Direct numerical simulation of scalar transport using unstructured finite-volume schemes
Rossi, Riccardo
2009-03-01
An unstructured finite-volume method for direct and large-eddy simulations of scalar transport in complex geometries is presented and investigated. The numerical technique is based on a three-level fully implicit time advancement scheme and central spatial interpolation operators. The scalar variable at cell faces is obtained by a symmetric central interpolation scheme, which is formally first-order accurate, or by further employing a high-order correction term which leads to formal second-order accuracy irrespective of the underlying grid. In this framework, deferred-correction and slope-limiter techniques are introduced in order to avoid numerical instabilities in the resulting algebraic transport equation. The accuracy and robustness of the code are initially evaluated by means of basic numerical experiments where the flow field is assigned a priori. A direct numerical simulation of turbulent scalar transport in a channel flow is finally performed to validate the numerical technique against a numerical dataset established by a spectral method. In spite of the linear character of the scalar transport equation, the computed statistics and spectra of the scalar field are found to be significantly affected by the spectral-properties of interpolation schemes. Although the results show an improved spectral-resolution and greater spatial-accuracy for the high-order operator in the analysis of basic scalar transport problems, the low-order central scheme is found superior for high-fidelity simulations of turbulent scalar transport.
A second order volume of fluid (VOF) scheme for numerical simulation of 2-D breaking waves
Institute of Scientific and Technical Information of China (English)
ZONG Zhi; DONG Guo-hai
2007-01-01
Among all environmental forces acting on ocean structures and marine vessels, those resulting from wave impacts are likely to yield the highest loads. Being highly nonlinear, transient and complex, a theoretical analysis of their impact would be impossible without numerical simulations. In this paper,a pressure-split two-stage numerical algorithm is proposed based on Volume Of Fluid (VOF) methodology.The algorithm is characterized by introduction of two pressures at each half and full cycle time step, and thus it is a second-order accurate algorithm in time. A simplified second-order Godunov-type solver is used for the continuity equations. The method is applied to simulation of breaking waves in a 2-D water tank, and a qualitative comparison with experimental photo observations is made. Quite consistent results are observed between simulations and experiments. Commercially available software and Boundary Integral Method (BIM) have also been used to simulate the same problem. The results from present code and BIM are in good agreement with respect to breaking location and timing, while the results obtained from the commercial software which is only first-order accurate in time has clearly showed a temporal and spatial lag, verifying the need to use a higher order numerical scheme.
Directory of Open Access Journals (Sweden)
Shun Zou
2015-02-01
Full Text Available An efficient IBLF-dts scheme is proposed to integrate the bounce-back LBM and FVM scheme to solve the Navier-Stokes equations and the constitutive equation, respectively, for the simulation of viscoelastic fluid flows. In order to improve the efficiency, the bounce-back boundary treatment for LBM is introduced in to improve the grid mapping of LBM and FVM, and the two processes are also decoupled in different time scales according to the relaxation time of polymer and the time scale of solvent Newtonian effect. Critical numerical simulations have been carried out to validate the integrated scheme in various benchmark flows at vanishingly low Reynolds number with open source CFD toolkits. The results show that the numerical solution with IBLF-dts scheme agrees well with the exact solution and the numerical solution with FVM PISO scheme and the efficiency and scalability could be remarkably improved under equivalent configurations.
Finite-volume scheme for anisotropic diffusion
Energy Technology Data Exchange (ETDEWEB)
Es, Bram van, E-mail: bramiozo@gmail.com [Centrum Wiskunde & Informatica, P.O. Box 94079, 1090GB Amsterdam (Netherlands); FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands); Koren, Barry [Eindhoven University of Technology (Netherlands); Blank, Hugo J. de [FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands" 1 (Netherlands)
2016-02-01
In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.
Finite volume renormalization scheme for fermionic operators
Energy Technology Data Exchange (ETDEWEB)
Monahan, Christopher; Orginos, Kostas [JLAB
2013-11-01
We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.
Discretized Volumes in Numerical Methods
Antal, Miklós
2007-01-01
We present two techniques novel in numerical methods. The first technique compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a boundary value problem is sought. We associate a group and a graph to that volume. When the group is symmetry of the boundary value problem under investigation, one can specify the structure of the solution, and find out if there are equispectral volumes of a given type. The second technique uses a complex mapping to transplant the solution from volume to volume and a correction function. Equation for the correction function is given. A simple example demonstrates the feasibility of the suggested method.
Finite volume schemes for Boussinesq type equations
2011-01-01
6 pages, 2 figures, 18 references. Published in proceedings of Colloque EDP-Normandie held at Caen (France), on 28 & 29 October 2010. Other author papers can be dowloaded at http://www.lama.univ-savoie.fr/~dutykh/; Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the m...
Finite volume schemes for Boussinesq type equations
Dutykh, Denys; Mitsotakis, Dimitrios
2011-01-01
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions.
A conservative numerical scheme for solving an autonomous Hamiltonian system
Petrov, A. G.; Uvarov, A. V.
2016-09-01
A new numerical scheme is proposed for solving Hamilton's equations that possesses the properties of symplecticity. Just as in all symplectic schemes known to date, in this scheme the conservation laws of momentum and angular momentum are satisfied exactly. A property that distinguishes this scheme from known schemes is proved: in the new scheme, the energy conservation law is satisfied for a system of linear oscillators. The new numerical scheme is implicit and has the third order of accuracy with respect to the integration step. An algorithm is presented by which the accuracy of the scheme can be increased up to the fifth and higher orders. Exact and numerical solutions to the two-body problem, calculated by known schemes and by the scheme proposed here, are compared.
High resolution finite volume scheme for the quantum hydrodynamic equations
Lin, Chin-Tien; Yeh, Jia-Yi; Chen, Jiun-Yeu
2009-03-01
The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10 -5 to 10 -12. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10 -4. To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were
Simple Numerical Schemes for the Korteweg-deVries Equation
Energy Technology Data Exchange (ETDEWEB)
C. J. McKinstrie; M. V. Kozlov
2000-12-01
Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves.
Towards a Singularity-Proof Scheme in Numerical Relativity
Seidel, E; Seidel, Edward; Suen, Wai-Mo
1992-01-01
Progress in numerical relativity has been hindered for 30 years because of the difficulties of avoiding spacetime singularities in numerical evolution. We propose a scheme which excises a region inside an apparent horizon containing the singularity. Two major ingredients of the scheme are the use of a horizon-locking coordinate and a finite differencing which respects the causal structure of the spacetime. Encouraging results of the scheme in the spherical collapse case are given.
A numerical relativity scheme for cosmological simulations
Daverio, David; Mitsou, Ermis
2016-01-01
Fully non-linear cosmological simulations may prove relevant in understanding relativistic/non-linear features and, therefore, in taking full advantage of the upcoming survey data. We propose a new 3+1 integration scheme which is based on the presence of a perfect fluid (hydro) field, evolves only physical states by construction and passes the robustness test on an FLRW space-time. Although we use General Relativity as an example, the idea behind that scheme is applicable to any generally-covariant modified gravity theory and/or matter content, including a N-body sector.
A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling.
Boileau, Etienne; Nithiarasu, Perumal; Blanco, Pablo J; Müller, Lucas O; Fossan, Fredrik Eikeland; Hellevik, Leif Rune; Donders, Wouter P; Huberts, Wouter; Willemet, Marie; Alastruey, Jordi
2015-10-01
Haemodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1D numerical schemes has led to the development of alternative experimental setups and the use of three-dimensional numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1D scheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1D blood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensional numerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1D models and numerical schemes.
Numerical Differentiation and Integration through Aitken-Neville Schemes
Directory of Open Access Journals (Sweden)
Ramesh Kumar Muthumalai
2013-09-01
Full Text Available Some new formulas are given to approximate higher order derivatives and integrals through Aitken-Neville iterative schemes for arbitrary spaced grids. An algorithm is given in MATLAB for numerical differentiation. Also, numerical examples are provided to study error analysis of new formulas for numerical differentiation and integration.
Hybrid flux splitting schemes for numerical resolution of two-phase flows
Energy Technology Data Exchange (ETDEWEB)
Flaatten, Tore
2003-07-01
This thesis deals with the construction of numerical schemes for approximating. solutions to a hyperbolic two-phase flow model. Numerical schemes for hyperbolic models are commonly divided in two main classes: Flux Vector Splitting (FVS) schemes which are based on scalar computations and Flux Difference Splitting (FDS) schemes which are based on matrix computations. FVS schemes are more efficient than FDS schemes, but FDS schemes are more accurate. The canonical FDS schemes are the approximate Riemann solvers which are based on a local decomposition of the system into its full wave structure. In this thesis the mathematical structure of the model is exploited to construct a class of hybrid FVS/FDS schemes, denoted as Mixture Flux (MF) schemes. This approach is based on a splitting of the system in two components associated with the pressure and volume fraction variables respectively, and builds upon hybrid FVS/FDS schemes previously developed for one-phase flow models. Through analysis and numerical experiments it is demonstrated that the MF approach provides several desirable features, including (1) Improved efficiency compared to standard approximate Riemann solvers, (2) Robustness under stiff conditions, (3) Accuracy on linear and nonlinear phenomena. In particular it is demonstrated that the framework allows for an efficient weakly implicit implementation, focusing on an accurate resolution of slow transients relevant for the petroleum industry. (author)
Diffusion and dispersion of numerical schemes for Hyperbolic problems
Petit, H.A.H
2001-01-01
In the following text an overview is given of numerical schemes which can be used to solve hyperbolic partial differential equations. The overview is far from extensive and the analysis of the schemes is limited to the application on the simplest hyperbolic equation conceivable, namely the so called
A finite-volume scheme for a kidney nephron model
Directory of Open Access Journals (Sweden)
Seguin Nicolas
2012-04-01
Full Text Available We present a finite volume type scheme to solve a transport nephron model. The model consists in a system of transport equations with specific boundary conditions. The transport velocity is driven by another equation that can undergo sign changes during the transient regime. This is the main difficulty for the numerical resolution. The scheme we propose is based on an explicit resolution and is stable under a CFL condition which does not depend on the stiffness of source terms. Nous présentons un schéma numérique de type volume fini que l’on applique à un modèle de transport dans le néphron. Ce modèle consiste en un système d’équations de transport, avec des conditions aux bords spécifiques. La vitesse du transport est la solution d’un autre système d’équation et peut changer de signe au cours du régime transitoire. Ceci constitue la principale difficulté pour la résolution numérique. Le schéma proposé, basé sur une résolution explicite, est stable sous une condition CFL non restrictive.
Numeric Analysis for Relationship-Aware Scalable Streaming Scheme
Directory of Open Access Journals (Sweden)
Heung Ki Lee
2014-01-01
Full Text Available Frequent packet loss of media data is a critical problem that degrades the quality of streaming services over mobile networks. Packet loss invalidates frames containing lost packets and other related frames at the same time. Indirect loss caused by losing packets decreases the quality of streaming. A scalable streaming service can decrease the amount of dropped multimedia resulting from a single packet loss. Content providers typically divide one large media stream into several layers through a scalable streaming service and then provide each scalable layer to the user depending on the mobile network. Also, a scalable streaming service makes it possible to decode partial multimedia data depending on the relationship between frames and layers. Therefore, a scalable streaming service provides a way to decrease the wasted multimedia data when one packet is lost. However, the hierarchical structure between frames and layers of scalable streams determines the service quality of the scalable streaming service. Even if whole packets of layers are transmitted successfully, they cannot be decoded as a result of the absence of reference frames and layers. Therefore, the complicated relationship between frames and layers in a scalable stream increases the volume of abandoned layers. For providing a high-quality scalable streaming service, we choose a proper relationship between scalable layers as well as the amount of transmitted multimedia data depending on the network situation. We prove that a simple scalable scheme outperforms a complicated scheme in an error-prone network. We suggest an adaptive set-top box (AdaptiveSTB to lower the dependency between scalable layers in a scalable stream. Also, we provide a numerical model to obtain the indirect loss of multimedia data and apply it to various multimedia streams. Our AdaptiveSTB enhances the quality of a scalable streaming service by removing indirect loss.
NUMERICAL SIMULATIONS OF SEA ICE WITH DIFFERENT ADVECTION SCHEMES
Institute of Scientific and Technical Information of China (English)
LIU Xi-ying
2011-01-01
Numerical simulations are carried out for sea ice with four different advection schemes to study their effects on the simulation results.The sea ice model employed here is the Sea Ice Simulator (SIS) of the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model version 4b (MOM4b) and the four advection schemes are, the upwind scheme originally used in the SIS, the Multi-Dimensional Positive Advection (MDPA) scheme, the Incremental Remapping Scheme (IRS) and the Two Step Shape Preserving (TSSP) scheme.The latter three schemes are newly introduced.To consider the interactions between sea ice and ocean, a mixed layer ocean model is introduced and coupled to the SIS.The coupled model uses a tri-polar coordinate with 120×65 grids,covering the whole earth globe, in the horizontal plane.Simulation results in the northern high latitudes are analyzed.In all simulations, the model reproduces the seasonal variation of sea ice in the northern high latitudes well.Compared with the results from the observation, the sea ice model produces some extra sea ice coverage in the Greenland Sea and Barents Sea in winter due to the exclusion of ocean current effects and the smaller simulated sea ice thickness in the Arctic basin.There are similar features among the results obtained with the introduced three advection schemes.The simulated sea ice thickness with the three newly introduced schemes are all smaller than that of the upwind scheme and the simulated sea ice velocities of movement are all smaller than that of the upwind scheme.There are more similarities shared in the results obtained with the MPDA and TSSP schemes.
The Numerical Scheme Development of a Simplified Frozen Soil Model
Institute of Scientific and Technical Information of China (English)
LI Qian; SUN Shufen; DAI Qiudan
2009-01-01
In almost all frozen soil models used currently,three variables of temperature,ice content and moisture content are used as prognostic variables and the rate term,accounting for the contribution of the phase change between water and ice,is shown explicitly in both the energy and mass balance equations.The models must be solved by a numerical method with an iterative process,and the rate term of the phase change needs to be pre-estimated at the beginning in each iteration step.Since the rate term of the phase change in the energy equation is closely related to the release or absorption of the great amount of fusion heat,a small error in the rate term estimation will introduce greater error in the energy balance,which will amplify the error in the temperature calculation and in turn,cause problems for the numerical solution convergence.In this work,in order to first reduce the trouble,the methodology of the variable transformation is applied to a simplified frozen soil model used currently,which leads to new frozen soil scheme used in this work.In the new scheme,the enthalpy and the total water equivalent are used as predictive variables in the governing equations to replace temperature,volumetric soil moisture and ice content used in many current models.By doing so,the rate terms of the phase change are not shown explicitly in both the mass and energy equations and its pre-estimation is avoided.Secondly,in order to solve this new scheme more functionally,the development of the numerical scheme to the new scheme is described and a numerical algorithm appropriate to the numerical scheme is developed.In order to evaluate the new scheme of the frozen soil model and its relevant algorithm,a series of model evaluations are conducted by comparing numerical results from the new model scheme with three observational data sets.The comparisons show that the results from the model are in good agreement with these data sets in both the change trend of variables and their
Institute of Scientific and Technical Information of China (English)
QingdongCAI
1999-01-01
A new technique in the formulation of numerical scheme for hyperbolic equation is developed.It is different from the classical FD and FE methods.We begin with the algebraic equations with some undefined parameters,and get the difference equation through Taylor-series expansion.When the parameters in the partial difference equation are defined,the equation is what the scheme will simulated.The numerical example of the viscous BUrgers equation shows the validity of the scheme.This method deals with the numerical viscosity and dispersion exactly ,giving a preliminary explanation to some problems that the CFD face now.
Finite-volume WENO scheme for viscous compressible multicomponent flows
Coralic, Vedran; Colonius, Tim
2014-01-01
We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin. PMID:25110358
Al Jarro, Ahmed
2012-11-01
An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.
Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions
Institute of Scientific and Technical Information of China (English)
2008-01-01
Based on a linear finite element space,two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and analyzed.Some relationships between the finite element method and the finite difference method are addressed,too.
Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions
Institute of Scientific and Technical Information of China (English)
DAI Xiaoying; YANG Zhang; ZHOU Aihui
2008-01-01
Based on a linear finite element space, two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and analyzed. Some relationships between the finite element method and the finite difference method are addressed, too.
Numerical Comparison of Optimal Charging Schemes for Electric Vehicles
DEFF Research Database (Denmark)
You, Shi; Hu, Junjie; Pedersen, Anders Bro
2012-01-01
The optimal charging schemes for Electric vehicles (EV) generally differ from each other in the choice of charging periods and the possibility of performing vehicle-to-grid (V2G), and have different impacts on EV economics. Regarding these variations, this paper presents a numerical comparison...
Energy Technology Data Exchange (ETDEWEB)
Lin Jaeyuh [Chang Jung Univ., Tainan (Taiwan, Province of China); Chen Hantaw [National Cheng Kung Univ., Tainan (Taiwan, Province of China). Dept. of Mechanical Engineering
1997-09-01
A hybrid numerical scheme combining the Laplace transform and control-volume methods is presented to solve nonlinear two-dimensional phase-change problems with the irregular geometry. The Laplace transform method is applied to deal with the time domain, and then the control-volume method is used to discretize the transformed system in the space domain. Nonlinear terms induced by the temperature-dependent thermal properties are linearized by using the Taylor series approximation. Control-volume meshes in the solid and liquid regions during simulations are generated by using the discrete transfinite mapping method. The location of the phase-change interface and the isothermal distributions are determined. Comparison of these results with previous results shows that the present numerical scheme has good accuracy for two-dimensional phase-change problems. (orig.). With 10 figs.
Entropy Stable Numerical Schemes for Two-Fluid Plasma Equations
Kumar, Harish
2011-01-01
Two-fluid ideal plasma equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of their non-linear nature and the presence of stiff source terms, especially for high charge to mass ratios and for low Larmor radii. In this article, we design entropy stable finite difference schemes for the two-fluid equations by combining entropy conservative fluxes and suitable numerical diffusion operators. Furthermore, to overcome the time step restrictions imposed by the stiff source terms, we devise time-stepping routines based on implicit-explicit (IMEX)-Runge Kutta (RK) schemes. The special structure of the two-fluid plasma equations is exploited by us to design IMEX schemes in which only local (in each cell) linear equations need to be solved at each time step. Benchmark numerical experiments are presented to illustrate the robustness and accuracy of these schem...
Convergence of discrete duality finite volume schemes for the cardiac bidomain model
Andreianov, Boris; Karlsen, Kenneth H; Pierre, Charles
2010-01-01
We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the heart. Both time-implicit and linearised time-implicit schemes are treated. A short description is given of the 3D DDFV meshes and of some of the associated discrete calculus tools. Several numerical tests are presented.
A finite volume scheme for the transport of radionucleides in porous media
Chénier, Eric; Eymard,, Robert; Nicolas, Xavier
2004-01-01
International audience; The COUPLEX1 Test case (Bourgeat et al., 2003) is devoted to the comparison of numerical schemes on a convection-diffusion-reaction problem. We first show that the results of the simulation can be mainly predicted by a simple analysis of the data. A finite volume scheme, with three different treatments of the convective term, is then shown to deliver accurate and stable results under a low computational cost.
Triviality of $\\varphi^4$ theory in a finite volume scheme adapted to the broken phase
Siefert, Johannes
2014-01-01
We study the standard one-component $\\varphi^4$-theory in four dimensions. A renormalized coupling is defined in a finite size renormalization scheme which becomes the standard scheme of the broken phase for large volumes. Numerical simulations are reported using the worm algorithm in the limit of infinite bare coupling. The cutoff dependence of the renormalized coupling closely follows the perturbative Callan Symanzik equation and the triviality scenario is hence further supported.
A Finite Volume Scheme on the Cubed Sphere Grid
Putman, William M.; Lin, S. J.
2008-01-01
The performance of a multidimensional finite-volume scheme for global atmospheric dynamics is evaluated on the cubed-sphere geometry. We will explore the properties of the finite volume scheme through traditional advection and shallow water test cases. Baroclinic evaluations performed via a recently developed deterministic initial value baroclinic test case from Jablonowski and Williamson that assesses the evolution of an idealized baroclinic wave in the Northern Hemisphere for a global 3-dimensional atmospheric dynamical core. Comparisons will be made when available to the traditional latitude longitude discretization of the finite-volume dynamical core, as well as other traditional gridpoint and spectral formulations for atmospheric dynamical cores.
