundamental Boiling and Two-Phase Problems

    Energy Technology Data Exchange (ETDEWEB)

    Uddin, Rizwan

    2012-01-01

    This report presents the progress made during the fourth (no cost extension) year of this three-year grant aimed at the development of a consistent Lattice Boltzmann formulation for boiling and two-phase flows. During the first year, a consistent LBM formulation for the simulation of a two-phase water-steam system was developed. Results of initial model validation in a range of thermo-dynamic conditions typical for Boiling Water Reactors (BWRs) were shown. Progress was made on several fronts during the second year. Most important of these included the simulation of the coalescence of two bubbles including the surface tension effects. Work during the third year focused on the development of a new lattice Boltzmann model, called the artificial interface lattice Boltzmann model (AILB model) for the 3 simulation of two-phase dynamics. The model is based on the principle of free energy minimization and invokes the Gibbs-Duhem equation in the formulation of non-ideal forcing function. This was reported in detail in the last progress report. Part of the efforts during the last (no-cost extension) year were focused on developing a parallel capability for the 2D as well as for the 3D codes developed in this project. This will be reported in the final report. Here we report the work carried out on testing the AILB model for conditions including the thermal effects. A simplified thermal LB model, based on the thermal energy distribution approach, was developed. The simplifications are made after neglecting the viscous heat dissipation and the work done by pressure in the original thermal energy distribution model. Details of the model are presented here, followed by a discussion of the boundary conditions, and then results for some two-phase thermal problems.

  1. Lattice Boltzmann Method used for the aircraft characteristics computation at high angle of attack

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    Traditional Finite Volume Method(FVM)and Lattice Boltzmann Method(LBM)are both used to compute the high angle attack aerodynamic characteristics of the benchmark aircraft model named CT-1.Even though the software requires flow on the order of Ma<0.4,simulation at Ma=0.5 is run in PowerFLOW after theoretical analysis.The consistency with the wind tunnel testing is satisfied,especially for the LBM which can produce perfect results at high angle attack.PowerFLOW can accurately capture the detail of flows because it is inherently time-dependent and parallel and suits large-scale computation very well.

  2. Flow simulation of fiber reinforced self compacting concrete using Lattice Boltzmann method

    DEFF Research Database (Denmark)

    Svec, Oldrich; Skocek, Jan; Stang, Henrik

    2011-01-01

    Self compacting concrete (SCC) is a promising material in the civil engineering industry. One of the benefits of the SCC is a fast and simplified casting followed by decreased labor costs. The SCC as any other type of concrete has a significantly lower tensile and shear strength in comparison to ....... A relatively new group of models - Lattice Boltzmann Modeling (LBM) - is presented in this paper. The conventional LBM is modified to include fiber and particle suspensions and non-Newtonian rheology and is used to model the fiber reinforced self compacting concrete flow....

  3. The Blood Flow at Arterial Bifurcations Simulated by the Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    JI Yu-Pin; KANG Xiu-Ying; LIU Da-He

    2009-01-01

    The Programmed model of non-Newtonian blood flow (the Casson model) at arterial bifurcations is established by the lattice Boltzmann method. The blood flow field under different Reynolds numbers is simulated, and distri-bution of dynamic factors such as flow velocity, shear stress, pressure and shear rate are presented. The existence of the fluid separation zone is analyzed. This provides a basis for further studies of the relationship between hemodynamic factors and pathogenesis, as well as a reference for a better understanding of the pathological changes and location of sediments, and the plague factor in arteries.

  4. Field-wide flow simulation in fractured porous media within lattice Boltzmann framework

    Science.gov (United States)

    Benamram, Z.; Tarakanov, A.; Nasrabadi, H.; Gildin, E.

    2016-10-01

    In this paper, a generalized lattice Boltzmann model for simulating fluid flow in porous media at the representative volume element scale is extended towards applications of hydraulically and naturally fractured reservoirs. The key element within the model is the development of boundary conditions for a vertical well and horizontal fracture with minimal node usage. In addition, the governing non-dimensional equations are derived and a new set of dimensionless numbers are presented for the simulation of a fractured reservoir system. Homogenous and heterogeneous vertical well and fracture systems are simulated and verified against commercial reservoir simulation suites. Results are in excellent agreement to analytical and finite difference solutions.

  5. Role of dissolved salts in thermophoresis of DNA: lattice-Boltzmann-based simulations.

    Science.gov (United States)

    Hammack, Audrey; Chen, Yeng-Long; Pearce, Jennifer Kreft

    2011-03-01

    We use a lattice Boltzmann based Brownian dynamics simulation to investigate the dependence of DNA thermophoresis on its interaction with dissolved salts. We find the thermal diffusion coefficient D{T} depends on the molecule size, in contrast with previous simulations without electrostatics. The measured S{T} also depends on the Debye length. This suggests thermophoresis of DNA is influenced by the electrostatic interactions between the polymer beads and the salt ions. However, when electrostatic forces are weak, DNA thermophoresis is not found, suggesting that other repulsive forces such as the excluded volume force prevent thermal migration.