Optimal Numerical Schemes for Compressible Large Eddy Simulations
Edoh, Ayaboe; Karagozian, Ann; Sankaran, Venkateswaran; Merkle, Charles
2014-11-01
The design of optimal numerical schemes for subgrid scale (SGS) models in LES of reactive flows remains an area of continuing challenge. It has been shown that significant differences in solution can arise due to the choice of the SGS model's numerical scheme and its inherent dissipation properties, which can be exacerbated in combustion computations. This presentation considers the individual roles of artificial dissipation, filtering, secondary conservation (Kinetic Energy Preservation), and collocated versus staggered grid arrangements with respect to the dissipation and dispersion characteristics and their overall impact on the robustness and accuracy for time-dependent simulations of relevance to reacting and non-reacting LES. We utilize von Neumann stability analysis in order to quantify these effects and to determine the relative strengths and weaknesses of the different approaches. Distribution A: Approved for public release, distribution unlimited. Supported by AFOSR (PM: Dr. F. Fahroo).
Numerical Evaluation of CPV Boundary Integrals with Symmetrical Quadrature Schemes
Institute of Scientific and Technical Information of China (English)
马杭; 徐凯宇
2003-01-01
Stemming from the definition of the Cauchy principal values (CPV) integrals, a newly developed symmetrical quadrature scheme was proposed in the paper for the accurate numerical evaluation of the singular boundary integrals in the sense of CPV encountered in the boundary element method. In the case of inner-element singularities, the CPV integrals could be evaluated in a straightforward way by dividing the element into the symmetrical part and the remainder(s). And in the case of end-singularities, the CPV integrals could be evaluated simply by taking a tangential distance transformation of the integrand after cutting out a symmetrical tiny zone around the singular point. In both cases, the operations are no longer necessary before the numerical implementation, which involves the dull routine work to separate out singularities from the integral kernels. Numerical examples were presented for both the two-and the three-dimensional boundary integrals in elasticity. Comparing the numerical results with those by other approaches demonstrates the feasibility and the effectiveness of the proposed scheme.
Finite volume schemes for dispersive wave propagation and runup
Dutykh, Denys; Katsaounis, Theodoros; Mitsotakis, Dimitrios
2011-04-01
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves.
Finite volume schemes for dispersive wave propagation and runup
Dutykh, Denys; Mitsotakis, Dimitrios
2010-01-01
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves.
Stability of Semi-implicit Finite Volume Scheme for Level Set Like Equation
Institute of Scientific and Technical Information of China (English)
Kim Kwang-il; Son Yong-chol
2015-01-01
We study numerical methods for level set like equations arising in im-age processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equation (image selective smoothing model) given by Alvarez et al. (Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer. Anal., 1992, 29: 845–866). Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes, unconditionally stable in L∞ and W 1,2 (W 1,1) sense in isotropic (anisotropic) diffu-sion domain.
Institute of Scientific and Technical Information of China (English)
Min LIU; Keqi WU
2008-01-01
Based on the immersed boundary method (IBM) and the finite volume optimized pre-factored compact (FVOPC) scheme, a numerical simulation of noise propagation inside and outside the casing of a cross flow fan is estab-lished. The unsteady linearized Euler equations are solved to directly simulate the aero-acoustic field. In order to validate the FVOPC scheme, a simulation case: one dimensional linear wave propagation problem is carried out using FVOPC scheme, DRP scheme and HOC scheme. The result of FVOPC is in good agreement with the ana-lytic solution and it is better than the results of DRP and HOC schemes, the FVOPC is less dispersion and dissi-pation than DRP and HOC schemes. Then, numerical simulation of noise propagation problems is performed. The noise field of 36 compact rotating noise sources is obtained with the rotating velocity of 1000r/min. The PML absorbing boundary condition is applied to the sound far field boundary condition for depressing the numerical reflection. Wall boundary condition is applied to the casing. The results show that there are reflections on the casing wall and sound wave interference in the field. The FVOPC with the IBM is suitable for noise propagation problems under the complex geometries for depressing the dispersion and dissipation, and also keeping the high order precision.
An Energy Preserving Monolithic Eulerian Fluid-Structure Numerical Scheme
Pironneau, Olivier
2016-01-01
The conservation laws of continuum mechanic written in an Eulerian frame make no difference between fluids and solids except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials of energy for hyperelastic solids. By taking the velocities as unknown , monolithic methods for fluid structure interactions (FSI) are built. In this article such a formulation is analyzed when the fluid is compressible and the fluid is incompressible. The idea is not new but the progress of mesh generators and numerical schemes like the Characteristics-Galerkin method render this approach feasible and reasonably robust. In this article the method and its discretization are presented, stability is discussed by through an energy estimate. A numerical section discusses implementation issues and presents a few simple tests.
2014-11-01
for Time Accurate Compressible Large Eddy Simulations : Comparison of Artificial Dissipation and Filtering Schemes 5b. GRANT NUMBER 5c. PROGRAM...Optimal Numerical Schemes for Time Accurate Compressible Large Eddy Simulations : Comparison of Artificial Dissipation and Filtering Schemes 67th
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
Ueckermann, M. P.; Lermusiaux, P. F. J.; Sapsis, T. P.
2013-01-01
The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier-Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.
A Numerical Scheme for Invariant Distributions of Constrained Diffusions
Budhiraja, Amarjit; Rubenthaler, Sylvain
2012-01-01
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the corresponding stochastic networks and thus it is important to develop reliable and efficient algorithms for numerical computation of such distributions. In this work we propose and analyze a Monte-Carlo scheme based on an Euler type discretization of the reflected stochastic differential equation using a single sequence of time discretization steps which decrease to zero as time approaches infinity. Appropriately weighted empirical measures constructed from the simulated discretized reflected diffusion are proposed as approximations for the invariant probability measure of the true diffusion model. Almost sure consistency results are established that in particular show that weighted averages of polynomially growing continuous functionals evaluated on the discretized simulate...
Alleviating the window problem in large volume renormalization schemes
Korcyl, Piotr
2017-01-01
We propose a strategy for large volume non-perturbative renormalization which alleviates the window problem by reducing cut-off effects. We perform a proof-of-concept study using position space renormalization scheme and the CLS $N_f=2+1$ ensembles generated at 5 different lattice spacings. We show that in the advocated strategy results for the renormalization constants are to a large extend independent of the specific lattice direction used to define the renormalization condition. Hence, ver...
Jones, T W
2005-01-01
We have developed a new, very efficient numerical scheme to solve the CR diffusion convection equation that can be applied to the study of the nonlinear time evolution of CR modified shocks for arbitrary spatial diffusion properties. The efficiency of the scheme derives from its use of coarse-grained finite momentum volumes. This approach has enabled us, using $\\sim 10 - 20$ momentum bins spanning nine orders of magnitude in momentum, to carry out simulations that agree well with results from simulations of modified shocks carried out with our conventional finite difference scheme requiring more than an order of magnitude more momentum points. The coarse-grained, CGMV scheme reduces execution times by a factor approximately half the ratio of momentum bins used in the two methods. Depending on the momentum dependence of the diffusion, additional economies in required spatial and time resolution can be utilized in the CGMV scheme, as well. These allow a computational speed-up of at least an order of magnitude i...
A quasi-positive family of continuous Darcy-flux finite-volume schemes with full pressure support
Edwards, Michael G.; Zheng, Hongwen
2008-11-01
A new family of flux-continuous, locally conservative, finite-volume schemes is presented for solving the general tensor pressure equation of subsurface flow in porous media. The new schemes have full pressure continuity imposed across control-volume faces. Previous families of flux-continuous schemes are point-wise continuous in pressure and flux. When applying the earlier point-wise flux-continuous schemes to strongly anisotropic full-tensor fields their failure to satisfy a maximum principle (as with other FEM and finite-volume methods) can result in loss of local stability for high anisotropy ratios which can cause strong spurious oscillations in the numerical pressure solution. An M-matrix analysis reveals the upper limits for guaranteeing a maximum principle for general 9-point schemes and aids in the design of schemes that minimize the occurrence of spurious oscillations in the discrete pressure field. The full pressure continuity schemes are shown to possess a larger range of flux-continuous schemes, than the previous point-wise counter parts. For strongly anisotropic full-tensor cases it is shown that the full quadrature range possessed by the new schemes permits these schemes to exploit quadrature points (previously out of range) that are shown to minimize spurious oscillations in discrete pressure solutions. The new formulation leads to a more robust quasi-positive family of flux-continuous schemes applicable to general discontinuous full-tensor fields.
Analysis of triangular C-grid finite volume scheme for shallow water flows
Shirkhani, Hamidreza; Mohammadian, Abdolmajid; Seidou, Ousmane; Qiblawey, Hazim
2015-08-01
In this paper, a dispersion relation analysis is employed to investigate the finite volume triangular C-grid formulation for two-dimensional shallow-water equations. In addition, two proposed combinations of time-stepping methods with the C-grid spatial discretization are investigated. In the first part of this study, the C-grid spatial discretization scheme is assessed, and in the second part, fully discrete schemes are analyzed. Analysis of the semi-discretized scheme (i.e. only spatial discretization) shows that there is no damping associated with the spatial C-grid scheme, and its phase speed behavior is also acceptable for long and intermediate waves. The analytical dispersion analysis after considering the effect of time discretization shows that the Leap-Frog time stepping technique can improve the phase speed behavior of the numerical method; however it could not damp the shorter decelerated waves. The Adams-Bashforth technique leads to slower propagation of short and intermediate waves and it damps those waves with a slower propagating speed. The numerical solutions of various test problems also conform and are in good agreement with the analytical dispersion analysis. They also indicate that the Adams-Bashforth scheme exhibits faster convergence and more accurate results, respectively, when the spatial and temporal step size decreases. However, the Leap-Frog scheme is more stable with higher CFL numbers.
Norman, Michael L; So, Geoffrey C; Harkness, Robsert P
2013-01-01
We describe an extension of the {\\em Enzo} code to enable the direct numerical simulation of inhomogeneous reionization in large cosmological volumes. By direct we mean all dynamical, radiative, and chemical properties are solved self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation, which we calibrate to observations. The numerical method presented is a modification of an earlier method presented in Reynolds et al. Radiation transport is done in the grey flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the {\\em hypre} optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a gri...
A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers
Bagci, Hakan
2015-01-07
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability
A new numerical scheme for the simulation of active magnetic regenerators
DEFF Research Database (Denmark)
Torregrosa-Jaime, B.; Engelbrecht, Kurt; Payá, J.;
2014-01-01
A 1D model of a parallel-plate active magnetic regenerator (AMR) has been developed based on a new numerical scheme. With respect to the implicit scheme, the new scheme achieves accurate results, minimizes computational time and prevents numerical errors. The model has been used to check the boun...
Variationally consistent discretization schemes and numerical algorithms for contact problems
Wohlmuth, Barbara
We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal-dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration schemes. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of
Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme
Lee, Duck-Joo; Hwang, Chang-Jeon; Ko, Duck-Kon; Kim, Jae-Wook
1995-01-01
Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.
Energy Technology Data Exchange (ETDEWEB)
Ismagilov, Timur Z., E-mail: ismagilov@academ.org
2015-02-01
This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.
The hybrid Eulerian Lagrangian numerical scheme tested with Chemistry
Directory of Open Access Journals (Sweden)
A. B. Hansen
2012-11-01
Full Text Available A newly developed advection scheme, the Hybrid Eulerian Lagrangian (HEL scheme, has been tested, including a module for atmospheric chemistry, including 58 chemical species, and compared to two other traditional advection schemes; a classical pseudospectral Eulerian method the Accurate Space Derivative (ASD scheme and the bi-cubic semi-Lagrangian (SL scheme using classical rotation tests. The rotation tests have been designed to test and compare the advection schemes for different spatial and temporal resolutions in different chemical conditions (rural and urban and for different shapes (cone and slotted cylinder giving the advection schemes different challenges with respect to relatively slow or fast chemistry and smooth or sharp gradients, respectively. In every test, error measures have been calculated and used for ranking of the advection schemes with respect to performance, i.e. lowest overall errors for all chemical species. Furthermore, the HEL and SL schemes have been compared in a shallow water model, demonstrating the performance in a more realistic non-linear deformation flow.
The results in this paper show that the new advection scheme, HEL, by far outperforms both the Eulerian and semi-Lagrangian schemes with very low error estimates compared to the two other schemes. Although no analytic solution can be obtained for the performance in the non-linear shallow water model flow, the tracer distribution appears realistic as compared to LMCSL when a mixing between local parcel concentrations is introduced in HEL.
Teaching Thermal Hydraulics & Numerical Methods: An Introductory Control Volume Primer
Energy Technology Data Exchange (ETDEWEB)
D. S. Lucas
2004-10-01
A graduate level course for Thermal Hydraulics (T/H) was taught through Idaho State University in the spring of 2004. A numerical approach was taken for the content of this course since the students were employed at the Idaho National Laboratory and had been users of T/H codes. The majority of the students had expressed an interest in learning about the Courant Limit, mass error, semi-implicit and implicit numerical integration schemes in the context of a computer code. Since no introductory text was found the author developed notes taught from his own research and courses taught for Westinghouse on the subject. The course started with a primer on control volume methods and the construction of a Homogeneous Equilibrium Model (HEM) (T/H) code. The primer was valuable for giving the students the basics behind such codes and their evolution to more complex codes for Thermal Hydraulics and Computational Fluid Dynamics (CFD). The course covered additional material including the Finite Element Method and non-equilibrium (T/H). The control volume primer and the construction of a three-equation (mass, momentum and energy) HEM code are the subject of this paper . The Fortran version of the code covered in this paper is elementary compared to its descendants. The steam tables used are less accurate than the available commercial version written in C Coupled to a Graphical User Interface (GUI). The Fortran version and input files can be downloaded at www.microfusionlab.com.
Derivation and Application of a Linear Multistep Numerical Scheme
Directory of Open Access Journals (Sweden)
Abdulrahman NDANUSA
2007-01-01
Full Text Available A great many physical occurrences give rise to problems that often result in differential equations. When we solve a differential equation, we are in effect solving the physical problem it represents. Traditionally, solutions to differential equations were derived using analytical or exact methods. These solutions are often useful as they provide excellent insight into the behavior of some systems. However, certain differential equations are very difficult to solve by any means other than an approximate solution by the application of numerical methods. These methods can be classified into two thus: One-step and multistep methods. However, in this work, our focus is on a class of multistep methods known as the Linear Multi-step Methods. We thus use Taylor series expansion to derive a linear multistep method of order eight. The method is tested for consistency and zero-stability in order to establish its convergence. Also, provided are some examples of problems solved using the new scheme, and the results compared with exact solution.
Bernuzzi, Sebastiano; Dietrich, Tim
2016-09-01
The theoretical modeling of gravitational waveforms from binary neutron star mergers requires precise numerical relativity simulations. Assessing convergence of the numerical data and building the error budget is currently challenging due to the low accuracy of general-relativistic hydrodynamics schemes and to the grid resolutions that can be employed in (3 +1 )-dimensional simulations. In this work, we explore the use of high-order weighted-essentially-nonoscillatory (WENO) schemes in neutron star merger simulations and investigate the accuracy of the waveforms obtained with such methods. We find that high-order WENO schemes can be robustly employed for simulating the inspiral-merger phase and they significantly improve the assessment of the waveform's error budget with respect to finite-volume methods. High-order WENO schemes can be thus efficiently used for high-quality waveform production, and in future large-scale investigations of the binary parameter space.
Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case
Energy Technology Data Exchange (ETDEWEB)
Fernández-Nieto, Enrique D., E-mail: edofer@us.es [Departamento de Matemática Aplicada I, Universidad de Sevilla, E.T.S. Arquitectura, Avda, Reina Mercedes, s/n, 41012 Sevilla (Spain); Gallardo, José M., E-mail: jmgallardo@uma.es [Departamento de Análisis Matemático, Universidad de Málaga, F. Ciencias, Campus Teatinos S/N (Spain); Vigneaux, Paul, E-mail: Paul.Vigneaux@math.cnrs.fr [Unitée de Mathématiques Pures et Appliquées, Ecole Normale Supérieure de Lyon, 46 allée d' Italie, 69364 Lyon Cedex 07 (France)
2014-05-01
This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez–Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.
Energy-preserving numerical schemes of high accuracy for one-dimensional Hamiltonian systems
Cieśliński, Jan L
2011-01-01
We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete gradient schemes and integrators of arbitrary high order. In numerical experiments we compare our integrators with some other numerical schemes, including the standard discrete gradient method, the leap-frog scheme and a symplectic scheme of 4th order. We study the error accumulation for very long time and the conservation of the energy integral.
Mishra, Siddhartha
2011-01-01
Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating conservation laws do not take into account this fact and converge to solutions that are not necessarily physically relevant. We design numerical schemes that incorporate explicit information about the underlying viscosity mechanism and approximate the physically relevant solution. Numerical experiments illustrating the robust performance of these schemes are presented.
Neusser, Jochen
2015-01-01
We present a numerical scheme for immiscible two-phase flows with one compressible and one incompressible phase. Special emphasis lies in the discussion of the coupling strategy for compressible and incompressible Euler equations to simulate inviscid liquid-vapour flows. To reduce the computational effort further, we also introduce two approximate coupling strategies. The resulting schemes are compared numerically to a fully compressible scheme and show good agreement with these standard algorithm at lower numerical costs.
WHAM: A WENO-based general relativistic numerical scheme I: Hydrodynamics
Tchekhovskoy, Alexander; Narayan, Ramesh
2007-01-01
Active galactic nuclei, x-ray binaries, pulsars, and gamma-ray bursts are all believed to be powered by compact objects surrounded by relativistic plasma flows driving phenomena such as accretion, winds, and jets. These flows are often accurately modelled by the relativistic magnetohydrodynamics (MHD) approximation. Time-dependent numerical MHD simulations have proven to be especially insightful, but one regime that remains difficult to simulate is when the energy scales (kinetic, thermal, magnetic) within the plasma become disparate. We develop a numerical scheme that significantly improves the accuracy and robustness of the solution in this regime. We use a modified form of the WENO method to construct a finite-volume general relativistic hydrodynamics code called WHAM that converges at fifth order. We avoid (1) field-by-field decomposition by adaptively reducing down to 2-point stencils near discontinuities for a more accurate treatment of shocks, and (2) excessive reduction to low order stencils, as in th...
Some considerations on numerical schemes for treating hyperbolicity issues in two-layer models
Sarno, L.; Carravetta, A.; Martino, R.; Papa, M. N.; Tai, Y.-C.
2017-02-01
Multi-layer depth-averaged models are widely employed in various hydraulic engineering applications. Yet, such models are not strictly hyperbolic. Their equation systems typically lose hyperbolicity when the relative velocities between layers become too large, which is associated with Kelvin-Helmholtz instabilities involving turbulent momentum exchanges between the layers. Focusing on the two-layer case, we present a numerical improvement that locally avoids the loss of hyperbolicity. The proposed modification introduces an additional momentum exchange between layers, whose value is iteratively calculated to be strictly sufficient to keep the system hyperbolic. The approach can be easily implemented in any finite volume scheme and there is no limitation concerning the density ratio between layers. Numerical examples, employing both HLL-type and Roe-type approximate Riemann solvers, are reported to validate the method and its key features.
ADER-WENO finite volume schemes with space-time adaptive mesh refinement
Dumbser, Michael; Zanotti, Olindo; Hidalgo, Arturo; Balsara, Dinshaw S.
2013-09-01
We present the first high order one-step ADER-WENO finite volume scheme with adaptive mesh refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resulting algorithm is particularly well suited for an AMR strategy on space-time adaptive meshes, i.e. with time-accurate local time stepping. The AMR property has been implemented 'cell-by-cell', with a standard tree-type algorithm, while the scheme has been parallelized via the message passing interface (MPI) paradigm. The new scheme has been tested over a wide range of examples for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations of compressible gas dynamics and the equations of magnetohydrodynamics (MHD). High order in space and time have been confirmed via a numerical convergence study and a detailed analysis of the computational speed-up with respect to highly refined uniform meshes is also presented. We also show test problems where the presented high order AMR scheme behaves clearly better than traditional second order AMR methods. The proposed scheme that combines for the first time high order ADER methods with space-time adaptive grids in two and three space dimensions is likely to become a useful tool in several fields of computational physics, applied mathematics and mechanics.
Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model.
Wang, Xiaofei; Fullana, Jose-Maria; Lagrée, Pierre-Yves
2015-01-01
A reliable and fast numerical scheme is crucial for the 1D simulation of blood flow in compliant vessels. In this paper, a 1D blood flow model is incorporated with a Kelvin-Voigt viscoelastic arterial wall. This leads to a nonlinear hyperbolic-parabolic system, which is then solved with four numerical schemes, namely: MacCormack, Taylor-Galerkin, monotonic upwind scheme for conservation law and local discontinuous Galerkin. The numerical schemes are tested on a single vessel, a simple bifurcation and a network with 55 arteries. The numerical solutions are checked favorably against analytical, semi-analytical solutions or clinical observations. Among the numerical schemes, comparisons are made in four important aspects: accuracy, ability to capture shock-like phenomena, computational speed and implementation complexity. The suitable conditions for the application of each scheme are discussed.
PROGRESS IN THE STUDY OF RETROSPECTIVE NUMERICAL SCHEME AND THE CLIMATE PREDICTION
Institute of Scientific and Technical Information of China (English)
DONG Wenjie; CHOU Jieming; FENG Guolin
2004-01-01
The retrospective numerical scheme (RNS) is a numerical computation scheme designed for multiple past value problems of the initial value in mathematics and considering the selfmemory property of the system in physics. This paper briefly presents the historical background of RNS, elaborates the relation of the scheme with other difference schemes and other meteorological prediction methods, and introduces the application of RNS to the regional climatic self-memory model,simplified climate model, barotropic model, spectral model, and mesoscale model. At last, the paper sums up and points out the application perspective of the scheme and the direction for the future study.
Implicit numerical schemes for the stochastic Liouville equation in Langevin form.
Håkansson, Pär; Nair, Prasanth B
2011-05-28
We present and numerically test implicit as well as explicit numerical schemes for solving the Stochastic Liouville Equation in Langevin form. It is found that implicit schemes provide significant gain in robustness, for example, when nonsecular Hamiltonian terms cannot be ignored in electron and nuclear spin resonance. Implicit schemes open up several spectroscopic relaxation problems for direct interpretation using the Stochastic Liouville Equation. To illustrate the proposed numerical schemes, studies are presented for an electron paramagnetic resonance problem involving a coordinated copper complex and a fluorescence problem.
Energy Technology Data Exchange (ETDEWEB)
Park, Ju Yeop; In, Wang Kee; Chun, Tae Hyun; Oh, Dong Seok [Korea Atomic Energy Research Institute, Taejeon (Korea)
2000-02-01
The development of orthogonal 2-dimensional numerical code is made. The present code contains 9 kinds of turbulence models that are widely used. They include a standard k-{epsilon} model and 8 kinds of low Reynolds number ones. They also include 6 kinds of numerical schemes including 5 kinds of low order schemes and 1 kind of high order scheme such as QUICK. To verify the present numerical code, pipe flow, channel flow and expansion pipe flow are solved by this code with various options of turbulence models and numerical schemes and the calculated outputs are compared to experimental data. Furthermore, the discretization error that originates from the use of standard k-{epsilon} turbulence model with wall function is much more diminished by introducing a new grid system than a conventional one in the present code. 23 refs., 58 figs., 6 tabs. (Author)
Some Numerical Quadrature Schemes of a Non-conforming Quadrilateral Finite Element
Institute of Scientific and Technical Information of China (English)
Xiao-fei GUAN; Ming-xia LI; Shao-chun CHEN
2012-01-01
Numerical quadrature schemes of a non-conforming finite element method for general second order elliptic problems in two dimensional (2-D) and three dimensional (3-D) space are discussed in this paper.We present and analyze some optimal numerical quadrature schemes. One of the schemes contains only three sampling points,which greatly improves the efficiency of numerical computations.The optimal error estimates are derived by using some traditional approaches and techniques.Lastly,some numerical results are provided to verify our theoretical analysis.
HARM A Numerical Scheme for General Relativistic Magnetohydrodynamics
Gammie, C F; Tóth, G; Gammie, Charles F.; Kinney, Jonathan C. Mc
2003-01-01
We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, and van Leer scheme. A variant of constrained transport, proposed earlier by T\\'oth, is used to maintain a divergence free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.
A class of the fourth order finite volume Hermite weighted essentially non-oscillatory schemes
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper,we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory(HWENO)schemes based on the work(Computers&Fluids,34:642-663(2005))by Qiu and Shu,with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws.The key idea of HWENO is to evolve both with the solution and its derivative,which allows for using Hermite interpolation in the reconstruction phase,resulting in a more compact stencil at the expense of the additional work.The main difference between this work and the formal one is the procedure to reconstruct the derivative terms.Comparing with the original HWENO schemes of Qiu and Shu,one major advantage of new HWENOschemes is its robust in computation of problem with strong shocks.Extensive numerical experiments are performed to illustrate the capability of the method.
A new shock-capturing numerical scheme for ideal hydrodynamics
Feckova, Zuzana
2015-01-01
We present a new algorithm for solving ideal relativistic hydrodynamics based on Godunov method with an exact solution of Riemann problem for an arbitrary equation of state. Standard numerical tests are executed, such as the sound wave propagation and the shock tube problem. Low numerical viscosity and high precision are attained with proper discretization.
ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
Dumbser, Michael; Hidalgo, Arturo; Balsara, Dinshaw S
2012-01-01
We present the first high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resulting algorithm is particularly well suited for an AMR strategy on space-time adaptive meshes, i.e.with time-accurate local time stepping. The AMR property has been implemented 'cell-by-cell', with a standard tree-type algorithm, while the scheme has been parallelized via the Message Passing Interface (MPI) paradigm. The new scheme has been tested over a wide range of examples for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations of compressible gas dynamics and the equations of magnetohydrodynamics (MHD). High order in space and time have been confirmed via a numerical convergenc...
Moczo, P.; Kristek, J.; Galis, M.; Pazak, P.
2009-12-01
Numerical prediction of earthquake ground motion in sedimentary basins and valleys often has to account for P-wave to S-wave speed ratios (Vp/Vs) as large as 5 and even larger, mainly in sediments below groundwater level. The ratio can attain values larger than 10 in unconsolidated sediments (e.g. in Ciudad de México). In a process of developing 3D optimally-accurate finite-difference schemes we encountered a serious problem with accuracy in media with large Vp/Vs ratio. This led us to investigate the very fundamental reasons for the inaccuracy. In order to identify the very basic inherent aspects of the numerical schemes responsible for their behavior with varying Vp/Vs ratio, we restricted to the most basic 2nd-order 2D numerical schemes on a uniform grid in a homogeneous medium. Although basic in the specified sense, the schemes comprise the decisive features for accuracy of wide class of numerical schemes. We investigated 6 numerical schemes: finite-difference_displacement_conventional grid (FD_D_CG) finite-element_Lobatto integration (FE_L) finite-element_Gauss integration (FE_G) finite-difference_displacement-stress_partly-staggered grid (FD_DS_PSG) finite-difference_displacement-stress_staggered grid (FD_DS_SG) finite-difference_velocity-stress_staggered grid (FD_VS_SG) We defined and calculated local errors of the schemes in amplitude and polarization. Because different schemes use different time steps, they need different numbers of time levels to calculate solution for a desired time window. Therefore, we normalized errors for a unit time. The normalization allowed for a direct comparison of errors of different schemes. Extensive numerical calculations for wide ranges of values of the Vp/Vs ratio, spatial sampling ratio, stability ratio, and entire range of directions of propagation with respect to the spatial grid led to interesting and surprising findings. Accuracy of FD_D_CG, FE_L and FE_G strongly depends on Vp/Vs ratio. The schemes are not
Directory of Open Access Journals (Sweden)
Jing Yin
2015-07-01
Full Text Available A total variation diminishing-weighted average flux (TVD-WAF-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer (HLL Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourth-order monotone upstream-centered scheme for conservation laws (MUSCL. The time marching scheme based on the third-order TVD Runge-Kutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.
A well-balanced finite volume scheme for 1D hemodynamic simulations
Delestre, Olivier
2011-01-01
We are interested in simulating blood flow in arteries with variable elasticity with a one dimensional model. We present a well-balanced finite volume scheme based on the recent developments in shallow water equations context. We thus get a mass conservative scheme which also preserves equilibria of Q=0. This numerical method is tested on analytical tests. Nous nous int\\'eressons \\`a la simulation d'\\'ecoulements sanguins dans des art\\`eres dont les parois sont \\`a \\'elasticit\\'e variable. Ceci est mod\\'elis\\'e \\`a l'aide d'un mod\\`ele unidimensionnel. Nous pr\\'esentons un sch\\'ema "volume fini \\'equilibr\\'e" bas\\'e sur les d\\'eveloppements r\\'ecents effectu\\'es pour la r\\'esolution du syst\\`eme de Saint-Venant. Ainsi, nous obtenons un sch\\'ema qui pr\\'eserve le volume de fluide ainsi que les \\'equilibres au repos: Q=0. Le sch\\'ema introduit est test\\'e sur des solutions analytiques.
A well-balanced finite volume scheme for 1D hemodynamic simulations*
Directory of Open Access Journals (Sweden)
Lagrée Pierre-Yves
2012-04-01
Full Text Available We are interested in simulating blood flow in arteries with variable elasticity with a one dimensional model. We present a well-balanced finite volume scheme based on the recent developments in shallow water equations context. We thus get a mass conservative scheme which also preserves equilibria of Q = 0. This numerical method is tested on analytical tests. Nous nous intéressons à la simulation d’écoulements sanguins dans des artères dont les parois sont à élasticité variable. Ceci est modélisé à l’aide d’un modèle unidimensionnel. Nous présentons un schéma ”volume fini équilibré” basé sur les développements récents effectués pour la résolution du système de Saint-Venant. Ainsi, nous obtenons un schéma qui préserve le volume de fluide ainsi que les équilibres au repos : Q = 0. Le schéma introduit est testé sur des solutions analytiques.
Finite-difference scheme for the numerical solution of the Schroedinger equation
Mickens, Ronald E.; Ramadhani, Issa
1992-01-01
A finite-difference scheme for numerical integration of the Schroedinger equation is constructed. Asymptotically (r goes to infinity), the method gives the exact solution correct to terms of order r exp -2.
Nuclear Reactor Component Code CUPID-I: Numerical Scheme and Preliminary Assessment Results
Energy Technology Data Exchange (ETDEWEB)
Cho, Hyoung Kyu; Jeong, Jae Jun; Park, Ik Kyu; Kim, Jong Tae; Yoon, Han Young
2007-12-15
A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components of a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAC, semi-implicit ICE, SIMPLE, Row Scheme and so on. Among them, the ICE scheme for the three-field model was presented in the present report. The CUPID code is utilizing unstructured mesh for the simulation of complicated geometries of the nuclear reactor components. The conventional ICE scheme that was applied to RELAP5 and COBRA-TF, therefore, were modified for the application to the unstructured mesh. Preliminary calculations for the unstructured semi-implicit ICE scheme have been conducted for a verification of the numerical method from a qualitative point of view. The preliminary calculation results showed that the present numerical scheme is robust and efficient for the prediction of phase changes and flow transitions due to a boiling and a flashing. These calculation results also showed the strong coupling between the pressure and void fraction changes. Thus, it is believed that the semi-implicit ICE scheme can be utilized for transient two-phase flows in a component of a nuclear reactor.
An efficient numerical scheme for the simulation of parallel-plate active magnetic regenerators
DEFF Research Database (Denmark)
Torregrosa-Jaime, Bárbara; Corberán, José M.; Payá, Jorge;
2015-01-01
A one-dimensional model of a parallel-plate active magnetic regenerator (AMR) is presented in this work. The model is based on an efficient numerical scheme which has been developed after analysing the heat transfer mechanisms in the regenerator bed. The new finite difference scheme optimally...
A CLASS OF TWO-STEP TVD MACCORMACK TYPE NUMERICAL SCHEME FOR MHD EQUATIONS
Institute of Scientific and Technical Information of China (English)
FENG Xueshang; WEI Fengsi; ZHONG Dingkun
2003-01-01
In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang's MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities.
Institute of Scientific and Technical Information of China (English)
罗振东; 朱江; 谢正辉; 张桂芳
2003-01-01
The non-stationary natural convection problem is studied. A lowest order finite difference scheme based on mixed finite element method for non-stationary natural convection problem, by the spatial variations discreted with finite element method and time with finite difference scheme was derived, where the numerical solution of velocity, pressure, and temperature can be found together, and a numerical example to simulate the close square cavity is given, which is of practical importance.
A Finite Volume Method with Unstructured Triangular Grids for Numerical Modeling of Tidal Current
Institute of Scientific and Technical Information of China (English)
SHI Hong-da; LIU zhen
2005-01-01
The finite volume method (FVM) has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker's problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.
Energy Technology Data Exchange (ETDEWEB)
Saas, L.
2004-05-01
This Thesis deals with sedimentary basin modeling whose goal is the prediction through geological times of the localizations and appraisal of hydrocarbons quantities present in the ground. Due to the natural and evolutionary decomposition of the sedimentary basin in blocks and stratigraphic layers, domain decomposition methods are requested to simulate flows of waters and of hydrocarbons in the ground. Conservations laws are used to model the flows in the ground and form coupled partial differential equations which must be discretized by finite volume method. In this report we carry out a study on finite volume methods on non-matching grids solved by domain decomposition methods. We describe a family of finite volume schemes on non-matching grids and we prove that the associated global discretized problem is well posed. Then we give an error estimate. We give two examples of finite volume schemes on non matching grids and the corresponding theoretical results (Constant scheme and Linear scheme). Then we present the resolution of the global discretized problem by a domain decomposition method using arbitrary interface conditions (for example Robin conditions). Finally we give numerical results which validate the theoretical results and study the use of finite volume methods on non-matching grids for basin modeling. (author)
A Numerical Minimization Scheme for the Complex Helmholtz Equation
Richins, Russell B
2010-01-01
We use the work of Milton, Seppecher, and Bouchitt\\'{e} on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method and illustrate the method with numerical experiments.
Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model
Wang, Xiaofei; Lagrée, Pierre-Yves
2013-01-01
In this paper, we present four numerical schemes for a 1D viscoelastic blood flow model. In the case with a small nonlinearity (small amplitude of wave), asymptotic analysis predicts several behaviours of the wave: propagation in a uniform tube, attenuation of the amplitude due to the skin friction, diffusion due to the viscosity of the wall, and reflection and transmission at a branching point. These predictions are compared very favorably with all of the numerical solutions. The schemes are also tested in case with a larger nonlinearity. Finally, we apply all of the schemes on a relatively realistic arterial system with 55 arteries. The schemes are compared in four aspects: the spatial and temporal convergence speed, the ability to capture shock phenomena, the computation speed and the complexity of the implementation. The suitable conditions for the application of the various schemes are discussed.
DEFF Research Database (Denmark)
Hyun, Jaeyub; Kook, Junghwan; Wang, Semyung
2015-01-01
and basis vectors for use according to the target system. The proposed model reduction scheme is applied to the numerical simulation of the simple mass-damping-spring system and the acoustic metamaterial systems (i.e., acoustic lens and acoustic cloaking device) for the first time. Through these numerical...
Bispen, Georgij; Lukáčová-Medvid'ová, Mária; Yelash, Leonid
2017-04-01
In this paper we will present and analyze a new class of the IMEX finite volume schemes for the Euler equations with a gravity source term. We will in particular concentrate on a singular limit of weakly compressible flows when the Mach number M ≪ 1. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non-stiff nonlinear part that models nonlinear advection effects. For time discretization we use a special class of the so-called globally stiffly accurate IMEX schemes and approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. For spatial discretization the finite volume approximation is used with the central and Rusanov/Lax-Friedrichs numerical fluxes for the linear and nonlinear subsystem, respectively. In the case of a constant background potential temperature we prove theoretically that the method is asymptotically consistent and asymptotically stable uniformly with respect to small Mach number. We also analyze experimentally convergence rates in the singular limit when the Mach number tends to zero.
Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics
Lukácová-Medvid'ová, Maria; Saibertova, Jitka
2004-01-01
In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which use bich...
Finite volume schemes for multidimensional hyperbolic systems based on the use of bicharacteristics
Lukácová-Medvid'ová, Maria
2003-01-01
In this survey paper we present an overview on recent results for the bicharacteristics based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multidimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteritics, or bicharacteritics. This is realized by combining the finite volume formulation with approximate evolution opera...
Numerical tests of efficiency of the retrospective time integration scheme in the self-memory model
Institute of Scientific and Technical Information of China (English)
GU Xiangqian; YOU Xingtian; ZHU He; CAO Hongxing
2004-01-01
A set of numerical tests was carried out to compare the retrospective time integral scheme in a self-memory model,whose dynamic kernel is the barotropical quasi-geostrophic model, with the ordinary centered difference scheme in the barotropical quasigeostrophic model. The Rossby-Haurwitz wave function was taken as the initial fields for both schemes. The results show that in comparison with the ordinary centered difference scheme, the retrospective time integral scheme reduces by 2 orders of magnitude the forecast error, and the forecast error increases very little with lengthening of the time-step. Therefore, the retrospective time integral scheme has advantages of improving the forecast accuracy, extending the predictable duration and reducing the computation amount.
Implicit numerical scheme based on SMAC method for unsteady incompressible Navier-Stokes equations
Institute of Scientific and Technical Information of China (English)
Li Zhenlin; Zhang Yongxue
2008-01-01
An implicit numerical scheme is developed based on the simplified marker and cell (SMAC)method to solve Reynolds-averaged equations in general curvilinear coordinates for three-dimensional (3-D) unsteady incompressible turbulent flow.The governing equations include the Reynolds-averaged momentum equations,in which contravariant velocities are unknown variables,pressure-correction Poisson equation and k- ε turbulent equations.The governing equations are discretized in a 3-D MAC staggered grid system.To improve the numerical stability of the implicit SMAC scheme,the higherorder high-resolution Chakravarthy-Osher total variation diminishing (TVD) scheme is used to discretize the convective terms in momentum equations and k-ε equations.The discretized algebraic momentum equations and k-εequations are solved by the time-diversion multiple access (CTDMA) method.The algebraic Poisson equations are solved by the Tschebyscheff SLOR (successive linear over relaxation)method with alternating computational directions.At the end of the paper,the unsteady flow at high Reynolds numbers through a simplified cascade made up of NACA65-410 blade are simulated with the program written according to the implicit numerical scheme.The reliability and accuracy of the implicit numerical scheme are verified through the satisfactory agreement between the numerical results of the surface pressure coefficient and experimental data.The numerical results indicate that Reynolds number and angle of attack are two primary factors affecting the characteristics of unsteady flow.
A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model
Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled
2017-02-01
We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Tokareva-Toro's HLLC scheme [44]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.
Numerical Investigation of Thin Film Spreading Driven by Surfactant Using Upwind Schemes
Directory of Open Access Journals (Sweden)
E. Momoniat
2013-01-01
Full Text Available Numerical solutions of a coupled system of nonlinear partial differential equations modelling the effects of surfactant on the spreading of a thin film on a horizontal substrate are investigated. A CFL condition is obtained from a von Neumann stability analysis of a linearised system of equations. Numerical solutions obtained from a Roe upwind scheme with a third-order TVD Runge-Kutta approximation to the time derivative are compared to solutions obtained with a Roe-Sweby scheme coupled to a minmod limiter and a TVD approximation to the time derivative. Results from both of these schemes are compared to a Roe upwind scheme and a BDF approximation to the time derivative. In all three cases high-order approximations to the spatial derivatives are employed on the interior points of the spatial domain. The Roe-BDF scheme is shown to be an efficient numerical scheme for capturing sharp changes in gradient in the free surface profile and surfactant concentration. Numerical simulations of an initial exponential free surface profile coupled with initial surfactant concentrations for both exogenous and endogenous surfactants are considered.