  6. Prandtl number effects in MRT lattice Boltzmann models for shocked and unshocked compressible fluids

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    This paper constructs a new multiple relaxation time lattice Boltzmann model which is not only for the shocked compressible fluids,but also for the unshocked compressible fluids.To make the model work for unshocked compressible fluids,a key step is to modify the collision operators of energy flux so that the viscous coefficient in momentum equation is consistent with that in energy equation even in the unshocked system.The unnecessity of the modification for systems under strong shock is analyzed.The model ...

  7. Simulation of residual oil displacement in a sinusoidal channel with the lattice Boltzmann method

    CERN Document Server

    Otomo, Hiroshi; Hazlett, Randy; Li, Yong; Staroselsky, Ilya; Zhang, Raoyang; Chen, Hudong

    2016-01-01

    We simulate oil slug displacement in a sinusoidal channel in order to validate computational models and algorithms for multi-component flow. This case fits in the gap between fully realistic cases characterized by complicated geometry and academic cases with simplistic geometry. Our computational model is based on the lattice Boltzmann method and allows for variation of physical parameters such as wettability and viscosity. The effect of variation of model parameters is analyzed, in particular via comparison with analytical solutions. We discuss the requirements for accurate solution of the oil slug displacement problem.

  8. Lattice Boltzmann modeling of boiling heat transfer: The boiling curve and the effects of wettability

    OpenAIRE

    Li, Q; Kang, Q. J.; Francois, M. M.; He, Y. L.; Luo, K. H.

    2015-01-01

    A hybrid thermal lattice Boltzmann (LB) model is presented to simulate thermal multiphase flows with phase change based on an improved pseudopotential LB approach [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 87, 053301 (2013)]. The present model does not suffer from the spurious term caused by the forcing-term effect, which was encountered in some previous thermal LB models for liquid-vapor phase change. Using the model, the liquid-vapor boiling process is simulated. The boiling curve togeth...

  9. Numerical simulation of bubbly two-phase flow using the lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

    Watanabe, Tadashi; Ebihara, Kenichi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

    2000-09-01

    The two-component two-phase lattice Boltzmann method, in which two distribution functions are used to represent two phases, is used to simulate bubbly flows as one of the fundamental two-phase flow phenomena in nuclear application fields. The inlet flow condition is proposed to simulate steady-state flow fields. The time variation and the spatial distribution of the volume fraction and the interfacial area are measured numerically. The simulation program is parallelized in one direction by the domain decomposition method using the MPI (Message Passing Interface) libraries, and parallel computations are performed on a workstation cluster. (author)

  10. Free surface entropic lattice Boltzmann simulations of film condensation on vertical hydrophilic plates

    DEFF Research Database (Denmark)

    Hygum, Morten Arnfeldt; Karlin, Iliya; Popok, Vladimir

    2015-01-01

    A model for vapor condensation on vertical hydrophilic surfaces is developed using the entropic lattice Boltzmann method extended with a free surface formulation of the evaporation–condensation problem. The model is validated with the steady liquid film formation on a flat vertical wall....... It is shown that the model is in a good agreement with the classical Nusselt equations for the laminar flow regime. Comparisons of the present model with other empirical models also demonstrate good agreement beyond the laminar regime. This allows the film condensation modeling at high film Reynolds numbers...

  11. A lattice Boltzmann study of non-hydrodynamic effects in shell models of turbulence

    Science.gov (United States)

    Benzi, R.; Biferale, L.; Sbragaglia, M.; Succi, S.; Toschi, F.

    2004-10-01

    A lattice Boltzmann scheme simulating the dynamics of shell models of turbulence is developed. The influence of high-order kinetic modes (ghosts) on the dissipative properties of turbulence dynamics is studied. It is analytically found that when ghost fields relax on the same timescale as the hydrodynamic ones, their major effect is a net enhancement of the fluid viscosity. The bare fluid viscosity is recovered by letting ghost fields evolve on a much longer timescale. Analytical results are borne out by high-resolution numerical simulations. These simulations indicate that the hydrodynamic manifold is very robust towards large fluctuations of non-hydrodynamic fields.

  12. A novel incompressible finite-difference lattice Boltzmann equation for particle-laden flow

    Institute of Scientific and Technical Information of China (English)

    Sheng Chen; Zhaohui Liu; Baochang Shi; Zhu He; Chuguang Zheng

    2005-01-01

    In this paper, we propose a novel incompressible finite-difference lattice Boltzmann Equation (FDLBE). Because source terms that reflect the interaction between phases can be accurately described, the new model is suitable for simulating two-way coupling incompressible multiphase flow.The 2-D particle-laden flow over a backward-facing step is chosen as a test case to validate the present method. Favorable results are obtained and the present scheme is shown to have good prospects in practical applications.