Hybrid finite volume scheme for a two-phase flow in heterogeneous porous media*
Directory of Open Access Journals (Sweden)
Brenner Konstantin
2012-04-01
Full Text Available We propose a finite volume method on general meshes for the numerical simulation of an incompressible and immiscible two-phase flow in porous media. We consider the case that can be written as a coupled system involving a degenerate parabolic convection-diffusion equation for the saturation together with a uniformly elliptic equation for the global pressure. The numerical scheme, which is implicit in time, allows computations in the case of a heterogeneous and anisotropic permeability tensor. The convective fluxes, which are non monotone with respect to the unknown saturation and discontinuous with respect to the space variables, are discretized by means of a special Godunov scheme. We prove the existence of a discrete solution which converges, along a subsequence, to a solution of the continuous problem. We present a number of numerical results in space dimension two, which confirm the efficiency of the numerical method. Nous proposons un schéma de volumes finis hybrides pour la discrétisation d’un problème d’écoulement diphasique incompressible et immiscible en milieu poreux. On suppose que ce problème a la forme d’une équation parabolique dégénérée de convection-diffusion en saturation couplée à une équation uniformément elliptique en pression. On considère un schéma implicite en temps, où les flux diffusifs sont discrétisés par la méthode des volumes finis hybride, ce qui permet de pouvoir traiter le cas d’un tenseur de perméabilité anisotrope et hétérogène sur un maillage très général, et l’on s’appuie sur un schéma de Godunov pour la discrétisation des flux convectifs, qui peuvent être non monotones et discontinus par rapport aux variables spatiales. On démontre l’existence d’une solution discrète, dont une sous-suite converge vers une solution faible du problème continu. On présente finalement des cas test bidimensionnels.
Development of Non-staggered, semi-implicit ICE numerical scheme for a two-fluid, three-field model
Energy Technology Data Exchange (ETDEWEB)
Jeong, Jae Jun; Yoon, H. Y.; Bae, S. W
2007-11-15
A pilot code for one-dimensional, transient, two-fluid, three-field model has been developed. In this code, the semi-implicit ICE numerical scheme has been adapted to a 'non-staggered' grid. Using several conceptual problems, the numerical scheme has been verified. The results of the verifications are summarized below: - It was confirmed that the basic pilot code can simulate various flow conditions (such as single-phase liquid flow, two-phase mixture flow, and single-phase vapor flow) and transitions of the flow conditions. A mist flow was not simulated, but it seems that the basic pilot code can simulate mist flow conditions. - The mass and energy conservation was confirmed for single-phase liquid and single-phase vapor flows. - It was confirmed that the inlet pressure and velocity boundary conditions work properly. - It was confirmed that, for single- and two-phase flows, the velocity and temperature of non-existing phase are calculated as intended. The non-staggered, semi-implicit ICE numerical scheme, which has been developed in this study, will be a starting point of a new code development that adopts an unstructured finite volume method.
Numerical Analysis on Ventilating and Air Conditioning Scheme of Shenyang Subway Station
Institute of Scientific and Technical Information of China (English)
LI Wei; NA Yanling
2007-01-01
Different cities have different climate conditions and outdoor temperature and humidity, so the scheme of an environment control in subway should be analyzed by considering objective conditions, project cost and operating status. In this paper, a physical and mathematical model is built according to the design of Shenyang subway (line 1), the boundary conditions of the model are defined by the design and experiments, the numerical analysis of ventilating scheme and air conditioning scheme is introduced individually, and the temperature field and air flow field of the two schemes are compared, so that the feasibility of using a ventilating scheme in subway of northeast cities is discussed. Considering comfort and economy, it can be concluded that mechanical ventilation is feasible in subway of northeast cities because the air temperature there is not very high in summer.
Institute of Scientific and Technical Information of China (English)
Serena Morigi; Fiorella Sgallari
2009-01-01
This paper introduces the use of partition of unity method for the develop-ment of a high order finite volume discretization scheme on unstructured grids for solv-ing diffusion models based on partial differential equations. The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions. The methodology proposed is applied to the noise removal prob-lem in functional surfaces and images. Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.
Directory of Open Access Journals (Sweden)
Xinhua Lu
2015-01-01
Full Text Available The first-order Lax-Friedrichs (LF scheme is commonly used in conjunction with other schemes to achieve monotone and stable properties with lower numerical diffusion. Nevertheless, the LF scheme and the schemes devised based on it, for example, the first-order centered (FORCE and the slope-limited centered (SLIC schemes, cannot achieve a time-step-independence solution due to the excessive numerical diffusion at a small time step. In this work, two time-step-convergence improved schemes, the C-FORCE and C-SLIC schemes, are proposed to resolve this problem. The performance of the proposed schemes is validated in solving the one-layer and two-layer shallow-water equations, verifying their capabilities in attaining time-step-independence solutions and showing robustness of them in resolving discontinuities with high-resolution.
A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension
Energy Technology Data Exchange (ETDEWEB)
Garrick, Daniel P. [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States); Owkes, Mark [Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, MT (United States); Regele, Jonathan D., E-mail: jregele@iastate.edu [Department of Aerospace Engineering, Iowa State University, Ames, IA (United States)
2017-06-15
Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge–Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten–Lax–van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas–liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.
A finite-volume HLLC-based scheme for compressible interfacial flows with surface tension
Garrick, Daniel P.; Owkes, Mark; Regele, Jonathan D.
2017-06-01
Shock waves are often used in experiments to create a shear flow across liquid droplets to study secondary atomization. Similar behavior occurs inside of supersonic combustors (scramjets) under startup conditions, but it is challenging to study these conditions experimentally. In order to investigate this phenomenon further, a numerical approach is developed to simulate compressible multiphase flows under the effects of surface tension forces. The flow field is solved via the compressible multicomponent Euler equations (i.e., the five equation model) discretized with the finite volume method on a uniform Cartesian grid. The solver utilizes a total variation diminishing (TVD) third-order Runge-Kutta method for time-marching and second order TVD spatial reconstruction. Surface tension is incorporated using the Continuum Surface Force (CSF) model. Fluxes are upwinded with a modified Harten-Lax-van Leer Contact (HLLC) approximate Riemann solver. An interface compression scheme is employed to counter numerical diffusion of the interface. The present work includes modifications to both the HLLC solver and the interface compression scheme to account for capillary force terms and the associated pressure jump across the gas-liquid interface. A simple method for numerically computing the interface curvature is developed and an acoustic scaling of the surface tension coefficient is proposed for the non-dimensionalization of the model. The model captures the surface tension induced pressure jump exactly if the exact curvature is known and is further verified with an oscillating elliptical droplet and Mach 1.47 and 3 shock-droplet interaction problems. The general characteristics of secondary atomization at a range of Weber numbers are also captured in a series of simulations.
Comparison of Numerical Schemes for Solving a Spherical Particle Diffusion Equation
Fong, Fred K.; Mulkey, Lee A.
1990-05-01
A new robust iterative numerical scheme was developed for a nonlinear diffusive model which described sorption dynamics in spherical particle suspensions. The numerical scheme had been applied to finite difference and finite element models which showed rapid convergence and stability under wide ranges of partition coefficients. Comparisons were made with explicit finite difference and orthogonal collocation methods. The diffusive model assumes complete mixing in the bulk aqueous solution and considers intraaggregate transport within the suspended particles. The effect of particle size distribution of suspensions was also included in the model. Sorption was described using both linear and nonlinear isotherms.
Eymard, Robert; Mercier, Sophie; Prignet, Alain
2008-12-01
We are interested here in the numerical approximation of a family of probability measures, solution of the Chapman-Kolmogorov equation associated to some non-diffusion Markov process with uncountable state space. Such an equation contains a transport term and another term, which implies redistribution of the probability mass on the whole space. An implicit finite volume scheme is proposed, which is intermediate between an upstream weighting scheme and a modified Lax-Friedrichs one. Due to the seemingly unusual probability framework, a new weak bounded variation inequality had to be developed, in order to prove the convergence of the discretised transport term. Such an inequality may be used in other contexts, such as for the study of finite volume approximations of scalar linear or nonlinear hyperbolic equations with initial data in L1. Also, due to the redistribution term, the tightness of the family of approximate probability measures had to be proven. Numerical examples are provided, showing the efficiency of the implicit finite volume scheme and its potentiality to be helpful in an industrial reliability context.
Design and Verification Methodology of Boundary Conditions for Finite Volume Schemes
2012-07-01
Finite Volume Schemes 5a. CONTRACT NUMBER In-House 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Folkner, D., Katz , A and Sankaran...July 9-13, 2012 ICCFD7-2012-1001 Design and Verification Methodology of Boundary Conditions for Finite Volume Schemes D. Folkner∗, A. Katz ∗ and V...Office (ARO), under the supervision of Dr. Frederick Ferguson. The authors would like to thank Dr. Ferguson for his continuing support of this research
Pathak, Harshavardhana S.; Shukla, Ratnesh K.
2016-08-01
A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of
Gas-kinetic numerical schemes for one- and two-dimensional inner flows
Institute of Scientific and Technical Information of China (English)
Zhi-hui LI; Lin BI; Zhi-gong TANG
2009-01-01
Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics of the gas-kinetic numerical algorithm for Boltzmann model equation.The peculiar flow phenomena and mechanism from various flow regimes are revealed in the numerical simulations of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers.The numerical remainder-effects of the difference schemes are investigated and analyzed based on the computed results.The ways of improving the computational efficiency of the gaskinetic numerical method and the computing principles of difference discretization are discussed.
Boscheri, Walter; Dumbser, Michael
2017-10-01
We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total
Numerical experiment of anharmonic oscillators by using the symplectic scheme-shooting method
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Symplectic scheme-shooting method (SSSM) is applied to solve the energy eigenvalues of anharmonic oscillators characterized by the potentials V(x)=λx4 and V(x)=(1/2)x2+λx2α with α=2,3,4 and doubly anharmonic oscillators characterized by the potentials V(x)=(1/2)x2+λ1x4+λ2x6, and a high order symplectic scheme tailored to the "time"-dependent Hamiltonian function is presented. The numerical results illustrate that the energy eigenvalues of anharmonic oscillators with the symplectic scheme-shooting method are in good agreement with the numerical accurate ones obtained from the non-perturbative method by using an appropriately scaled basis for the expansion of each eigenfunction; and the energy eigenvalues of doubly anharmonic oscillators with the sympolectic scheme-shooting method are in good agreement with the exact ones and are better than the results obtained from the four-term asymptotic series. Therefore, the symplectic scheme-shooting method, which is very simple and is easy to grasp, is a good numerical algorithm.
Energy Technology Data Exchange (ETDEWEB)
Goudon, Thierry, E-mail: thierry.goudon@inria.fr [Team COFFEE, INRIA Sophia Antipolis Mediterranee (France); Labo. J.A. Dieudonne CNRS and Univ. Nice-Sophia Antipolis (UMR 7351), Parc Valrose, 06108 Nice cedex 02 (France); Parisot, Martin, E-mail: martin.parisot@gmail.com [Project-Team SIMPAF, INRIA Lille Nord Europe, Park Plazza, 40 avenue Halley, F-59650 Villeneuve d' Ascq cedex (France)
2012-10-15
In the so-called Spitzer-Haerm regime, equations of plasma physics reduce to a nonlinear parabolic equation for the electronic temperature. Coming back to the derivation of this limiting equation through hydrodynamic regime arguments, one is led to construct a hierarchy of models where the heat fluxes are defined through a non-local relation which can be reinterpreted as well by introducing coupled diffusion equations. We address the question of designing numerical methods to simulate these equations. The basic requirement for the scheme is to be asymptotically consistent with the Spitzer-Haerm regime. Furthermore, the constraints of physically realistic simulations make the use of unstructured meshes unavoidable. We develop a Finite Volume scheme, based on Vertex-Based discretization, which reaches these objectives. We discuss on numerical grounds the efficiency of the method, and the ability of the generalized models in capturing relevant phenomena missed by the asymptotic problem.
Toward a Consistent Framework for High Order Mesh Refinement Schemes in Numerical Relativity
Mongwane, Bishop
2015-01-01
It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. To this end, different modifications to the standard Berger-Oliger adaptive mesh refinement algorithm have been proposed. In this work we present a fourth order stable mesh refinement scheme with sub-cycling in time for numerical relativity. We do not use buffer zones to deal with refinement boundaries but explicitly specify boundary data for refined grids. We argue that the incompatibility of the standard mesh refinement algorithm with higher order Runge Kutta methods is a manifestation of order reduction phenomena, caused by inconsistent application of boundary data in the refined grids. Our scheme also addresses the problem of spurious reflections that are generated when propagating waves cross mesh refinement boundaries. We introduce a transition zone on refined levels within which the phase velocity of propagating modes is allowed to decelerate in order to smoothl...
Wen, W. B.; Duan, S. Y.; Yan, J.; Ma, Y. B.; Wei, K.; Fang, D. N.
2017-03-01
An explicit time integration scheme based on quartic B-splines is presented for solving linear structural dynamics problems. The scheme is of a one-parameter family of schemes where free algorithmic parameter controls stability, accuracy and numerical dispersion. The proposed scheme possesses at least second-order accuracy and at most third-order accuracy. A 2D wave problem is analyzed to demonstrate the effectiveness of the proposed scheme in reducing high-frequency modes and retaining low-frequency modes. Except for general structural dynamics, the proposed scheme can be used effectively for wave propagation problems in which numerical dissipation is needed to reduce spurious oscillations.
Wen, W. B.; Duan, S. Y.; Yan, J.; Ma, Y. B.; Wei, K.; Fang, D. N.
2016-11-01
An explicit time integration scheme based on quartic B-splines is presented for solving linear structural dynamics problems. The scheme is of a one-parameter family of schemes where free algorithmic parameter controls stability, accuracy and numerical dispersion. The proposed scheme possesses at least second-order accuracy and at most third-order accuracy. A 2D wave problem is analyzed to demonstrate the effectiveness of the proposed scheme in reducing high-frequency modes and retaining low-frequency modes. Except for general structural dynamics, the proposed scheme can be used effectively for wave propagation problems in which numerical dissipation is needed to reduce spurious oscillations.
Modified pause schemes and working days for more volume flexibility in manufactering
Rhijn, G.; Looze, M. de; Bosch, T.
2005-01-01
The effects of two measures to increase the volume flexibility, namely the introduction of an alternating pause scheme and the elongation of the working day, were evaluated in two manufacturing companies. Both measures led to an increase in volume output of about 16% at relatively low costs. The
Rotating star initial data for a constrained scheme in numerical relativity
Lin, L M; Lin, Lap-Ming; Novak, Jerome
2006-01-01
A new numerical code for computing stationary axisymmetric rapidly rotating stars in general relativity is presented. The formulation is based on a fully constrained-evolution scheme for 3+1 numerical relativity using the Dirac gauge and maximal slicing. We use both the polytropic and MIT bag model equations of state to demonstrate that the code can construct rapidly rotating neutron star and strange star models. We compare numerical models obtained by our code and a well-established code, which uses a different gauge condition, and show that the two codes agree to high accuracy.
Numerical simulation of thin layer coffee drying by control volumes
CIRO-VELÁSQUEZ, HÉCTOR J.; ABUD-CANO, LUIS C.; PÉREZ-ALEGRÍA, LUIS. R.
2011-01-01
The thin layer drying model proposed by Sokhansanj and Bruce (1987) was implemented to model the drying process of parchment coffee beans. A computational model based on a control volume approach was developed to simulate the drying process of parchment coffee. A one dimensional transient analysis was implemented in the radial direction applied to a spherical coffee bean of equivalent radius. The results found that, even though the numerical value for the mass transfer coefficient is a small ...
A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation
Liu, Yang
2010-03-01
We propose an efficient scheme to absorb reflections from the model boundaries in numerical solutions of wave equations. This scheme divides the computational domain into boundary, transition, and inner areas. The wavefields within the inner and boundary areas are computed by the wave equation and the one-way wave equation, respectively. The wavefields within the transition area are determined by a weighted combination of the wavefields computed by the wave equation and the one-way wave equation to obtain a smooth variation from the inner area to the boundary via the transition zone. The results from our finite-difference numerical modeling tests of the 2D acoustic wave equation show that the absorption enforced by this scheme gradually increases with increasing width of the transition area. We obtain equally good performance using pseudospectral and finite-element modeling with the same scheme. Our numerical experiments demonstrate that use of 10 grid points for absorbing edge reflections attains nearly perfect absorption. © 2010 Society of Exploration Geophysicists.
3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"
Douglass, A.
2005-01-01
The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.
VERIFICATION OF HYBRID NUMERICAL SCHEME FOR THE CASE OF COMPRESSIBLE JET IMPINGIMENT ON FLAT PLATE
Directory of Open Access Journals (Sweden)
2016-01-01
Full Text Available The article deals with the questions of mathematical modeling of compressible jet outflow from model nozzle and jet impingiment on flat plate at various values of n. pisoCentralFoam solver which is based on the Kurganov-Tadmor hy- brid numerical scheme, PISO algorithm and finite volume method, is used for the solution of this problem. The model, based on unsteady Reynolds equation and K-omega SST turbulence model with boundary functions is used for compressi- ble jet calculation. The problem definition for calculation of jet impingiment on flat plate is given. The simulation domainwas selected as a rectangle. Only a half of the nozzle was considered for simplification. The mixed boundary condition for pressure setting in case of free jet was used on the outlet of simulation domain. The special condition for the pressure with table data, allowed to increase the value of pressure gradually, was used on the inlet of simulation domain. The value of the jet pressure degree was selected as n = 2.5 and n = 5.0. The results of distribution of the velocity magnitude, field pressure, upon symmetry axes were received. The simulations were done with grids 100 000-500 000 cells. The average value of y+ was equal to 270. The calculations were done for the end time Tend = 0.01 s. Comparison of the results of pressure distribution calculation based on nozzle length on different grids with the results of the experiment is carried out. The coin- cidence to engineering accuracy of 5 % is received.
A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations
Bernal, Francisco; Acebróon, Juan A.
2016-09-01
We review, implement, and compare numerical integration schemes for spatially bounded diffusions stopped at the boundary which possess a convergence rate of the discretization error with respect to the timestep $h$ higher than ${\\cal O}(\\sqrt{h})$. We address specific implementation issues of the most general-purpose of such schemes. They have been coded into a single Matlab program and compared, according to their accuracy and computational cost, on a wide range of problems in up to ${\\mathbb R}^{48}$. The paper is self-contained and the code will be made freely downloadable.
A hybrid convection scheme for use in non-hydrostatic numerical weather prediction models
Directory of Open Access Journals (Sweden)
Volker Kuell
2008-12-01
Full Text Available The correct representation of convection in numerical weather prediction (NWP models is essential for quantitative precipitation forecasts. Due to its small horizontal scale convection usually has to be parameterized, e.g. by mass flux convection schemes. Classical schemes originally developed for use in coarse grid NWP models assume zero net convective mass flux, because the whole circulation of a convective cell is confined to the local grid column and all convective mass fluxes cancel out. However, in contemporary NWP models with grid sizes of a few kilometers this assumption becomes questionable, because here convection is partially resolved on the grid. To overcome this conceptual problem we propose a hybrid mass flux convection scheme (HYMACS in which only the convective updrafts and downdrafts are parameterized. The generation of the larger scale environmental subsidence, which may cover several grid columns, is transferred to the grid scale equations. This means that the convection scheme now has to generate a net convective mass flux exerting a direct dynamical forcing to the grid scale model via pressure gradient forces. The hybrid convection scheme implemented into the COSMO model of Deutscher Wetterdienst (DWD is tested in an idealized simulation of a sea breeze circulation initiating convection in a realistic manner. The results are compared with analogous simulations with the classical Tiedtke and Kain-Fritsch convection schemes.
A New Framework to Compare Mass-Flux Schemes Within the AROME Numerical Weather Prediction Model
Riette, Sébastien; Lac, Christine
2016-08-01
In the Application of Research to Operations at Mesoscale (AROME) numerical weather forecast model used in operations at Météo-France, five mass-flux schemes are available to parametrize shallow convection at kilometre resolution. All but one are based on the eddy-diffusivity-mass-flux approach, and differ in entrainment/detrainment, the updraft vertical velocity equation and the closure assumption. The fifth is based on a more classical mass-flux approach. Screen-level scores obtained with these schemes show few discrepancies and are not sufficient to highlight behaviour differences. Here, we describe and use a new experimental framework, able to compare and discriminate among different schemes. For a year, daily forecast experiments were conducted over small domains centred on the five French metropolitan radio-sounding locations. Cloud base, planetary boundary-layer height and normalized vertical profiles of specific humidity, potential temperature, wind speed and cloud condensate were compared with observations, and with each other. The framework allowed the behaviour of the different schemes in and above the boundary layer to be characterized. In particular, the impact of the entrainment/detrainment formulation, closure assumption and cloud scheme were clearly visible. Differences mainly concerned the transport intensity thus allowing schemes to be separated into two groups, with stronger or weaker updrafts. In the AROME model (with all interactions and the possible existence of compensating errors), evaluation diagnostics gave the advantage to the first group.
Numerical scheme for riser motion calculation during 3-D VIV simulation
Huang, Kevin; Chen, Hamn-Ching; Chen, Chia-Rong
2011-10-01
This paper presents a numerical scheme for riser motion calculation and its application to riser VIV simulations. The discretisation of the governing differential equation is studied first. The top tensioned risers are simplified as tensioned beams. A centered space and forward time finite difference scheme is derived from the governing equations of motion. Then an implicit method is adopted for better numerical stability. The method meets von Neumann criteria and is shown to be unconditionally stable. The discretized linear algebraic equations are solved using a LU decomposition method. This approach is then applied to a series of benchmark cases with known solutions. The comparisons show good agreement. Finally the method is applied to practical riser VIV simulations. The studied cases cover a wide range of riser VIV problems, i.e. different riser outer diameter, length, tensioning conditions, and current profiles. Reasonable agreement is obtained between the numerical simulations and experimental data on riser motions and cross-flow VIV a/D . These validations and comparisons confirm that the present numerical scheme for riser motion calculation is valid and effective for long riser VIV simulation.
Liu, Hongxu; Jiao, Xiangmin
2016-06-01
ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth solutions. For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities. For unstructured meshes, which are needed for complex geometries, similar schemes are required but they are much more challenging. We propose a new family of non-oscillatory schemes, called WLS-ENO, in the context of solving hyperbolic conservation laws using finite-volume methods over unstructured meshes. WLS-ENO is derived based on Taylor series expansion and solved using a weighted least squares formulation. Unlike other non-oscillatory schemes, the WLS-ENO does not require constructing sub-stencils, and hence it provides a more flexible framework and is less sensitive to mesh quality. We present rigorous analysis of the accuracy and stability of WLS-ENO, and present numerical results in 1-D, 2-D, and 3-D for a number of benchmark problems, and also report some comparisons against WENO.
Badrot-Nico, Fabiola; Brissaud, François; Guinot, Vincent
2007-09-01
A finite volume upwind numerical scheme for the solution of the linear advection equation in multiple dimensions on Cartesian grids is presented. The small-stencil, Modified Discontinuous Profile Method (MDPM) uses a sub-cell piecewise constant reconstruction and additional information at the cell interfaces, rather than a spatial extension of the stencil as in usual methods. This paper presents the MDPM profile reconstruction method in one dimension and its generalization and algorithm to two- and three-dimensional problems. The method is extended to the advection-diffusion equation in multiple dimensions. The MDPM is tested against the MUSCL scheme on two- and three-dimensional test cases. It is shown to give high-quality results for sharp gradients problems, although some scattering appears. For smooth gradients, extreme values are best preserved with the MDPM than with the MUSCL scheme, while the MDPM does not maintain the smoothness of the original shape as well as the MUSCL scheme. However the MDPM is proved to be more efficient on coarse grids in terms of error and CPU time, while on fine grids the MUSCL scheme provides a better accuracy at a lower CPU.
Global communication schemes for the numerical solution of high-dimensional PDEs
DEFF Research Database (Denmark)
Hupp, Philipp; Heene, Mario; Jacob, Riko;
2016-01-01
rounds or the total communication volume. Experiments on two different supercomputers show that either of the schemes outperforms the other depending on the size of the problem. Furthermore, we present a communication model based on the system’s latency and bandwidth and validate the model...... with the experiments. The model can be used to predict the runtime of the reduce/broadcast step for dimensionalities that are yet out of scope on current supercomputers....
A multirate numerical scheme for large-scale vehicle traffic simulation
Kurtc, Valentina
2016-01-01
Nowadays the city-wide traffic contains hundreds of thousands of vehicles with different scenarios of their behavior. If a microscopic approach is used it leads to solving tremendous systems of ordinary differential equations whose components have a wide range of variation rates. The given paper has introduced a multirate numerical scheme with a self-adjusting time stepping strategy. Instead of using a single step size for the whole system we have determined the step size for each component by estimating its own local variation. We also performed the stability analysis for the developed scheme. The presented multirate scheme provides a significant speed-up in processor times compared to the corresponding single-rate one. The use of multiple time steps admits parallel computing.
A NEW NUMERICAL SCHEME FOR ELASTIC-PLASTIC SIMULATION OF EXCAVATION IN GEO-ENGINEERING
Institute of Scientific and Technical Information of China (English)
Wang Jianxue; Shen Xinpu; Liu Tianquan
2000-01-01
For the path dependency and nonlinearity introduced by incremental construction, numerical method has been widely used in deformation analysis of geo-engineering.In the numerical simulation scheme commonly used in the past, the excavating loads are extracted from nodal stresses, which are deduced linearly from the stresses at Gauss-point in finite element method.The unneglectable calculation error is contained in this process when elastic-plastic constitutive model is employed.The error mentioned above is analyzed in detail.Based on the analysis of excavation process and the principle of finite element theory, a new simulation scheme for excavation is proposed.At the end of this paper, an application in rock engineering is given out.
Liu, Jianjun; Zhang, Feimin; Pu, Zhaoxia
2017-04-01
Accurate forecasting of the intensity changes of hurricanes is an important yet challenging problem in numerical weather prediction. The rapid intensification of Hurricane Katrina (2005) before its landfall in the southern US is studied with the Advanced Research version of the WRF (Weather Research and Forecasting) model. The sensitivity of numerical simulations to two popular planetary boundary layer (PBL) schemes, the Mellor-Yamada-Janjic (MYJ) and the Yonsei University (YSU) schemes, is investigated. It is found that, compared with the YSU simulation, the simulation with the MYJ scheme produces better track and intensity evolution, better vortex structure, and more accurate landfall time and location. Large discrepancies (e.g., over 10 hPa in simulated minimum sea level pressure) are found between the two simulations during the rapid intensification period. Further diagnosis indicates that stronger surface fluxes and vertical mixing in the PBL from the simulation with the MYJ scheme lead to enhanced air-sea interaction, which helps generate more realistic simulations of the rapid intensification process. Overall, the results from this study suggest that improved representation of surface fluxes and vertical mixing in the PBL is essential for accurate prediction of hurricane intensity changes.
Crouseilles, Nicolas; Lemou, Mohammed
2016-01-01
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\\em in both space and time}.Such PDE models arise in semiclassical modeling of quantum dynamics with band-crossings, and otherhighly oscillatory waves. Our first main idea is to use the nonlinear geometric optics ansatz, which builds theoscillatory phase into an independent variable. We then choose suitable initial data, based on the Chapman-Enskog expansion, for the new model. For a scalar model, we prove that so constructed model will have certain smoothness, and consequently, for a first order approximation scheme we prove uniform error estimates independent of the (possibly small) wave length. The method is extended to systems arising from a semiclassical model for surface hopping, a non-adiabatic quantum dynamic phenomenon. Numerous numerical examples demonstrate that the method has the desired properties...
Romá, Federico; Cugliandolo, Leticia F; Lozano, Gustavo S
2014-08-01
We introduce a numerical method to integrate the stochastic Landau-Lifshitz-Gilbert equation in spherical coordinates for generic discretization schemes. This method conserves the magnetization modulus and ensures the approach to equilibrium under the expected conditions. We test the algorithm on a benchmark problem: the dynamics of a uniformly magnetized ellipsoid. We investigate the influence of various parameters, and in particular, we analyze the efficiency of the numerical integration, in terms of the number of steps needed to reach a chosen long time with a given accuracy.
A numerical scheme for optimal transition paths of stochastic chemical kinetic systems
Liu, Di
2008-10-01
We present a new framework for finding the optimal transition paths of metastable stochastic chemical kinetic systems with large system size. The optimal transition paths are identified to be the most probable paths according to the Large Deviation Theory of stochastic processes. Dynamical equations for the optimal transition paths are derived using the variational principle. A modified Minimum Action Method (MAM) is proposed as a numerical scheme to solve the optimal transition paths. Applications to Gene Regulatory Networks such as the toggle switch model and the Lactose Operon Model in Escherichia coli are presented as numerical examples.
A hybrid Eulerian Lagrangian numerical scheme for solving prognostic equations in fluid dynamics
Directory of Open Access Journals (Sweden)
E. Kaas
2013-07-01
Full Text Available A new hybrid Eulerian Lagrangian numerical scheme (HEL for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow. The time stepping in Eulerian representation is achieved in two steps: first a mass conserving Eulerian or semi-Lagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space. The HEL scheme has been designed to be accurate, multi-tracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place, i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely. The properties of HEL are here verified in two-dimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.
A finite volume method for numerical grid generation
Beale, S. B.
1999-07-01
A novel method to generate body-fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables , and is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re-zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid-correction procedure. The scalar variables are re-mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet-Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local-boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point-by-point and whole-field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright
FINITE VOLUME NUMERICAL ANALYSIS FOR PARABOLIC EQUATION WITH ROBIN BOUNDARY CONDITION
Institute of Scientific and Technical Information of China (English)
Xia Cui
2005-01-01
In this paper, finite volume method on unstructured meshes is studied for a parabolic convection-diffusion problem on an open bounded set of Rd (d = 2 or 3) with Robin boundary condition. Upwinding approximations are adapted to treat both the convection term and Robin boundary condition. By directly getting start from the formulation of the finite volume scheme, numerical analysis is done. By using several discrete functional analysis techniques such as summation by parts, discrete norm inequality, et al, the stability and error estimates on the approximate solution are established, existence and uniqueness of the approximate solution and the 1st order temporal norm and L2 and H1 spacial norm convergence properties are obtained.
Numerical simulations of volume holographic imaging system resolution characteristics
Sun, Yajun; Jiang, Zhuqing; Liu, Shaojie; Tao, Shiquan
2009-05-01
Because of the Bragg selectivity of volume holographic gratings, it helps VHI system to optically segment the object space. In this paper, properties of point-source diffraction imaging in terms of the point-spread function (PSF) are investigated, and characteristics of depth and lateral resolutions in a VHI system is numerically simulated. The results show that the observed diffracted field obviously changes with the displacement in the z direction, and is nearly unchanged with displacement in the x and y directions. The dependence of the diffracted imaging field on the z-displacement provides a way to possess 3-D image by VHI.
Numerical Modeling of Deep Mantle Convection: Advection and Diffusion Schemes for Marker Methods
Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard
2013-04-01
Thermal and chemical evolution of Earth's deep mantle can be studied by modeling vigorous convection in a chemically heterogeneous fluid. Numerical modeling of such a system poses several computational challenges. Dominance of heat advection over the diffusive heat transport, and a negligible amount of chemical diffusion results in sharp gradients of thermal and chemical fields. The exponential dependence of the viscosity of mantle materials on temperature also leads to high gradients of the velocity field. The accuracy of many numerical advection schemes degrades quickly with increasing gradient of the solution, while the computational effort, in terms of the scheme complexity and required resolution, grows. Additional numerical challenges arise due to a large range of length-scales characteristic of a thermochemical convection system with highly variable viscosity. To examplify, the thickness of the stem of a rising thermal plume may be a few percent of the mantle thickness. An even thinner filament of an anomalous material that is entrained by that plume may consitute less than a tenth of a percent of the mantle thickness. We have developed a two-dimensional FEM code to model thermochemical convection in a hollow cylinder domain, with a depth- and temperature-dependent viscosity representative of the mantle (Steinberger and Calderwood, 2006). We use marker-in-cell method for advection of chemical and thermal fields. The main advantage of perfoming advection using markers is absence of numerical diffusion during the advection step, as opposed to the more diffusive field-methods. However, in the common implementation of the marker-methods, the solution of the momentum and energy equations takes place on a computational grid, and nodes do not generally coincide with the positions of the markers. Transferring velocity-, temperature-, and chemistry- information between nodes and markers introduces errors inherent to inter- and extrapolation. In the numerical scheme
He, Yuan-Yao; Wu, Han-Qing; Meng, Zi Yang; Lu, Zhong-Yi
2016-05-01
The aim of this series of two papers is to discuss topological invariants for interacting topological insulators (TIs). In the first paper (I), we provide a paradigm of efficient numerical evaluation scheme for topological invariants, in which we demystify the procedures and techniques employed in calculating Z2 invariant and spin Chern number via zero-frequency single-particle Green's function in quantum Monte Carlo (QMC) simulations. Here we introduce an interpolation process to overcome the ubiquitous finite-size effect, so that the calculated spin Chern number shows ideally quantized values. We also show that making use of symmetry properties of the underlying systems can greatly reduce the computational effort. To demonstrate the effectiveness of our numerical evaluation scheme, especially the interpolation process, for calculating topological invariants, we apply it on two independent two-dimensional models of interacting topological insulators. In the subsequent paper (II), we apply the scheme developed here to wider classes of models of interacting topological insulators, for which certain limitation of constructing topological invariant via single-particle Green's functions will be presented.
An assessment of unstructured grid finite volume schemes for cold gas hypersonic flow calculations
Directory of Open Access Journals (Sweden)
João Luiz F. Azevedo
2009-06-01
Full Text Available A comparison of five different spatial discretization schemes is performed considering a typical high speed flow application. Flowfields are simulated using the 2-D Euler equations, discretized in a cell-centered finite volume procedure on unstructured triangular meshes. The algorithms studied include a central difference-type scheme, and 1st- and 2nd-order van Leer and Liou flux-vector splitting schemes. These methods are implemented in an efficient, edge-based, unstructured grid procedure which allows for adaptive mesh refinement based on flow property gradients. Details of the unstructured grid implementation of the methods are presented together with a discussion of the data structure and of the adaptive refinement strategy. The application of interest is the cold gas flow through a typical hypersonic inlet. Results for different entrance Mach numbers and mesh topologies are discussed in order to assess the comparative performance of the various spatial discretization schemes.
Chen, Huangxin
2017-09-01
In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.
A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation
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Hakon A. Hoel
2007-07-01
Full Text Available We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi equation $u_t - u_{xxt} + 4uu_x = 3u_{x}u_{xx}+ uu_{xxx}$. Multi-shockpeakons, functions of the form $$ u(x,t =sum_{i=1}^n(m_i(t -hbox{sign}(x-x_i(ts_i(te^{-|x-x_i(t|}, $$ are solutions of the DP equation with a special property; their evolution in time is described by a dynamical system of ODEs. This property makes multi-shockpeakons relatively easy to simulate numerically. We prove that if we are given a non-negative initial function $u_0 in L^1(mathbb{R}cap BV(mathbb{R}$ such that $u_{0} - u_{0,x}$ is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in $mathbb{R}imes[0,T$ for any $T>0$. From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation.
Institute of Scientific and Technical Information of China (English)
Zhi-yue Zhang
2002-01-01
Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a coupled system of three dimensional nonlinear partial differential equations with initial-boundary value problems. In this paper, according to the actual conditions of molecular and three-dimensional characteristic of the problem,we construct the characteristic finite element alternating-direction schemes which can be divided into three continuous one-dimensional problems. By making use of tensor product algorithm, and priori estimation theory and techniques, the optimal order estimates in H1 norm are derived for the error in the approximate solution.
A one-parameter family of difference schemes for the numerical solution of the Keplerian problem
Elenin, G. G.; Elenina, T. G.
2015-08-01
A family of numerical methods for solving the Keplerian problem is proposed. All the methods in this family are symplectic. They preserve the angular momentum, the total energy, the components of the Laplace-Runge-Lenz vector, and the phase volume. The underlying idea is an exact linearization of the problem based on the Levi-Civita transformation and two-stage symmetricsymplectic Runge-Kutta methods.
Institute of Scientific and Technical Information of China (English)
HEJRANFAR Kazem; FATTAH-HESARY Kasra
2011-01-01
A numerical treatment for the prediction of cavitating flows is presented and assessed.The algorithm uses the preconditioned multiphase Euler equations with appropriate mass transfer terms.A central difference finite volume scheme with suitable dissipation terms to account for density jumps across the cavity interface is shown to yield an effective method for solving the multiphase Euler equations.The Euler equations are utilized herein for the cavitation modeling, because some certain characteristics of cavitating flows can be obtained using the solution of this system of equations with relative low computational effort.In addition, the Euler equations are appropriate for the assessment of the numerical method used, because of the sensitivity of the solution to the numerical instabilities.For this reason, a sensitivity study is conducted to evaluate the effects of various parameters, such as numerical dissipation coefficients and grid size, on the accuracy and performance of the solution.The computations are performed for steady cavitating flows around the NACA 0012 and NACA 66 (MOD) hydrofoils and also an axisymmetric hemispherical fore-body under different conditions and the results are compared with the available numerical and experimental data.The solution procedure presented is shown to be accurate and efficient for predicting steady sheet- and super-cavitation for 2D/axisymmetric geometries.
Gilchrist, S A; Barnes, G
2016-01-01
Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin (Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.
Gilchrist, S. A.; Braun, D. C.; Barnes, G.
2016-12-01
Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin ( Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.
Directory of Open Access Journals (Sweden)
B. C. Backeberg
2009-02-01
Full Text Available A 4th order advection scheme is applied in a nested eddy-resolving Hybrid Coordinate Ocean Model (HYCOM of the greater Agulhas Current system for the purpose of testing advanced numerics as a means for improving the model simulation for eventual operational implementation. Model validation techniques comparing sea surface height variations, sea level skewness and variogram analyses to satellite altimetry measurements quantify that generally the 4th order advection scheme improves the realism of the model simulation. The most striking improvement over the standard 2nd order momentum advection scheme, is that the Southern Agulhas Current is simulated as a well-defined meandering current, rather than a train of successive eddies. A better vertical structure and stronger poleward transports in the Agulhas Current core contribute toward a better southwestward penetration of the current, and its temperature field, implying a stronger Indo-Atlantic inter-ocean exchange. It is found that the transport, and hence this exchange, is sensitive to the occurrences of mesoscale features originating upstream in the Mozambique Channel and Southern East Madagascar Current, and that the improved HYCOM simulation is well suited for further studies of these inter-actions.
Numerical simulation of transonic limit cycle oscillations using high-order low-diffusion schemes
Wang, Baoyuan; Zha, Ge-Cheng
2010-05-01
This paper simulates the NLR7301 airfoil limit cycle oscillation (LCO) caused by fluid-structure interaction (FSI) using Reynolds averaged Navier-Stokes equations (RANS) coupled with Spalart-Allmaras (S-A) one-equation turbulence model. A low diffusion E-CUSP (LDE) scheme with 5th order weighted essentially nonoscillatory scheme (WENO) is employed to calculate the inviscid fluxes. A fully conservative 4th order central differencing is used for the viscous terms. A fully coupled fluid-structural interaction model is employed. For the case computed in this paper, the predicted LCO frequency, amplitudes, averaged lift and moment, all agree excellently with the experiment performed by Schewe et al. The solutions appear to have bifurcation and are dependent on the initial fields or initial perturbation. The developed computational fluid dynamics (CFD)/computational structure dynamics (CSD) simulation is able to capture the LCO with very small amplitudes measured in the experiment. This is attributed to the high order low diffusion schemes, fully coupled FSI model, and the turbulence model used. This research appears to be the first time that a numerical simulation of LCO matches the experiment. The simulation confirms several observations of the experiment.