  13. Sedimentation of a Single Charged Elliptic Cylinder in a Newtonian Fluid by Lattice Boltzmann Method

    Institute of Scientific and Technical Information of China (English)

    ZHANG Chao-Ying; SHI Juan; TAN Hui-Li; LIU Mu-Ren; KONG Ling-Jiang

    2004-01-01

    @@ We simulate the sedimentation of single charged and single uncharged elliptic cylinders in a Newtonian fluid by using the lattice Boltzmann method. Due to the polarizing effects and non-axial symmetry shape, there are the Coulomb force and corresponding torque exerted on the charged elliptic cylinder during the sedimentation, which significantly change the horizontal translation and rotation of the cylinder. When the dielectric constant of the liquid is smaller than that of the wall, the direction of the Coulomb force is opposite to that of the hydrodynamic force. Therefore there appears to be a critical linear charge density qc at which the elliptic cylinder will fall vertically off the centreline.

  14. Lattice Boltzmann Simulation of Sedimentation of a Single Charged Elastic Dumbbell in a Newtonian Fluid

    Institute of Scientific and Technical Information of China (English)

    ZHANG Chao-Ying; TAN Hui-Li; LIU Mu-Ren; KONG Ling-Jiang; SHI Juan

    2005-01-01

    @@ Based on the lattice Boltzmann method, the sedimentations of elastic dumbbells with different charges in a Newtonian fluid under the same and different initial conditions are simulated.Due to the polarizing effects, there are Coulomb forces exerted on the charged elastic dumbbells during their sedimentations, which change their original motions significantly.All of the numerical results show that, if the charged elastic dumbbells are released at offset-centreline positions with zero velocity and settle under gravity, they fall down vertically off the centreline and their orientations tend to be the horizontal finally, and the distances apart from the centreline increase with the increasing charges of the elastic dumbbells.

  15. Ternary Free Energy Lattice Boltzmann Model with Tunable Surface Tensions and Contact Angles

    CERN Document Server

    Semprebon, Ciro; Kusumaatmaja, Halim

    2015-01-01

    We present a new ternary free energy lattice Boltzmann model. The distinguishing feature of our model is that we are able to analytically derive and independently vary all fluid-fluid surface tensions and the solid surface contact angles. We carry out a number of benchmark tests: (i) double emulsions and liquid lenses to validate the surface tensions, (ii) ternary fluids in contact with a square well to compare the contact angles against analytical predictions, and (iii) ternary phase separation to verify that the multicomponent fluid dynamics is accurately captured. Additionally we also describe how the model here presented here can be extended to include an arbitrary number of fluid components.

  16. GPU phase-field lattice Boltzmann simulations of growth and motion of a binary alloy dendrite

    Science.gov (United States)

    Takaki, T.; Rojas, R.; Ohno, M.; Shimokawabe, T.; Aoki, T.

    2015-06-01

    A GPU code has been developed for a phase-field lattice Boltzmann (PFLB) method, which can simulate the dendritic growth with motion of solids in a dilute binary alloy melt. The GPU accelerated PFLB method has been implemented using CUDA C. The equiaxed dendritic growth in a shear flow and settling condition have been simulated by the developed GPU code. It has been confirmed that the PFLB simulations were efficiently accelerated by introducing the GPU computation. The characteristic dendrite morphologies which depend on the melt flow and the motion of the dendrite could also be confirmed by the simulations.

  17. Lattice Boltzmann method to study the contraction of a viscous ligament

    CERN Document Server

    Srivastava, Sudhir; Jeurissen, Roger; Wijshoff, Herman; Toschi, Federico

    2013-01-01

    We employ a recently formulated axisymmetric version of the multiphase Shan-Chen (SC) lattice Boltzmann method (LBM) [Srivastava et al, in preparation (2013)] to simulate the contraction of a liquid ligament. We compare the axisymmetric LBM simulation against the slender jet (SJ) approximation model [T. Driessen and R. Jeurissen, IJCFD {\\bf 25}, 333 (2011)]. We compare the retraction dynamics of the tail-end of the liquid ligament from the LBM simulation, the SJ model, Flow3D simulations and a simple model based on the force balance (FB). We find good agreement between the theoretical prediction (FB), the SJ model, and the LBM simulations.

  18. Effect of Rolling Massage on the Vortex Flow in Blood Vessels with Lattice Boltzmann Simulation

    Science.gov (United States)

    Yi, Hou Hui

    The rolling massage manipulation is a classic Chinese Medical Massage, which is a nature therapy in eliminating many diseases. Here, the effect of the rolling massage on the cavity flows in blood vessel under the rolling manipulation is studied by the lattice Boltzmann simulation. The simulation results show that the vortex flows are fully disturbed by the rolling massage. The flow behavior depends on the rolling velocity and the rolling depth. Rolling massage has a better effect on the flows in the cavity than that of the flows in a planar blood vessel. The result is helpful to understand the mechanism of the massage and develop the rolling techniques.

  19. Numerical Simulation of Flows about a Stationary and a Free-Falling Cylinder Using Immersed Boundary-Finite Difference Lattice Boltzmann Method

    Directory of Open Access Journals (Sweden)

    Roberto Rojas

    2013-03-01

    Full Text Available The applicability of the immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM to high Reynolds number flows about a circular cylinder is examined. Two-dimensional simulations of flows past a stationary circular cylinder are carried out for a wide range of the Reynolds number, Re, i.e., 1 ≤ Re ≤ 1×105. An immersed boundary-lattice Boltzmann method (IB-LBM is also used for comparison. Then free-falling circular cylinders are simulated to demonstrate the feasibility of predicting moving particles at high Reynolds numbers. The main conclusions obtained are as follows: (1 steady and unsteady flows about a stationary cylinder are well predicted with IB-LBM and IB-FDLBM, provided that the spatial resolution is high enough to satisfy the conditions of numerical stability, (2 high spatial resolution is required for stable IB-LBM simulation of high Reynolds number flows, (3 IB-FDLBM can stably simulate flows at very high Reynolds numbers without increasing the spatial resolution, (4 IB-FDLBM gives reasonable predictions of the drag coefficient for 1 ≤ Re ≤ 1×105, and (5 IB-FDLBM gives accurate predictions for the motion of free-falling cylinders at intermediate Reynolds numbers.

  20. Numerical investigation of non-Newtonian fluids in annular ducts with finite aspect ratio using lattice Boltzmann method.

    Science.gov (United States)

    Khali, S; Nebbali, R; Ameziani, D E; Bouhadef, K

    2013-05-01

    In this work the instability of the Taylor-Couette flow for Newtonian and non-Newtonian fluids (dilatant and pseudoplastic fluids) is investigated for cases of finite aspect ratios. The study is conducted numerically using the lattice Boltzmann method (LBM). In many industrial applications, the apparatuses and installations drift away from the idealized case of an annulus of infinite length, and thus the end caps effect can no longer be ignored. The inner cylinder is rotating while the outer one and the end walls are maintained at rest. The lattice two-dimensional nine-velocity (D2Q9) Boltzmann model developed from the Bhatnagar-Gross-Krook approximation is used to obtain the flow field for fluids obeying the power-law model. The combined effects of the Reynolds number, the radius ratio, and the power-law index n on the flow characteristics are analyzed for an annular space of finite aspect ratio. Two flow modes are obtained: a primary Couette flow (CF) mode and a secondary Taylor vortex flow (TVF) mode. The flow structures so obtained are different from one mode to another. The critical Reynolds number Re(c) for the passage from the primary to the secondary mode exhibits the lowest value for the pseudoplastic fluids and the highest value for the dilatant fluids. The findings are useful for studies of the swirling flow of non-Newtonians fluids in axisymmetric geometries using LBM. The flow changes from the CF to TVF and its structure switches from the two-cells to four-cells regime for both Newtonian and dilatant fluids. Contrariwise for pseudoplastic fluids, the flow exhibits 2-4-2 structure passing from two-cells to four cells and switches again to the two-cells configuration. Furthermore, the critical Reynolds number presents a monotonic increase with the power-law index n of the non-Newtonian fluid, and as the radius ratio grows, the transition flow regimes tend to appear for higher critical Reynolds numbers.

  1. Peierls-Nabarro energy surfaces and directional mobility of discrete solitons in two-dimensional saturable nonlinear Schr\\"odinger lattices

    CERN Document Server

    Naether, Uta; Johansson, Magnus

    2010-01-01

    We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schr\\"odinger model with saturable on-site nonlinearity. A numerical constrained Newton-Raphson method is used to calculate two-dimensional Peierls-Nabarro energy surfaces, which describe a pseudopotential landscape for the slow mobility of coherent localized excitations, corresponding to continuous phase-space trajectories passing close to stationary modes. Investigating the two-parameter space of the model through independent variations of the nonlinearity constant and the power, we show how parameter regimes and directions of good mobility are connected to existence of smooth surfaces connecting the stationary states. In particular, directions where solutions can move with minimum radiation can be predicted from flatter parts of the surfaces. For such mobile solutions, slight perturbations in the transverse direction yield additional transverse oscillations w...

  2. Solitary wave of the Korteweg-de Vries equation based on lattice Boltzmann model with three conservation laws

    Science.gov (United States)

    Wang, Huimin

    2017-01-01

    In this paper, a new lattice Boltzmann model for the Korteweg-de Vries (KdV) equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales and several higher- order moments of equilibrium distribution functions are obtained. In order to make the scheme obey the three conservation laws of the KdV equation, two equilibrium distribution functions are used and a correlation between the first conservation law and the second conservation law is constructed. In numerical examples, the numerical results of the KdV equation obtained by this scheme are compared with those results obtained by the previous lattice Boltzmann model. Numerical experiments demonstrate this scheme can be used to reduce the truncation error of the lattice Boltzmann scheme and preserve the three conservation laws.