Numerical simulation of shallow-water flooding using a two-dimensional finite volume model
Institute of Scientific and Technical Information of China (English)
YUAN Bing; SUN Jian; YUAN De-kui; TAO Jian-hua
2013-01-01
A 2-D Finite Volume Model (FVM) is developed for shallow water flows over a complex topography with wetting and drying processes.The numerical fluxes are computed using the Harten,Lax,and van Leer (HLL) approximate Riemann solver.Second-order accuracy is achieved by employing the MUSCL reconstruction method with a slope limiter in space and an explicit two-stage Runge-Kutta method for time integration.A simple and efficient method is introduced to deal with the wetting and drying processes without any correction of the numerical flux term or the source term.In this new method,a switch of alternative schemes is used to compute the water depths at the cell interface to obtain the numerical flux.The model is verified against benchmark tests with analytical solutions and laboratory experimental data.The numerical results show that the model can simulate different types of flood waves from the ideal flood wave to cases over complex terrains.The satisfactory performance indicates an extensive application prospect of the present model in view of its simplicity and effectiveness.
Institute of Scientific and Technical Information of China (English)
QIU Zhongfeng; Andrea M. DOGLIOLI; HE Yijun; Francois CARLOTTI
2011-01-01
This paper presents two comparisons or tests for a Lagrangian model of zooplankton dispersion: numerical schemes and time steps. Firstly, we compared three numerical schemes using idealized circulations. Results show that the precisions of the advanced Adams-Bashfold-Moulton (ABM) method and the Runge-Kutta (RK) method were in the same order and both were much higher than that of the Euler method. Furthermore, the advanced ABM method is more efficient than the RK method in computational memory requirements and time consumption. We therefore chose the advanced ABM method as the Lagrangian particle-tracking algorithm. Secondly, we performed a sensitivity test for time steps, using outputs of the hydrodynamic model, Symphonie. Results show that the time step choices depend on the fluid response time that is related to the spatial resolution of velocity fields. The method introduced by Oliveira et al. in 2002 is suitable for choosing time steps of Lagrangian particle-tracking models, at least when only considering advection.
A Symmetric Characteristic Finite Volume Element Scheme for Nonlinear Convection-Diffusion Problems
Institute of Scientific and Technical Information of China (English)
Min Yang; Yi-rang Yuan
2008-01-01
In this paper, we implement alternating direction strategy and construct a symmetric FVE scheme for nonlinear convection-diffusion problems. Comparing to general FVE methods, our method has two advantages. First, the coefficient matrices of the discrete schemes will be symmetric even for nonlinear problems.Second, since the solution of the algebraic equations at each time step can be inverted into the solution of several one-dimensional problems, the amount of computation work is smaller. We prove the optimal H1-norm error estimates of order O(△t2 + h) and present some numerical examples at the end of the paper.
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
Energy Technology Data Exchange (ETDEWEB)
Ku, S. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Hager, R. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Chang, C. S. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Kwon, J. M. [National Fusion Research Institute, Republic of Korea; Parker, S. E. [University of Colorado Boulder, USA
2016-06-01
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
Energy Technology Data Exchange (ETDEWEB)
Ku, S., E-mail: sku@pppl.gov [Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 (United States); Hager, R.; Chang, C.S. [Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 (United States); Kwon, J.M. [National Fusion Research Institute (Korea, Republic of); Parker, S.E. [University of Colorado Boulder (United States)
2016-06-15
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
Ku, S.; Hager, R.; Chang, C. S.; Kwon, J. M.; Parker, S. E.
2016-06-01
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation - e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others - can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function - driven by ionization, charge exchange and wall loss - is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.
Timofeev, Evgeny; Norouzi, Farhang
2016-06-01
The motivation for using hybrid, explicit-implicit, schemes rather than fully implicit or explicit methods for some unsteady high-speed compressible flows with shocks is firstly discussed. A number of such schemes proposed in the past are briefly overviewed. A recently proposed hybridization approach is then introduced and used for the development of a hybrid, explicit-implicit, TVD (Total Variation Diminishing) scheme of the second order in space and time on smooth solutions in both, explicit and implicit, modes for the linear advection equation. Further generalizations of this finite-volume method for the Burgers, Euler and Navier-Stokes equations discretized on unstructured grids are mentioned in the concluding remarks.
Navas-Montilla, A.; Murillo, J.
2017-07-01
When designing a numerical scheme for the resolution of conservation laws, the selection of a particular source term discretization (STD) may seem irrelevant whenever it ensures convergence with mesh refinement, but it has a decisive impact on the solution. In the framework of the Shallow Water Equations (SWE), well-balanced STD based on quiescent equilibrium are unable to converge to physically based solutions, which can be constructed considering energy arguments. Energy based discretizations can be designed assuming dissipation or conservation, but in any case, the STD procedure required should not be merely based on ad hoc approximations. The STD proposed in this work is derived from the Generalized Hugoniot Locus obtained from the Generalized Rankine Hugoniot conditions and the Integral Curve across the contact wave associated to the bed step. In any case, the STD must allow energy-dissipative solutions: steady and unsteady hydraulic jumps, for which some numerical anomalies have been documented in the literature. These anomalies are the incorrect positioning of steady jumps and the presence of a spurious spike of discharge inside the cell containing the jump. The former issue can be addressed by proposing a modification of the energy-conservative STD that ensures a correct dissipation rate across the hydraulic jump, whereas the latter is of greater complexity and cannot be fixed by simply choosing a suitable STD, as there are more variables involved. The problem concerning the spike of discharge is a well-known problem in the scientific community, also known as slowly-moving shock anomaly, it is produced by a nonlinearity of the Hugoniot locus connecting the states at both sides of the jump. However, it seems that this issue is more a feature than a problem when considering steady solutions of the SWE containing hydraulic jumps. The presence of the spurious spike in the discharge has been taken for granted and has become a feature of the solution. Even though
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Mohammad Iranmanesh
2014-12-01
Full Text Available Many standard brands sell products under the volume discount scheme (VDS as more and more consumers are fond of purchasing products under this scheme. Despite volume discount being commonly practiced, there is a dearth of research, both conceptual and empirical, focusing on purchase characteristics factors and consumer internal evaluation concerning the purchase of products under VDS. To attempt to fill this void, this article develops a conceptual model on VDS with the intention of delineating the influence of the purchase characteristics factors on the consumer intention to purchase products under VDS and provides an explanation of their effects through consumer internal evaluation. Finally, the authors discuss the managerial implications of their research and offer guidelines for future empirical research.
Salamatin, A.
2016-11-01
Numerical algorithm is developed for modelling non-linear mass transfer process in supercritical fluid extraction (SFE). The ground raw material is considered as polydisperse, characterized by discrete number of effective particle fractions. Two continuous interacting counterparts separated by permeable membrane are distinguished in plant material build-up. The apoplast plays role of transport channels during extraction, and symplast contains extractable oil. The complete SFE model is non-linear as a result of non-linearity of oil dissolution kinetics. The computational scheme is based on the finite-volume approximation method and Thomas elimination procedure. The resulting system of algebraic equations is solved iteratively. Special attention is paid to polydisperse substrates, when particle scale characteristics of all fractions interact with each other through pore phase concentration on the vessel scale. Stability of the developed algorithm is demonstrated in numerical tests. Special iterative procedure guarantees a monotonic decrease of oil content in individual particles of substrate. It is also shown that in the limit of the so-called shrinking core approach the number of mesh nodes on a particle scale should be increased.
Energy Technology Data Exchange (ETDEWEB)
López, R., E-mail: ralope1@ing.uc3m.es; Lecuona, A., E-mail: lecuona@ing.uc3m.es; Nogueira, J., E-mail: goriba@ing.uc3m.es; Vereda, C., E-mail: cvereda@ing.uc3m.es
2017-03-15
Highlights: • A two-phase flows numerical algorithm with high order temporal schemes is proposed. • Transient solutions route depends on the temporal high order scheme employed. • ESDIRK scheme for two-phase flows events exhibits high computational performance. • Computational implementation of the ESDIRK scheme can be done in a very easy manner. - Abstract: An extension for 1-D transient two-phase flows of the SIMPLE-ESDIRK method, initially developed for incompressible viscous flows by Ijaz is presented. This extension is motivated by the high temporal order of accuracy demanded to cope with fast phase change events. This methodology is suitable for boiling heat exchangers, solar thermal receivers, etc. The methodology of the solution consist in a finite volume staggered grid discretization of the governing equations in which the transient terms are treated with the explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) method. It is suitable for stiff differential equations, present in instant boiling or condensation processes. It is combined with the semi-implicit pressure linked equations algorithm (SIMPLE) for the calculation of the pressure field. The case of study consists of the numerical reproduction of the Bartolomei upward boiling pipe flow experiment. The steady-state validation of the numerical algorithm is made against these experimental results and well known numerical results for that experiment. In addition, a detailed study reveals the benefits over the first order Euler Backward method when applying 3rd and 4th order schemes, making emphasis in the behaviour when the system is subjected to periodic square wave wall heat function disturbances, concluding that the use of the ESDIRK method in two-phase calculations presents remarkable accuracy and computational advantages.
Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong
2016-02-01
Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.
Amano, Takanobu
2016-01-01
A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell's equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron-positron or an electron-proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten-Lax-Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell's equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small sca...
Numerical study of the systematic error in Monte Carlo schemes for semiconductors
Energy Technology Data Exchange (ETDEWEB)
Muscato, Orazio [Univ. degli Studi di Catania (Italy). Dipt. di Matematica e Informatica; Di Stefano, Vincenza [Univ. degli Studi di Messina (Italy). Dipt. di Matematica; Wagner, Wolfgang [Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany)
2008-07-01
The paper studies the convergence behavior of Monte Carlo schemes for semiconductors. A detailed analysis of the systematic error with respect to numerical parameters is performed. Different sources of systematic error are pointed out and illustrated in a spatially one-dimensional test case. The error with respect to the number of simulation particles occurs during the calculation of the internal electric field. The time step error, which is related to the splitting of transport and electric field calculations, vanishes sufficiently fast. The error due to the approximation of the trajectories of particles depends on the ODE solver used in the algorithm. It is negligible compared to the other sources of time step error, when a second order Runge-Kutta solver is used. The error related to the approximate scattering mechanism is the most significant source of error with respect to the time step. (orig.)
Comparing Numerical Integration Schemes for Time-Continuous Car-Following Models
Treiber, Martin
2014-01-01
When simulating trajectories by integrating time-continuous car-following models, standard integration schemes such as the forth-order Runge-Kutta method (RK4) are rarely used while the simple Euler's method is popular among researchers. We compare four explicit methods: Euler's method, ballistic update, Heun's method (trapezoidal rule), and the standard forth-order RK4. As performance metrics, we plot the global discretization error as a function of the numerical complexity. We tested the methods on several time-continuous car-following models in several multi-vehicle simulation scenarios with and without discontinuities such as stops or a discontinuous behavior of an external leader. We find that the theoretical advantage of RK4 (consistency order~4) only plays a role if both the acceleration function of the model and the external data of the simulation scenario are sufficiently often differentiable. Otherwise, we obtain lower (and often fractional) consistency orders. Although, to our knowledge, Heun's met...
A PREDICT-CORRECT NUMERICAL INTEGRATION SCHEME FOR SOLVING NONLINEAR DYNAMIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Fan Jianping; Huang Tao; Tang Chak-yin; Wang Cheng
2006-01-01
A new numerical integration scheme incorporating a predict-correct algorithm for solving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic system governed by the equaton (v) = F(v, t) was transformed into the form as (v) = Hv+ f(v, t). The nonlinear part f(v, t) was then expanded by Taylor series and only the first-order term retained in the polynomial. Utilizing the theory of linear differential equation and the precise time-integration method, an exact solution for linearizing equation was obtained. In order to find the solution of the original system, a third-order interpolation polynomial of v was used and an equivalent nonlinear ordinary differential equation was regenerated. With a predicted solution as an initial value and an iteration scheme, a corrected result was achieved. Since the error caused by linearization could be eliminated in the correction process, the accuracy of calculation was improved greatly. Three engineering scenarios were used to assess the accuracy and reliability of the proposed method and the results were satisfactory.
ADI FD schemes for the numerical solution of the three-dimensional Heston-Cox-Ingersoll-Ross PDE
Haentjens, Tinne
2012-09-01
This paper deals with the numerical solution of the time-dependent, three-dimensional Heston-Cox-Ingersoll- Ross PDE, with all correlations nonzero, for the fair pricing of European call options. We apply a finite difference dis-cretization on non-uniform spatial grids and then numerically solve the semi-discrete system in time by using an Alternating Direction Implicit scheme. We show that this leads to a highly efficient and stable numerical solution method.
Kazolea, M.; Delis, A. I.; Synolakis, C. E.
2014-08-01
A new methodology is presented to handle wave breaking over complex bathymetries in extended two-dimensional Boussinesq-type (BT) models which are solved by an unstructured well-balanced finite volume (FV) scheme. The numerical model solves the 2D extended BT equations proposed by Nwogu (1993), recast in conservation law form with a hyperbolic flux identical to that of the Non-linear Shallow Water (NSW) equations. Certain criteria, along with their proper implementation, are established to characterize breaking waves. Once breaking waves are recognized, we switch locally in the computational domain from the BT to NSW equations by suppressing the dispersive terms in the vicinity of the wave fronts. Thus, the shock-capturing features of the FV scheme enable an intrinsic representation of the breaking waves, which are handled as shocks by the NSW equations. An additional methodology is presented on how to perform a stable switching between the BT and NSW equations within the unstructured FV framework. Extensive validations are presented, demonstrating the performance of the proposed wave breaking treatment, along with some comparisons with other well-established wave breaking mechanisms that have been proposed for BT models.
A Bicharacteristic Scheme for the Numerical Computation of Two-Dimensional Converging Shock Waves
Meier, U E; Meier, Uwe E.; Demmig, Frank
1997-01-01
A 2d unsteady bicharacteristic scheme with shock fitting is presented and its characteristic step, shock point step and boundary step are described. The bicharacteristic scheme is compared with an UNO scheme and the Moretti scheme. Its capabilities are illustrated by computing a converging, deformed shock wave.
Goloviznin, V. M.; Karabasov, S. A.; Kozubskaya, T. K.; Maksimov, N. V.
2009-12-01
A generalization of the CABARET finite difference scheme is proposed for linearized one-dimensional Euler equations based on the characteristic decomposition into local Riemann invariants. The new method is compared with several central finite difference schemes that are widely used in computational aeroacoustics. Numerical results for the propagation of an acoustic wave in a homogeneous field and the refraction of this wave through a contact discontinuity obtained on a strongly nonuniform grid are presented.
Energy Technology Data Exchange (ETDEWEB)
Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)
2016-02-15
We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.
Angstmann, C. N.; Donnelly, I. C.; Henry, B. I.; Jacobs, B. A.; Langlands, T. A. M.; Nichols, J. A.
2016-02-01
We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction-diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.
A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2de
Lopez Ortega, Alejandro; Mikellides, Ioannis G.
2014-01-01
We present a new algorithm in the Hall2De code to simulate the ion hydrodynamics in the acceleration channel and near plume regions of Hall-effect thrusters. This implementation constitutes an upgrade of the capabilities built in the Hall2De code. The equations of mass conservation and momentum for unmagnetized ions are solved using a conservative, finite-volume, cell-centered scheme on a magnetic-field-aligned grid. Major computational savings are achieved by making use of an implicit predictor/multi-corrector algorithm for time evolution. Inaccuracies in the prediction of the motion of low-energy ions in the near plume in hydrodynamics approaches are addressed by implementing a multi-fluid algorithm that tracks ions of different energies separately. A wide range of comparisons with measurements are performed to validate the new ion algorithms. Several numerical experiments with the location and value of the anomalous collision frequency are also presented. Differences in the plasma properties in the near-plume between the single fluid and multi-fluid approaches are discussed. We complete our validation by comparing predicted erosion rates at the channel walls of the thruster with measurements. Erosion rates predicted by the plasma properties obtained from simulations replicate accurately measured rates of erosion within the uncertainty range of the sputtering models employed.
NUMERICAL COMPUTATIONS OF CO-EXISTING SUPER-CRITICAL AND SUB-CRITICAL FLOWS BASED UPON CRD SCHEMES
Horie, Katsuya; Okamura, Seiji; Kobayashi, Yusuke; Hyodo, Makoto; Hida, Yoshihisa; Nishimoto, Naoshi; Mori, Akio
Stream flows in steep gradient bed form complicating flow configurations, where co-exist super-critical and sub-critical flows. Computing numerically such flows are the key to successful river management. This study applied CRD schemes to 1D and 2D stream flow computations and proposed genuine ways to eliminate expansion shock waves. Through various cases of computing stream flows conducted, CRD schemes showed that i) conservativeness of discharge and accuracy of four significant figures are ensured, ii) artificial viscosity is not explicitly used for computational stabilization, and thus iii) 1D and 2D computations based upon CRD schemes are applicable to evaluating complicating stream flows for river management.
3D skewing and de-skewing scheme for conflict-free access to rays in volume rendering
Energy Technology Data Exchange (ETDEWEB)
Cohen-or, D.; Kaufman, A. [Tel-Aviv Univ., Ramat Aviv (Israel)
1995-05-01
We extend a 2D linear skewed memory organization to 3D and introduce the associated de-skewing scheme designed to provide conflict-free access to projection rays of voxels for use in a volume rendering architecture. This is an application of a 3D linear skewing scheme which supports real-time axonometric projection from 26 primary orientations. 17 refs.
Institute of Scientific and Technical Information of China (English)
ZHAO Ming; CAO Yihua
2012-01-01
A numerical method based on solutions of Euler/Navier-Stokes (N-S) equations is developed for calculating the flow field over a rotor in hover.Jameson central scheme,van Leer flux-vector splitting scheme,advection upwind splitting method (AUSM) scheme,upwind AUSM/van Leer scheme,AUSM+ scheme and AUSMDV scheme are implemented for spatial discretization,and van Albada limiter is also applied.For temporal discretization,both explicit Runge-Kutta method and implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method are attempted.Simultaneously,overset grid technique is adopted.In detail,hole-map method is utilized to identify intergrid boundary points (IGBPs).Furthermore,aimed at identification issue of donor elements,inverse-map method is implemented.Eventually,blade surface pressure distributions derived from numerical simulation are validated compared with experimental data,showing that all the schemes mentioned above have the capability to predict the rotor flow field accurately.At the same time,vorticity contours are illustrated for analysis,and other characteristics are also analyzed.
Towards a reference numerical scheme using MCNPX for PWR control rod tip fluence estimations
Energy Technology Data Exchange (ETDEWEB)
Ferroukhi, H.; Vasiliev, A. [Paul Scherrer Institut, CH-5232 Villigen-PSI (Switzerland); Dufresne, A. [Dept. of Physics, EPFL, 1015 Lausanne (Switzerland); Chawla, R. [Dept. of Physics, EPFL, 1015 Lausanne (Switzerland); Paul Scherrer Institut (Switzerland)
2012-07-01
Recent occurrences of cracks and fissures on the cladding tubes of PWR control rod (CR) fingers employed in the Swiss reactors prompted the need to develop more reliable analytical methods for CR tip fluence estimations. To partly address this need, a deterministic methodology based on SIMULATE-3/CASMO-4 was in recent years developed at PSI. Although this methodology has already been applied for independent support to licensing issues related to CR lifetime, two main questions are currently being the center of attention for further enhancements. First, the methodology relies on several assumptions that have so far not been verified. Secondly, an assessment of the achieved accuracy has not been addressed. In an attempt to answer both these open questions, it was considered appropriate to develop an alternative computational scheme based on the stochastic MCNPX code with the objective to provide reference numerical solutions. This paper presents the first steps undertaken in that direction. To start, a methodology for a volumetric neutron source transfer to full core MCNPX models with detailed CR as well as axial reflector representations is established. On this basis, the assumptions of the deterministic methodology are studied for selected CR configurations for two Beginning-of-Life cores by comparing the spatial neutron flux distributions obtained with the two approaches for the entire spectrum. Finally, for the high-energy range (E> 1 MeV) and for a few CRs, the new MCNPX scheme is applied to estimate the accumulated fluence over one real operated cycle and the results are compared with the deterministic approach. (authors)
Mukkavilli, S. K.; Kay, M. J.; Taylor, R.; Prasad, A. A.; Troccoli, A.