  3. Simulations of time harmonic blood flow in the Mesenteric artery: comparing finite element and lattice Boltzmann methods

    Directory of Open Access Journals (Sweden)

    Hose Rod

    2009-10-01

    Full Text Available Abstract Background Systolic blood flow has been simulated in the abdominal aorta and the superior mesenteric artery. The simulations were carried out using two different computational hemodynamic methods: the finite element method to solve the Navier Stokes equations and the lattice Boltzmann method. Results We have validated the lattice Boltzmann method for systolic flows by comparing the velocity and pressure profiles of simulated blood flow between methods. We have also analyzed flow-specific characteristics such as the formation of a vortex at curvatures and traces of flow. Conclusion The lattice Boltzmann Method is as accurate as a Navier Stokes solver for computing complex blood flows. As such it is a good alternative for computational hemodynamics, certainly in situation where coupling to other models is required.

  4. Performance engineering for the Lattice Boltzmann method on GPGPUs: Architectural requirements and performance results

    CERN Document Server

    Habich, Johannes; Köstler, Harald; Hager, Georg; Wellein, Gerhard

    2011-01-01

    GPUs offer several times the floating point performance and memory bandwidth of current standard two socket CPU servers, e.g. NVIDIA C2070 vs. Intel Xeon Westmere X5650. The lattice Boltzmann method has been established as a flow solver in recent years and was one of the first flow solvers to be successfully ported and that performs well on GPUs. We demonstrate advanced optimization strategies for a D3Q19 lattice Boltzmann based incompressible flow solver for GPGPUs and CPUs based on NVIDIA CUDA and OpenCL. Since the implemented algorithm is limited by memory bandwidth, we concentrate on improving memory access. Basic data layout issues for optimal data access are explained and discussed. Furthermore, the algorithmic steps are rearranged to improve scattered access of the GPU memory. The importance of occupancy is discussed as well as optimization strategies to improve overall concurrency. We arrive at a well-optimized GPU kernel, which is integrated into a larger framework that can handle single phase fluid ...

  5. Third-order analysis of pseudopotential lattice Boltzmann model for multiphase flow

    CERN Document Server

    Huang, Rongzong

    2016-01-01

    In this work, a third-order Chapman-Enskog analysis of the multiple-relaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model for multiphase flow is performed for the first time. The leading terms on the interaction force, consisting of an anisotropic and an isotropic term, are successfully identified in the third-order macroscopic equation recovered by the lattice Boltzmann equation (LBE), and then new mathematical insights into the pseudopotential LB model are provided. For the third-order anisotropic term, numerical tests show that it can cause the stationary droplet to become out-of-round, which suggests the isotropic property of the LBE needs to be seriously considered in the pseudopotential LB model. By adopting the classical equilibrium moment or setting the so-called "magic" parameter to 1/12, the anisotropic term can be eliminated, which is found from the present third-order analysis and also validated numerically. As for the third-order isotropic term, when and only when it is considered, a...

  6. Simulation of arrested salt wedges with a multi-layer Shallow Water Lattice Boltzmann model

    Science.gov (United States)

    Prestininzi, P.; Montessori, A.; La Rocca, M.; Sciortino, G.

    2016-10-01

    The ability to accurately and efficiently model the intrusion of salt wedges into river beds is crucial to assay its interaction with human activities and the natural environment. We present a 2D multi-layer Shallow Water Lattice Boltzmann (SWLB) model able to predict the salt wedge intrusion in river estuaries. The formulation usually employed for the simulation of gravity currents is here equipped with proper boundary conditions to handle both the downstream seaside outlet and the upstream river inlet. Firstly, the model is validated against highly accurate semi-analytical solutions of the steady state 1D two-layer Shallow Water model. Secondly, the model is applied to a more complex, fully 3D geometry, to assess its capability to handle realistic cases. The simple formulation proposed for the shear interlayer stress is proven to be consistent with the general 3D viscous solution. In addition to the accuracy, the model inherits the efficiency of the Lattice Boltzmann approach to fluid dynamics problems.

  7. An improved lattice Boltzmann scheme for multiphase fluid with multi-range interactions

    Energy Technology Data Exchange (ETDEWEB)

    Maquignon, Nicolas; Duchateau, Julien; Roussel, Gilles; Rousselle, François; Renaud, Christophe [Laboratoire Informatique Signal et Image de la Côte d' Opale, 50 rue Ferdinand Buisson, 62100 Calais (France); Université du Littoral Côte d' Opale, 1 place de l' Yser, 59140, Dunkerque (France); Association INNOCOLD, MREI 1, 145 (France)

    2014-10-06

    Modeling of fluids with liquid to gas phase transition has become important for understanding many environmental or industrial processes. Such simulations need new techniques, because traditional solvers are often limited. The Lattice Boltzmann Model (LBM) allows simulate complex fluids, because its mesoscopic nature gives possibility to incorporate additional physics in comparison to usual methods. In this work, an improved lattice Boltzmann model for phase transition flow will be introduced. First, the state of art for Shan and Chen (SC) type of LBM will be reminded. Then, link to real thermodynamics will be established with Maxwell equal areas construction. Convergence to isothermal liquid vapor equilibrium will be shown and discussed. Inclusion of an equation of state for real fluid and better incorporation of force term is presented. Multi-range interactions have been used for SC model, but it hasn't been yet applied to real fluid with non-ideal equation of state. In this work, we evaluate this model when it is applied to real liquid-vapor equilibrium. We show that important differences are found for evaluation of gas density. In order to recover thermodynamic consistency, we use a new scheme for calculation of force term, which is a combination of multi range model and numerical weighting used by Gong and Cheng. We show the superiority of our new model by studying convergence to equilibrium values over a large temperature range. We prove that spurious velocities remaining at equilibrium are decreased.

  8. Fourth-order analysis of a diffusive lattice Boltzmann method for barrier coatings.

    Science.gov (United States)

    Strand, Kyle T; Feickert, Aaron J; Wagner, Alexander J

    2017-06-01

    We examine the applicability of diffusive lattice Boltzmann methods to simulate the fluid transport through barrier coatings, finding excellent agreement between simulations and analytical predictions for standard parameter choices. To examine more interesting non-Fickian behavior and multiple layers of different coatings, it becomes necessary to explore a wider range of parameters. However, such a range of parameters exposes deficiencies in such an implementation. To investigate these discrepancies, we examine the form of higher-order terms in the hydrodynamic limit of our lattice Boltzmann method. We identify these corrections to fourth order and validate these predictions with high accuracy. However, it is observed that the validated correction terms do not fully explain the bulk of observed error. This error was instead caused by the standard finite boundary conditions for the contact of the coating with the imposed environment. We identify a self-consistent form of these boundary conditions for which these errors are dramatically reduced. The instantaneous switching used as a boundary condition for the barrier problem proves demanding enough that any higher-order corrections meaningfully contribute for a small range of parameters. There is a large parameter space where the agreement between simulations and analytical predictions even in the second-order form are below 0.1%, making further improvements to the algorithm unnecessary for such an application.

  9. Thermohydrodynamics of an evaporating droplet studied using a multiphase lattice Boltzmann method.

    Science.gov (United States)

    Zarghami, Ahad; Van den Akker, Harry E A

    2017-04-01

    In this paper, the thermohydrodynamics of an evaporating droplet is investigated by using a single-component pseudopotential lattice Boltzmann model. The phase change is applied to the model by adding source terms to the thermal lattice Boltzmann equation in such a way that the macroscopic energy equation of multiphase flows is recovered. In order to gain an exhaustive understanding of the complex hydrodynamics during evaporation, a single droplet is selected as a case study. At first, some tests for a stationary (non-)evaporating droplet are carried out to validate the method. Then the model is used to study the thermohydrodynamics of a falling evaporating droplet. The results show that the model is capable of reproducing the flow dynamics and transport phenomena of a stationary evaporating droplet quite well. Of course, a moving droplet evaporates faster than a stationary one due to the convective transport. Our study shows that our single-component model for simulating a moving evaporating droplet is limited to low Reynolds numbers.

  10. Enhancement of the stability of lattice Boltzmann methods by dissipation control

    Science.gov (United States)

    Gorban, A. N.; Packwood, D. J.

    2014-11-01

    Artificial dissipation is a well known tool for the improvement of stability of numerical algorithms. However, the use of this technique affects the accuracy of the computation. We analyse various approaches proposed for enhancement of the Lattice Boltzmann Methods’ (LBM) stability. In addition to some previously known methods, the Multiple Relaxation Time (MRT) models, the entropic lattice Boltzmann method (ELBM), and filtering (including entropic median filtering), we develop and analyse new filtering techniques with independent filtering of different modes. All these methods affect dissipation in the system and may adversely affect the reproduction of the proper physics. To analyse the effect of dissipation on accuracy and to prepare practical recommendations, we test the enhanced LBM methods on the standard benchmark, the 2D lid driven cavity on a coarse grid (101×101 nodes). The accuracy was estimated by the position of the first Hopf bifurcation points in these systems. We find that two techniques, MRT and median filtering, succeed in yielding a reasonable value of the Reynolds number for the first bifurcation point. The newly created limiters, which filter the modes independently, also pick a reasonable value of the Reynolds number for the first bifurcation.

  11. Non-Newtonian particulate flow simulation: A direct-forcing immersed boundary-lattice Boltzmann approach

    Science.gov (United States)

    Amiri Delouei, A.; Nazari, M.; Kayhani, M. H.; Kang, S. K.; Succi, S.