2014-12-01
The Australian Solar Energy Forecasting System (ASEFS) project requires forecasting timeframes which range from nowcasting to long-term forecasts (minutes to two years). As concentrating solar power (CSP) plant operators are one of the key stakeholders in the national energy market, research and development enhancements for direct normal irradiance (DNI) forecasts is a major subtask. This project involves comparing different radiative scheme codes to improve day ahead DNI forecasts on the national supercomputing infrastructure running mesoscale simulations on NOAA's Weather Research & Forecast (WRF) model. ASEFS also requires aerosol data fusion for improving accurate representation of spatio-temporally variable atmospheric aerosols to reduce DNI bias error in clear sky conditions over southern Queensland & New South Wales where solar power is vulnerable to uncertainities from frequent aerosol radiative events such as bush fires and desert dust. Initial results from thirteen years of Bureau of Meteorology's (BOM) deseasonalised DNI and MODIS NASA-Terra aerosol optical depth (AOD) anomalies demonstrated strong negative correlations in north and southeast Australia along with strong variability in AOD (~0.03-0.05). Radiative transfer schemes, DNI and AOD anomaly correlations will be discussed for the population and transmission grid centric regions where current and planned CSP plants dispatch electricity to capture peak prices in the market. Aerosol and solar irradiance datasets include satellite and ground based assimilations from the national BOM, regional aerosol researchers and agencies. The presentation will provide an overview of this ASEFS project task on WRF and results to date. The overall goal of this ASEFS subtask is to develop a hybrid numerical weather prediction (NWP) and statistical/machine learning multi-model ensemble strategy that meets future operational requirements of CSP plant operators.
The HIRLAM fast radiation scheme for mesoscale numerical weather prediction models
Directory of Open Access Journals (Sweden)
L. Rontu
2017-07-01
Full Text Available This paper provides an overview of the HLRADIA shortwave (SW and longwave (LW broadband radiation schemes used in the HIRLAM numerical weather prediction (NWP model and available in the HARMONIE-AROME mesoscale NWP model. The advantage of broadband, over spectral, schemes is that they can be called more frequently within the model, without compromising on computational efficiency. In mesoscale models fast interactions between clouds and radiation and the surface and radiation can be of greater importance than accounting for the spectral details of clear-sky radiation; thus calling the routines more frequently can be of greater benefit than the deterioration due to loss of spectral details. Fast but physically based radiation parametrizations are expected to be valuable for high-resolution ensemble forecasting, because as well as the speed of their execution, they may provide realistic physical perturbations. Results from single-column diagnostic experiments based on CIRC benchmark cases and an evaluation of 10 years of radiation output from the FMI operational archive of HIRLAM forecasts indicate that HLRADIA performs sufficiently well with respect to the clear-sky downwelling SW and longwave LW fluxes at the surface. In general, HLRADIA tends to overestimate surface fluxes, with the exception of LW fluxes under cold and dry conditions. The most obvious overestimation of the surface SW flux was seen in the cloudy cases in the 10-year comparison; this bias may be related to using a cloud inhomogeneity correction, which was too large. According to the CIRC comparisons, the outgoing LW and SW fluxes at the top of atmosphere are mostly overestimated by HLRADIA and the net LW flux is underestimated above clouds. The absorption of SW radiation by the atmosphere seems to be underestimated and LW absorption seems to be overestimated. Despite these issues, the overall results are satisfying and work on the improvement of HLRADIA for the use in HARMONIE
The HIRLAM fast radiation scheme for mesoscale numerical weather prediction models
Rontu, Laura; Gleeson, Emily; Räisänen, Petri; Pagh Nielsen, Kristian; Savijärvi, Hannu; Hansen Sass, Bent
2017-07-01
This paper provides an overview of the HLRADIA shortwave (SW) and longwave (LW) broadband radiation schemes used in the HIRLAM numerical weather prediction (NWP) model and available in the HARMONIE-AROME mesoscale NWP model. The advantage of broadband, over spectral, schemes is that they can be called more frequently within the model, without compromising on computational efficiency. In mesoscale models fast interactions between clouds and radiation and the surface and radiation can be of greater importance than accounting for the spectral details of clear-sky radiation; thus calling the routines more frequently can be of greater benefit than the deterioration due to loss of spectral details. Fast but physically based radiation parametrizations are expected to be valuable for high-resolution ensemble forecasting, because as well as the speed of their execution, they may provide realistic physical perturbations. Results from single-column diagnostic experiments based on CIRC benchmark cases and an evaluation of 10 years of radiation output from the FMI operational archive of HIRLAM forecasts indicate that HLRADIA performs sufficiently well with respect to the clear-sky downwelling SW and longwave LW fluxes at the surface. In general, HLRADIA tends to overestimate surface fluxes, with the exception of LW fluxes under cold and dry conditions. The most obvious overestimation of the surface SW flux was seen in the cloudy cases in the 10-year comparison; this bias may be related to using a cloud inhomogeneity correction, which was too large. According to the CIRC comparisons, the outgoing LW and SW fluxes at the top of atmosphere are mostly overestimated by HLRADIA and the net LW flux is underestimated above clouds. The absorption of SW radiation by the atmosphere seems to be underestimated and LW absorption seems to be overestimated. Despite these issues, the overall results are satisfying and work on the improvement of HLRADIA for the use in HARMONIE-AROME NWP system
Schemes for aggregating preferential tariffs in agriculture,export volume effects and African LDCs
DEFF Research Database (Denmark)
Yu, Wusheng
Trade-weighted aggregated tariffs (TWPT) are often used in analyzing the issues of erosion of non-reciprocal preferences. This paper argues that commonly used TWPTs under-estimate the true protection on imports originated from preference-receiving countries, including LDCs. When used in numerical...... simulations of preference erosion and expansion scenarios, the TWPTs tend to incorrectly downplay preference erosion effect of MFN tariff cuts, and understate the export promotion effect of expanding preferences. In light of these claims, an alternative aggregation scheme is developed to calculate aggregated...
Accurate B-spline-based 3-D interpolation scheme for digital volume correlation
Ren, Maodong; Liang, Jin; Wei, Bin
2016-12-01
An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.
Schemes for aggregating preferential tariffs in agriculture,export volume effects and African LDCs
DEFF Research Database (Denmark)
Yu, Wusheng
Trade-weighted aggregated tariffs (TWPT) are often used in analyzing the issues of erosion of non-reciprocal preferences. This paper argues that commonly used TWPTs under-estimate the true protection on imports originated from preference-receiving countries, including LDCs. When used in numerical...... simulations of preference erosion and expansion scenarios, the TWPTs tend to incorrectly downplay preference erosion effect of MFN tariff cuts, and understate the export promotion effect of expanding preferences. In light of these claims, an alternative aggregation scheme is developed to calculate aggregated...... preferential tariffs imposed by a number of developed countries on African LDCs. These are shown to be higher than the TWPTs aggregated from the same disaggregated tariff data set. Numerical simulations conducted with the two sets of aggregated tariffs confirm the two claims and suggest that TWPTs may lead...
Amano, Takanobu
2016-11-01
A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell’s equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron-positron or an electron-proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten-Lax-Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell’s equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small scales. This shows that the RTFED model is a promising tool for high energy astrophysics application.
Nguyen, T. T.; Laurent, F.; Fox, R. O.; Massot, M.
2016-11-01
The accurate description and robust simulation, at relatively low cost, of global quantities (e.g. number density or volume fraction) as well as the size distribution of a population of fine particles in a carrier fluid is still a major challenge for many applications. For this purpose, two types of methods are investigated for solving the population balance equation with aggregation, continuous particle size change (growth and size reduction), and nucleation: the extended quadrature method of moments (EQMOM) based on the work of Yuan et al. [52] and a hybrid method (TSM) between the sectional and moment methods, considering two moments per section based on the work of Laurent et al. [30]. For both methods, the closure employs a continuous reconstruction of the number density function of the particles from its moments, thus allowing evaluation of all the unclosed terms in the moment equations, including the negative flux due to the disappearance of particles. Here, new robust and efficient algorithms are developed for this reconstruction step and two kinds of reconstruction are tested for each method. Moreover, robust and accurate numerical methods are developed, ensuring the realizability of the moments. The robustness is ensured with efficient and tractable algorithms despite the numerous couplings and various algebraic constraints thanks to a tailored overall strategy. EQMOM and TSM are compared to a sectional method for various simple but relevant test cases, showing their ability to describe accurately the fine-particle population with a much lower number of variables. These results demonstrate the efficiency of the modeling and numerical choices, and their potential for the simulation of real-world applications.
Gas Evolution Dynamics in Godunov-Type Schemes and Analysis of Numerical Shock Instability
Xu, Kun
1999-01-01
In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers, e.g., the Flux Vector Splitting (FVS) and the Flux Difference Splitting (FDS) schemes. Since the FVS scheme and the Kinetic Flux Vector Splitting (KFVS) scheme have the same physical mechanism and similar flux function, based on the analysis of the discretized KFVS scheme the weakness and advantage of the FVS scheme are closely observed. The subtle dissipative mechanism of the Godunov method in the 2D case is also analyzed, and the physical reason for shock instability, i.e., carbuncle phenomena and odd-even decoupling, is presented.
Sánchez Burillo, Guillermo; Beguería, Santiago; Latorre, Borja; Burguete, Javier
2014-05-01
Debris flows, snow and rock avalanches, mud and earth flows are often modeled by means of a particular realization of the so called shallow water equations (SWE). Indeed, a number of simulation models have been already developed [1], [2], [3], [4], [5], [6], [7]. Debris flow equations differ from shallow water equations in two main aspects. These are (a) strong bed gradient and (b) rheology friction terms that differ from the traditional SWE. A systematic analysis of the numerical solution of the hyperbolic system of equations rising from the shallow water equations with different rheological laws has not been done. Despite great efforts have been done to deal with friction expressions common in hydraulics (such as Manning friction), landslide rheologies are characterized by more complicated expressions that may deal to unphysical solutions if not treated carefully. In this work, a software that solves the time evolution of sliding masses over complex bed configurations is presented. The set of non- linear equations is treated by means of a first order upwind explicit scheme, and the friction contribution to the dynamics is treated with a suited numerical scheme [8]. In addition, the software incorporates various rheological models to accommodate for different flow types, such as the Voellmy frictional model [9] for rock and debris avalanches, or the Herschley-Bulkley model for debris and mud flows. The aim of this contribution is to release this code as a free, open source tool for the simulation of mass movements, and to encourage the scientific community to make use of it. The code uses as input data the friction coefficients and two input files: the topography of the bed and the initial (pre-failure) position of the sliding mass. In addition, another file with the final (post-event) position of the sliding mass, if desired, can be introduced to be compared with the simulation obtained result. If the deposited mass is given, an error estimation is computed by
Yang, Xiaofeng
2016-12-01
In this paper, we develop a series of efficient numerical schemes to solve the phase field model for homopolymer blends. The governing system is derived from the energetic variational approach of a total free energy, that consists of a nonlinear logarithmic Flory-Huggins potential, and a gradient entropy with a concentration-dependent de-Gennes type coefficient. The main challenging issue to solve this kind of models numerically is about the time marching problem, i.e., how to develop suitable temporal discretizations for the nonlinear terms in order to preserve the energy stability at the discrete level. We solve this issue in this paper, by developing the first and second order temporal approximation schemes based on the "Invariant Energy Quadratization" method, where all nonlinear terms are treated semi-explicitly. Consequently, the resulting numerical schemes lead to a symmetric positive definite linear system to be solved at each time step. The unconditional energy stabilities are further proved. Various numerical simulations of 2D and 3D are presented to demonstrate the stability and the accuracy of the proposed schemes.
Han, Lanshan; Camlibel, M. Kanat; Pang, Jong-Shi; Heemels, W. P. Maurice H.
2012-01-01
This paper presents a numerical scheme for solving the continuous-time convex linear-quadratic (LQ) optimal control problem with mixed polyhedral state and control constraints. Unifying a discretization of this optimal control problem as often employed in model predictive control and that obtained
Energy Technology Data Exchange (ETDEWEB)
Okazaki, Motoaki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1997-11-01
A new numerical method to achieve a rigorous numerical calculation of each phase using a simple explicit method with volume-junction model is proposed. For this purpose, difference equations for numerical use are carefully derived so as to preserve the physical meaning of the basic equations. Specifically, momentum equations for the flow in the volume are newly derived to keep strict conservation of energy within the volume. To prove the validity of the numerical method and of previously proposed basic equations, including the original phase change equations, which were rigorously derived, some numerical calculations were made for each phase independently to examine the correctness of calculated results. The numerical calculation is advanced by simple integration of an explicitly obtained solution of difference equations without any special treatment. Calculated results of density and specific internal energy of each phase for saturated two-phase blowdown behavior are consistent for two different solution scheme as described below. Further, no accumulation of error in mass or energy was found. These results prove the consistency among basic equations, including phase change equations, and the correctness of numerical calculation method. The two different solution schemes used were: (1) solutions of pressure and void fraction in saturated condition were obtained by using mass conservation equation of each phase simultaneously, and (2) fluid properties were calculated directly from mass and energy conservation equation of each phase. (author)
Directory of Open Access Journals (Sweden)
Nopparat Pochai
2011-01-01
Full Text Available The stream water quality model of water quality assessment problems often involves numerical methods to solve the equations. The governing equation of the uniform flow model is one-dimensional advection-dispersion-reaction equations (ADREs. In this paper, a better finite difference scheme for solving ADRE is focused, and the effect of nonuniform water flows in a stream is considered. Two mathematical models are used to simulate pollution due to sewage effluent. The first is a hydrodynamic model that provides the velocity field and elevation of the water flow. The second is a advection-dispersion-reaction model that gives the pollutant concentration fields after input of the velocity data from the hydrodynamic model. For numerical techniques, we used the Crank-Nicolson method for system of a hydrodynamic model and the explicit schemes to the dispersion model. The revised explicit schemes are modified from two computation techniques of uniform flow stream problems: forward time central space (FTCS and Saulyev schemes for dispersion model. A comparison of both schemes regarding stability aspect is provided so as to illustrate their applicability to the real-world problem.
Energy Technology Data Exchange (ETDEWEB)
Gwo, D
2006-03-20
The article proposes a scheme to break a catch-22 loop in an optical-figure/wavefont measurement. For instance, to measure the tilt-independent optical-figure of a nominal optical flat at cryogenic temperatures, it requires a cryogenic dewar-window system for a Fizeau interferometer outside the dewar to see through. The issue is: how to calibrate in situ the window system using the yet-to-be-calibrated nominal optical flat, and vice versa, in only one cryogenic cooldown? The proposition includes: (a) interferometric phase-map measurements with the test piece slightly offset in different transverse directions, and (b) for synthesizing the 2-dimensional WDF, an unconventional numerical scheme starting with 1-dimensional bi-direction integration. The numerical scheme helps minimize the non-uniformity in integrated noise-power distribution that results from integrating data, and thus the associated uncorrelated random noise, from raw phase-maps. The numerical scheme represents a new concept specifically for integrating noise-carrying experimental data.
A Semi-implicit Numerical Scheme for a Two-dimensional, Three-field Thermo-Hydraulic Modeling
Energy Technology Data Exchange (ETDEWEB)
Hwang, Moonkyu; Jeong, Jaejoon
2007-07-15
The behavior of two-phase flow is modeled, depending on the purpose, by either homogeneous model, drift flux model, or separated flow model, Among these model, in the separated flow model, the behavior of each flow phase is modeled by its own governing equation, together with the interphase models which describe the thermal and mechanical interactions between the phases involved. In this study, a semi-implicit numerical scheme for two-dimensional, transient, two-fluid, three-field is derived. The work is an extension to the previous study for the staggered, semi-implicit numerical scheme in one-dimensional geometry (KAERI/TR-3239/2006). The two-dimensional extension is performed by specifying a relevant governing equation set and applying the related finite differencing method. The procedure for employing the semi-implicit scheme is also described in detail. Verifications are performed for a 2-dimensional vertical plate for a single-phase and two-phase flows. The calculations verify the mass and energy conservations. The symmetric flow behavior, for the verification problem, also confirms the momentum conservation of the numerical scheme.
Numerical Fourier method and second-order Taylor scheme for backward SDEs in finance
Ruijter, M.J.; Oosterlee, C.W.
2016-01-01
We develop a Fourier method to solve quite general backward stochastic differential equa-tions (BSDEs) with second-order accuracy. The underlying forward stochastic differential equation (FSDE) is approximated by different Taylor schemes, such as the Euler, Milstein, and Order2.0 weak Taylor schemes
A numerical scheme for modelling reacting flow with detailed chemistry and transport.
Energy Technology Data Exchange (ETDEWEB)
Knio, Omar M. (The Johns Hopkins University, Baltimore, MD); Najm, Habib N.; Paul, Phillip H. (Eksigent Technologies LLC, Livermore, CA)
2003-09-01
An efficient projection scheme is developed for the simulation of reacting flow with detailed kinetics and transport. The scheme is based on a zero-Mach-number formulation of the compressible conservation equations for an ideal gas mixture. It is a modified version of the stiff operator-split scheme developed by Knio, Najm & Wyckoff (1999, J. Comput. Phys. 154, 428). Similar to its predecessor, the new scheme relies on Strang splitting of the discrete evolution equations, where diffusion is integrated in two half steps that are symmetrically distributed around a single stiff step for the reaction source terms. The diffusive half-step is integrated using an explicit single-step, multistage, Runge-Kutta-Chebyshev (RKC) method, which replaces the explicit, multi-step, fractional sub-step approach used in the previous formulation. This modification maintains the overall second-order convergence properties of the scheme and enhances the efficiency of the computations by taking advantage of the extended real-stability region of the RKC scheme. Two additional efficiency-enhancements are also explored, based on an extrapolation procedure for the transport coefficients and on the use of approximate Jacobian data evaluated on a coarse mesh. By including these enhancement schemes, performance tests using 2D computations with a detailed C{sub 1}C{sub 2} methane-air mechanism and a detailed mixture-averaged transport model indicate that speedup factors of about 15 are achieved over the previous split-stiff scheme.
Mignone, A
2014-01-01
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the zone-average values to reconstruct left and right interface states from within a computational zone to arbitrary order of accuracy by inverting a Vandermonde-like linear system of equations with spatially varying coefficients. The approach is general and can be used on uniform and non-uniform meshes although explicit expressions are derived for polynomials from second to fifth degree in cylindrical and spherical geometries with uniform grid spacing. It is shown that, in regions of large curvature, the resulting expressions differ considerably from their Cartesian counterparts and that the lack of such corrections can severely degrade the accuracy of the solution close to the coordinate origin. Limiting techniques and monotonicity constraints are revised for conventional reconstruct...
Sayed, Sadeed Bin
2015-05-05
A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert- Wilton-Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations can not be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.
1D and 2D Numerical Modeling for Solving Dam-Break Flow Problems Using Finite Volume Method
Directory of Open Access Journals (Sweden)
Szu-Hsien Peng
2012-01-01
Full Text Available The purpose of this study is to model the flow movement in an idealized dam-break configuration. One-dimensional and two-dimensional motion of a shallow flow over a rigid inclined bed is considered. The resulting shallow water equations are solved by finite volumes using the Roe and HLL schemes. At first, the one-dimensional model is considered in the development process. With conservative finite volume method, splitting is applied to manage the combination of hyperbolic term and source term of the shallow water equation and then to promote 1D to 2D. The simulations are validated by the comparison with flume experiments. Unsteady dam-break flow movement is found to be reasonably well captured by the model. The proposed concept could be further developed to the numerical calculation of non-Newtonian fluid or multilayers fluid flow.
Energy Technology Data Exchange (ETDEWEB)
Oki, Y.; Tanahashi, T. [Keio University, Tokyo (Japan). Faculty of Science and Technology
1995-07-25
In the present paper, the natural convections of thermo-electrically conducting fluids in a square cavity under a uniform magnetic field are calculated using GSMAC-FEM in conjunction with the so-called B method. This scheme efficiently satisfies conservation laws of both mass and magnetic flux. In order to establish a stable numerical scheme at low magnetic Reynolds number problems, we introduce both the generalized trapezoidal method and the 3-level fully implicit method into the conventional numerical residual method. The numerical results obtained are in good agreement with the past numerical and experimental results. 13 refs., 7 figs., 2 tabs.