    2016-04-01

    In the current study, a direct-forcing immersed boundary-non-Newtonian lattice Boltzmann method (IB-NLBM) is developed to investigate the sedimentation and interaction of particles in shear-thinning and shear-thickening fluids. In the proposed IB-NLBM, the non-linear mechanics of non-Newtonian particulate flows is detected by combination of the most desirable features of immersed boundary and lattice Boltzmann methods. The noticeable roles of non-Newtonian behavior on particle motion, settling velocity and generalized Reynolds number are investigated by simulating benchmark problem of one-particle sedimentation under the same generalized Archimedes number. The effects of extra force due to added accelerated mass are analyzed on the particle motion which have a significant impact on shear-thinning fluids. For the first time, the phenomena of interaction among the particles, such as Drafting, Kissing, and Tumbling in non-Newtonian fluids are investigated by simulation of two-particle sedimentation and twelve-particle sedimentation. The results show that increasing the shear-thickening behavior of fluid leads to a significant increase in the kissing time. Moreover, the transverse position of particles for shear-thinning fluids during the tumbling interval is different from Newtonian and the shear-thickening fluids. The present non-Newtonian particulate study can be applied in several industrial and scientific applications, like the non-Newtonian sedimentation behavior of particles in food industrial and biological fluids.

  12. Study on the melting process of phase change materials in metal foams using lattice Boltzmann method

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    A thermal lattice Boltzmann model is developed for the melting process of phase change material (PCM) embedded in open-cell metal foams. Natural convection in the melt PCM is considered. Under the condition of local thermal non-equilibrium between the metal matrix and PCM, two evolution equations of temperature distribution function are pre-sented through selecting an equilibrium distribution function and a nonlinear source term properly. The enthalpy-based method is employed to copy with phase change problem. Melting process in a cavity of the metal foams is simulated using the present model. The melting front locations and the temperature distributions in the metal foams filled with PCM are obtained by the lattice Boltzmann method. The effects of the porosity and pore size on the melting are also investigated and discussed. The re-sults indicate that the effects of foam porosity play important roles in the overall heat transfer. For the lower porosity foams, the melting rate is comparatively greater than the higher porosity foams, due to greater heat conduction from metal foam with high heat conductivity. The foam pore size has a limited effect on the melting rate due to two counteracting effects between conduction and convection heat transfer.

  13. Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows.

    Science.gov (United States)

    Liu, Haihu; Valocchi, Albert J; Zhang, Yonghao; Kang, Qinjun

    2013-01-01

    A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions.

  14. Lattice Boltzmann simulations of turbulent shear flow between parallel porous walls

    Institute of Scientific and Technical Information of China (English)

    唐政; 刘难生; 董宇红

    2014-01-01

    The effects of two parallel porous walls are investigated, consisting of the Darcy number and the porosity of a porous medium, on the behavior of turbulent shear flows as well as skin-friction drag. The turbulent channel flow with a porous surface is directly simulated by the lattice Boltzmann method (LBM). The Darcy-Brinkman-Forcheimer (DBF) acting force term is added in the lattice Boltzmann equation to simu-late the turbulent flow bounded by porous walls. It is found that there are two opposite trends (enhancement or reduction) for the porous medium to modify the intensities of the velocity fluctuations and the Reynolds stresses in the near wall region. The parametric study shows that flow modification depends on the Darcy number and the porosity of the porous medium. The results show that, with respect to the conventional impermeable wall, the degree of turbulence modification does not depend on any simple set of param-eters obviously. Moreover, the drag in porous wall-bounded turbulent flow decreases if the Darcy number is smaller than the order of O(10−4) and the porosity of porous walls is up to 0.4.

  15. Simulation of finite size particles in turbulent flows using entropic lattice boltzmann method

    Science.gov (United States)

    Gupta, Abhineet; Clercx, Herman J. H.; Toschi, Federico

    2016-11-01

    Particle-laden turbulent flows occur in variety of industrial applications. While the numerical simulation of such flows has seen significant advances in recent years, it still remains a challenging problem. Many studies investigated the rheology of dense suspensions in laminar flows as well as the dynamics of point-particles in turbulence. Here we will present results on the development of numerical methods, based on the Lattice Boltzmann method, suitable for the study of suspensions of finite-size particles under turbulent flow conditions and with varying geometrical complexity. The turbulent flow is modeled by an entropic lattice Boltzmann method, and the interaction between particles and carrier fluid is modeled using bounce back rule. Direct contact and lubrication force models for particle-particle interactions and particle-wall interaction are taken into account to allow for a full four-way coupled interaction. The accuracy and robustness of the method is discussed by validating velocity profile in turbulent pipe flow, sedimentation velocity of spheres in duct flow and resistance functions of approaching particles. Results show that the velocity profiles and turbulence statistics can be significantly altered by the presence of the dispersed solid phase. The author is supported by Shell-NWO computational sciences for energy research (CSER) Grant (12CSER034).

  16. Grid refinement for aeroacoustics in the lattice Boltzmann method: A directional splitting approach

    Science.gov (United States)

    Gendre, Félix; Ricot, Denis; Fritz, Guillaume; Sagaut, Pierre

    2017-08-01

    This study focuses on grid refinement techniques for the direct simulation of aeroacoustics, when using weakly compressible lattice Boltzmann models, such as the D3Q19 athermal velocity set. When it comes to direct noise computation, very small errors on the density or pressure field may have great negative consequences. Even strong acoustic density fluctuations have indeed a clearly lower amplitude than the hydrodynamic ones. This work deals with such very weak spurious fluctuations that emerge when a vortical structure crosses a refinement interface, which may contaminate the resulting aeroacoustic field. We show through an extensive literature review that, within the framework described above, this issue has never been addressed before. To tackle this problem, we develop an alternative algorithm and compare its behavior to a classical one, which fits our in-house vertex-centered data structure. Our main idea relies on a directional splitting of the continuous discrete velocity Boltzmann equation, followed by an integration over specific characteristics. This method can be seen as a specific coupling between finite difference and lattice Boltzmann, locally on the interface between the two grids. The method is assessed considering two cases: an acoustic pulse and a convected vortex. We show how very small errors on the density field arise and propagate throughout the domain when a vortical flow crosses the refinement interface. We also show that an increased free stream Mach number (but still within the weakly compressible regime) strongly deteriorates the situation, although the magnitude of the errors may remain negligible for purely aerodynamic studies. A drastically reduced level of error for the near-field spurious noise is obtained with our approach, especially for under-resolved simulations, a situation that is crucial for industrial applications. Thus, the vortex case is proved useful for aeroacoustic validations of any grid refinement algorithm.

  17. Determination of the Critical Exponents for the Isotropic-Nematic Phase Transition in a System of Long Rods on Two-dimensional Lattices: Universality of the Transition

    OpenAIRE

    Matoz-Fernandez, D. A.; Linares, D. H.; Ramirez-Pastor, A. J.

    2007-01-01

    Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior and universality for the isotropic-nematic phase transition in a system of long straight rigid rods of length $k$ ($k$-mers) on two-dimensional lattices. The nematic phase, characterized by a big domain of parallel $k$-mers, is separated from the isotropic state by a continuous transition occurring at a finite density. The determination of the critical exponents, along with the behavi...

  18. Similarity between the superconductivity in the graphene with the spin transport in the two-dimensional antiferromagnet in the honeycomb lattice

    Science.gov (United States)

    Lima, L. S.

    2017-02-01

    We have used the Dirac's massless quasi-particles together with the Kubo's formula to study the spin transport by electrons in the graphene monolayer. We have calculated the electric conductivity and verified the behavior of the AC and DC currents of this system, that is a relativistic electron plasma. Our results show that the AC conductivity tends to infinity in the limit ω → 0 , similar to the behavior obtained for the spin transport in the two-dimensional frustrated antiferromagnet in the honeycomb lattice. We have made a diagrammatic expansion for the Green's function and we have not gotten significative change in the results.

  19. Finite differences numerical method for two-dimensional superlattice Boltzmann transport equation and case comparison of CPU(C) and GPGPU(CUDA) implementations

    CERN Document Server

    Priimak, Dmitri

    2014-01-01

    We present finite differences numerical algorithm for solving 2D spatially homogeneous Boltzmann transport equation for semiconductor superlattices (SL) subject to time dependant electric field along SL axis and constant perpendicular magnetic field. Algorithm is implemented in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPUs. We compare performance and merits of one implementation versus another and discuss various methods of optimization.

  20. GPU accelerated study of heat transfer and fluid flow by lattice Boltzmann method on CUDA

    Science.gov (United States)

    Ren, Qinlong

    Lattice Boltzmann method (LBM) has been developed as a powerful numerical approach to simulate the complex fluid flow and heat transfer phenomena during the past two decades. As a mesoscale method based on the kinetic theory, LBM has several advantages compared with traditional numerical methods such as physical representation of microscopic interactions, dealing with complex geometries and highly parallel nature. Lattice Boltzmann method has been applied to solve various fluid behaviors and heat transfer process like conjugate heat transfer, magnetic and electric field, diffusion and mixing process, chemical reactions, multiphase flow, phase change process, non-isothermal flow in porous medium, microfluidics, fluid-structure interactions in biological system and so on. In addition, as a non-body-conformal grid method, the immersed boundary method (IBM) could be applied to handle the complex or moving geometries in the domain. The immersed boundary method could be coupled with lattice Boltzmann method to study the heat transfer and fluid flow problems. Heat transfer and fluid flow are solved on Euler nodes by LBM while the complex solid geometries are captured by Lagrangian nodes using immersed boundary method. Parallel computing has been a popular topic for many decades to accelerate the computational speed in engineering and scientific fields. Today, almost all the laptop and desktop have central processing units (CPUs) with multiple cores which could be used for parallel computing. However, the cost of CPUs with hundreds of cores is still high which limits its capability of high performance computing on personal computer. Graphic processing units (GPU) is originally used for the computer video cards have been emerged as the most powerful high-performance workstation in recent years. Unlike the CPUs, the cost of GPU with thousands of cores is cheap. For example, the GPU (GeForce GTX TITAN) which is used in the current work has 2688 cores and the price is only 1