Litta, A. J.; Chakrapani, B.; Mohankumar, K.
2007-07-01
Heavy rainfall events become significant in human affairs when they are combined with hydrological elements. The problem of forecasting heavy precipitation is especially difficult since it involves making a quantitative precipitation forecast, a problem well recognized as challenging. Chennai (13.04°N and 80.17°E) faced incessant and heavy rain about 27 cm in 24 hours up to 8.30 a.m on 27th October 2005 completely threw life out of gear. This torrential rain caused by deep depression which lay 150km east of Chennai city in Bay of Bengal intensified and moved west north-west direction and crossed north Tamil Nadu and south Andhra Pradesh coast on 28th morning. In the present study, we investigate the predictability of the MM5 mesoscale model using different cumulus parameterization schemes for the heavy rainfall event over Chennai. MM5 Version 3.7 (PSU/NCAR) is run with two-way triply nested grids using Lambert Conformal Coordinates (LCC) with a nest ratio of 3:1 and 23 vertical layers. Grid sizes of 45, 15 and 5 km are used for domains 1, 2 and 3 respectively. The cumulus parameterization schemes used in this study are Anthes-Kuo scheme (AK), the Betts-Miller scheme (BM), the Grell scheme (GR) and the Kain-Fritsch scheme (KF). The present study shows that the prediction of heavy rainfall is sensitive to cumulus parameterization schemes. In the time series of rainfall, Grell scheme is in good agreement with observation. The ideal combination of the nesting domains, horizontal resolution and cloud parameterization is able to simulate the heavy rainfall event both qualitatively and quantitatively.
A hybrid numerical prediction scheme for solar radiation estimation in un-gauged catchments.
Shamim, M. A.; Bray, M.; Ishak, A. M.; Remesan, R.; Han, D.
2009-09-01
The importance of solar radiation on earth's surface is depicted in its wide range of applications in the fields of meteorology, agricultural sciences, engineering, hydrology, crop water requirements, climatic changes and energy assessment. It is quite random in nature as it has to go through different processes of assimilation and dispersion while on its way to earth. Compared to other meteorological parameters, solar radiation is quite infrequently measured, for example, the worldwide ratio of stations collecting solar radiation to those collecting temperature is 1:500 (Badescu, 2008). Researchers, therefore, have to rely on indirect techniques of estimation that include nonlinear models, artificial intelligence (e.g. neural networks), remote sensing and numerical weather predictions (NWP). This study proposes a hybrid numerical prediction scheme for solar radiation estimation in un-gauged catchments. It uses the PSU/NCAR's Mesoscale Modelling system (MM5) (Grell et al., 1995) to parameterise the cloud effect on extraterrestrial radiation by dividing the atmosphere into four layers of very high (6-12 km), high (3-6 km), medium (1.5-3) and low (0-1.5) altitudes from earth. It is believed that various cloud forms exist within each of these layers. An hourly time series of upper air pressure and relative humidity data sets corresponding to all of these layers is determined for the Brue catchment, southwest UK, using MM5. Cloud Index (CI) was then determined using (Yang and Koike, 2002): 1 p?bi [ (Rh - Rh )] ci =------- max 0.0,---------cri dp pbi - ptipti (1- Rhcri) where, pbi and pti represent the air pressure at the top and bottom of each layer and Rhcri is the critical value of relative humidity at which a certain cloud type is formed. Output from a global clear sky solar radiation model (MRM v-5) (Kambezidis and Psiloglu, 2008) is used along with meteorological datasets of temperature and precipitation and astronomical information. The analysis is aided by the
Strumik, Marek
2016-01-01
We present a numerical solver for plasma dynamics simulations in Hall magnetohydrodynamic (HMHD) approximation in one, two and three dimensions. We consider both isotropic and anisotropic thermal pressure cases, where a general gyrotropic approximation is used. Both explicit energy conservation equation and general polytropic state equations are considered. The numerical scheme incorporates second-order Runge-Kutta advancing in time and Kurganov-Tadmor scheme with van Leer flux limiter for the approximation of fluxes. A flux-interpolated constrained-transport approach is used to preserve solenoidal magnetic field in the simulations. The implemented code is validated using several test problems previously described in the literature. Additionally, we propose a new validation method for HMHD codes based on solitary waves that provides a possibility of quantitative rigorous testing in nonlinear (large amplitude) regime as an extension to standard tests using small-amplitude whistler waves. Quantitative tests of ...
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Parovik Roman I.
2016-09-01
Full Text Available The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.
Anitescu, Mihai; Layton, William J.; Pahlevani, Faranak
2003-01-01
A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit in local and stabilizing terms in the underlying PDE and explicit in nonlocal and unstabilizing terms. Unconditional stability and convergence of the numerical scheme are proven by the energy method and by algebraic techniques. This stability result is sur...
Hirschel, Ernst Heinrich; Fujii, Kozo
2009-01-01
This volume contains 37 invited contributions, collected to celebrate one hundred volumes of the ""NNFM Series"". After a general introduction, overviews are given in five parts of the developments in numerical fluid mechanics and related fields. In the first part information about the series is given, its origins are discussed, as well as its environment and the German and European high-performance computer scene. In Part II the co-editors of the series give short surveys over developments in their countries. Current applications, mainly in the aerospace sector, but also in the automotive sec
Numerical Schemes for Dynamically Orthogonal Equations of Stochastic Fluid and Ocean Flows
2011-11-03
Report TM 109112, NASA Langley Research Center, Hampton, VA [4] Chapra SC, Canale RP (2006) Numerical Methods for Engineers, 5th edn. McGraw-Hill...that we reduced the number of PPEs from s2 + s+ 1 to the expected s+ 1. 3.3. Projection Methods for the Mean and Modes To obtain a numerically divergence...any additional error in the projection method . However, it is necessary to verify that its numerical implementation is sufficiently accurate, and
Numerical stability analysis of an acceleration scheme for step size constrained time integrators
Vandekerckhove, Christophe; Roose, Dirk; Lust, Kurt
2007-01-01
Time integration schemes with a fixed time step, much smaller than the dominant slow time scales of the dynamics of the system, arise in the context of stiff ordinary differential equations or in multiscale computations, where a microscopic time-stepper is used to compute macroscopic behaviour. We d
Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer
Vreman, A.W.; Geurts, Bernardus J.; Kuerten, Johannes G.M.
1996-01-01
A posteriori tests of large-eddy simulations for the temporal mixing layer are performed using a variety of numerical methods in conjunction with the dynamic mixed subgrid model for the turbulent stress tensor. The results of the large-eddy simulations are compared with filtered direct numerical
Recent advances in marching-on-in-time schemes for solving time domain volume integral equations
Sayed, Sadeed Bin
2015-05-16
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are constructed by setting the summation of the incident and scattered field intensities to the total field intensity on the volumetric support of the scatterer. The unknown can be the field intensity or flux/current density. Representing the total field intensity in terms of the unknown using the relevant constitutive relation and the scattered field intensity in terms of the spatiotemporal convolution of the unknown with the Green function yield the final form of the TDVIE. The unknown is expanded in terms of local spatial and temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation at discrete times yield a system of equations that is solved by the marching on-in-time (MOT) scheme. At each time step, a smaller system of equations, termed MOT system is solved for the coefficients of the expansion. The right-hand side of this system consists of the tested incident field and discretized spatio-temporal convolution of the unknown samples computed at the previous time steps with the Green function.
Test of some numerical limiters for the conservative PSM scheme for 4D Drift-Kinetic simulations
Guterl, Jerome; Crouseilles, Nicolas; Grandgirard, Virginie; Latu, Guillaume; Mehrenberger, Michel; Sonnendrücker, Eric
2010-01-01
The purpose of this work is simulation of magnetised plasmas in the ITER project framework. In this context, Vlasov-Poisson like models are used to simulate core turbulence in the tokamak in a toroidal geometry. This leads to heavy simulation because a 6D dimensional problem has to be solved, 3D in space and 3D in velocity. The model is reduced to a 5D gyrokinetic model, taking advantage of the particular motion of particles due to the presence of a strong magnetic field. However, accurate schemes, parallel algorithms need to be designed to bear these simulations. This paper describes a Hermite formulation of the conservative PSM scheme which is very generic and allows to implement different semi-Lagrangian schemes. We also test and propose numerical limiters which should improve the robustness of the simulations by diminishing spurious oscillations. We only consider here the 4D drift-kinetic model which is the backbone of the 5D gyrokinetic models and relevant to build a robust and accurate numerical method.
Role of numerical scheme choice on the results of mathematical modeling of combustion and detonation
Yakovenko, I. S.; Kiverin, A. D.; Pinevich, S. G.; Ivanov, M. F.
2016-11-01
The present study discusses capabilities of dissipation-free CABARET numerical method application to unsteady reactive gasdynamic flows modeling. In framework of present research the method was adopted for reactive flows governed by real gas equation of state and applied for several typical problems of unsteady gas dynamics and combustion modeling such as ignition and detonation initiation by localized energy sources. Solutions were thoroughly analyzed and compared with that derived by using of the modified Euler-Lagrange method of “coarse” particles. Obtained results allowed us to distinguish range of phenomena where artificial effects of numerical approach may counterfeit their physical nature and to develop guidelines for numerical approach selection appropriate for unsteady reactive gasdynamic flows numerical modeling.
Directory of Open Access Journals (Sweden)
Saulo Frietas
2012-01-01
Full Text Available An advection scheme, which maintains the initial monotonic characteristics of a tracer field being transported and at the same time produces low numerical diffusion, is implemented in the Coupled Chemistry-Aerosol-Tracer Transport model to the Brazilian developments on the Regional Atmospheric Modeling System (CCATT-BRAMS. Several comparisons of transport modeling using the new and original (non-monotonic CCATT-BRAMS formulations are performed. Idealized 2-D non-divergent or divergent and stationary or time-dependent wind fields are used to transport sharply localized tracer distributions, as well as to verify if an existent correlation of the mass mixing ratios of two interrelated tracers is kept during the transport simulation. Further comparisons are performed using realistic 3-D wind fields. We then perform full simulations of real cases using data assimilation and complete atmospheric physics. In these simulations, we address the impacts of both advection schemes on the transport of biomass burning emissions and the formation of secondary species from non-linear chemical reactions of precursors. The results show that the new scheme produces much more realistic transport patterns, without generating spurious oscillations and under- and overshoots or spreading mass away from the local peaks. Increasing the numerical diffusion in the original scheme in order to remove the spurious oscillations and maintain the monotonicity of the transported field causes excessive smoothing in the tracer distribution, reducing the local gradients and maximum values and unrealistically spreading mass away from the local peaks. As a result, huge differences (hundreds of % for relatively inert tracers (like carbon monoxide are found in the smoke plume cores. In terms of the secondary chemical species formed by non-linear reactions (like ozone, we found differences of up to 50% in our simulations.
Numerical Investigation of a Novel Wiring Scheme Enabling Simple and Accurate Impedance Cytometry
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Federica Caselli
2017-09-01
Full Text Available Microfluidic impedance cytometry is a label-free approach for high-throughput analysis of particles and cells. It is based on the characterization of the dielectric properties of single particles as they flow through a microchannel with integrated electrodes. However, the measured signal depends not only on the intrinsic particle properties, but also on the particle trajectory through the measuring region, thus challenging the resolution and accuracy of the technique. In this work we show via simulation that this issue can be overcome without resorting to particle focusing, by means of a straightforward modification of the wiring scheme for the most typical and widely used microfluidic impedance chip.
A Numerical Scheme for Computing Stable and Unstable Manifolds in Nonautonomous Flows
Balasuriya, Sanjeeva
2016-12-01
There are many methods for computing stable and unstable manifolds in autonomous flows. When the flow is nonautonomous, however, difficulties arise since the hyperbolic trajectory to which these manifolds are anchored, and the local manifold emanation directions, are changing with time. This article utilizes recent results which approximate the time-variation of both these quantities to design a numerical algorithm which can obtain high resolution in global nonautonomous stable and unstable manifolds. In particular, good numerical approximation is possible locally near the anchor trajectory. Nonautonomous manifolds are computed for two examples: a Rossby wave situation which is highly chaotic, and a nonautonomus (time-aperiodic) Duffing oscillator model in which the manifold emanation directions are rapidly changing. The numerical method is validated and analyzed in these cases using finite-time Lyapunov exponent fields and exactly known nonautonomous manifolds.
A numerical scheme for space-time fractional advection-dispersion equation
Javadi, S; Jani, M
2015-01-01
In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. After time discretization, we utilize collocation technique and implement a product integration method in order to simplify the evaluation of the terms involving spatial fractional order derivatives. Then utilizing Bernstein polynomials as basis, the problem is transformed into a linear system of algebraic equations. Error analysis and order of convergence for the proposed method are also discussed. Some numerical experiments are presented to demonstrate the effectiveness of the proposed method and to confirm the analytic results.
A reaction-based river/stream water quality model: Model development and numerical schemes
Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C.; Jardine, Philip M.
2008-01-01
SummaryThis paper presents the conceptual and mathematical development of a numerical model of sediment and reactive chemical transport in rivers and streams. The distribution of mobile suspended sediments and immobile bed sediments is controlled by hydrologic transport as well as erosion and deposition processes. The fate and transport of water quality constituents involving a variety of chemical and physical processes is mathematically described by a system of reaction equations for immobile constituents and advective-dispersive-reactive transport equations for mobile constituents. To circumvent stiffness associated with equilibrium reactions, matrix decomposition is performed via Gauss-Jordan column reduction. After matrix decomposition, the system of water quality constituent reactive transport equations is transformed into a set of thermodynamic equations representing equilibrium reactions and a set of transport equations involving no equilibrium reactions. The decoupling of equilibrium and kinetic reactions enables robust numerical integration of the partial differential equations (PDEs) for non-equilibrium-variables. Solving non-equilibrium-variable transport equations instead of individual water quality constituent transport equations also reduces the number of PDEs. A variety of numerical methods are investigated for solving the mixed differential and algebraic equations. Two verification examples are compared with analytical solutions to demonstrate the correctness of the code and to illustrate the importance of employing application-dependent numerical methods to solve specific problems.
Influence of numerical schemes on current-topography interactions in 1/4° global ocean simulations
Directory of Open Access Journals (Sweden)
G. Madec
2007-06-01
Full Text Available The combined use of partial steps and of an energy-enstrophy conserving momentum advection scheme was shown by Barnier et al. (2006 to yield substantial improvements in the surface solution of the DRAKKAR ¼° global sea-ice/ocean model. The present study extends this investigation below the surface with a special focus on the Atlantic and reveals many improvements there as well: e.g. more realistic path, structure and transports of major currents (Gulf Stream, North Atlantic Current, Confluence region, Zapiola anticyclone, behavior of shedded rings, narrower subsurface boundary currents, stronger mean and eddy flows (MKE and EKE at depth, beneficial enhancement of cyclonic (anticyclonic flows around topographic depressions (mountains. Interestingly, adding a no-slip boundary condition to this improved model setup cancels most of these improvements, bringing back the biases diagnosed without the improved momentum advection scheme and partial steps (these biases are typical of other models at comparable or higher resolutions. This shows that current-topography interactions and full-depth eddy-admitting model solutions can be seriously deteriorated by near-bottom sidewall friction, either explicit or inherent to inadequate numerical schemes.
Influence of numerical schemes on current-topography interactions in 1/4° global ocean simulations
Directory of Open Access Journals (Sweden)
G. Madec
2007-12-01
Full Text Available The combined use of partial steps and of an energy-enstrophy conserving momentum advection scheme was shown by Barnier et al. (2006 to yield substantial improvements in the surface solution of the DRAKKAR ¼° global sea-ice/ocean model. The present study extends this investigation below the surface with a special focus on the Atlantic and reveals many improvements there as well: e.g. more realistic path, structure and transports of major currents (Gulf Stream, North Atlantic Current, Confluence region, Zapiola anticyclone, behavior of shedded rings, narrower subsurface boundary currents, stronger mean and eddy flows (MKE and EKE at depth, beneficial enhancement of cyclonic (anticyclonic flows around topographic depressions (mountains. Interestingly, adding a no-slip boundary condition to this improved model setup cancels most of these improvements, bringing back the biases diagnosed without the improved momentum advection scheme and partial steps (these biases are typical of other models at comparable or higher resolutions. This shows that current-topography interactions and full-depth eddy-admitting model solutions can be seriously deteriorated by near-bottom sidewall friction, either explicit or inherent to inadequate numerical schemes.
Jiang, Zhongzheng; Zhao, Wenwen
2016-01-01
Non-equilibrium effects play a vital role in high-speed and rarefied gas flows and the accurate simulation of these flow regimes are far beyond the capability of near-local-equilibrium Navier-Stokes-Fourier equations. Eu proposed generalized hydrodynamic equations which are consistent with the laws of irreversible thermodynamics to solve this problem. Based on Eu's generalized hydrodynamics equations, a computational model, namely the nonlinear coupled constitutive relations(NCCR),was developed by R.S.Myong and applied successfully to one-dimensional shock wave structure and two-dimensional rarefied flows. In this paper, finite volume schemes, including LU-SGS time advance scheme, MUSCL interpolation and AUSMPW+ scheme, are fistly adopted to investigate NCCR model's validity and potential in three-dimensional complex hypersonic rarefied gas flows. Moreover, in order to solve the computational stability problems in 3D complex flows,a modified solution is developed for the NCCR model. Finally, the modified solu...
Strumik, Marek; Stasiewicz, Krzysztof
2017-02-01
We present a numerical solver for plasma dynamics simulations in Hall magnetohydrodynamic (HMHD) approximation in one, two and three dimensions. We consider both isotropic and anisotropic thermal pressure cases, where a general gyrotropic approximation is used. Both explicit energy conservation equation and general polytropic state equations are considered. The numerical scheme incorporates second-order Runge-Kutta advancing in time and Kurganov-Tadmor scheme with van Leer flux limiter for the approximation of fluxes. A flux-interpolated constrained-transport approach is used to preserve solenoidal magnetic field in the simulations. The implemented code is validated using several test problems previously described in the literature. Additionally, we propose a new validation method for HMHD codes based on solitary waves that provides a possibility of quantitative rigorous testing in nonlinear (large amplitude) regime as an extension to standard tests using small-amplitude whistler waves. Quantitative tests of accuracy and performance of the implemented code show the fidelity of the proposed approach.
Directory of Open Access Journals (Sweden)
B. Kafash
2014-04-01
Full Text Available In this paper, we present a computational method for solving optimal control problems and the controlled Duffing oscillator. This method is based on state parametrization. In fact, the state variable is approximated by Boubaker polynomials with unknown coefficients. The equation of motion, performance index and boundary conditions are converted into some algebraic equations. Thus, an optimal control problem converts to a optimization problem, which can then be solved easily. By this method, the numerical value of the performance index is obtained. Also, the control and state variables can be approximated as functions of time. Convergence of the algorithms is proved. Numerical results are given for several test examples to demonstrate the applicability and efficiency of the method.
European Workshop on High Order Nonlinear Numerical Schemes for Evolutionary PDEs
Beaugendre, Héloïse; Congedo, Pietro; Dobrzynski, Cécile; Perrier, Vincent; Ricchiuto, Mario
2014-01-01
This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.
Numerical and experimental investigation into passive hydrogen recovery scheme using vacuum ejector
Hwang, Jenn-Jiang; Cho, Ching-Chang; Wu, Wei; Chiu, Ching-Huang; Chiu, Kuo-Ching; Lin, Chih-Hong
2015-02-01
The current work presents a numerical and experimental investigation into a passive ejector for recovering the anode off-gas in a proton exchange membrane fuel cell (PEMFC) system. The proposed ejector is consisted of a convergent-divergent channel and a suction channel, and it is connected with the anode outlet of PEMFC system for recovery the anode off-gas into the main gas supply. Numerical simulations based on a three-dimensional compressible steady-state k-ɛ turbulent model are performed to examine the effects of the inlet mass flow rate and nozzle throat diameter on the pressure, Mach number, temperature, suction channel mass flow rate, outlet channel mass flow rate, and suction channel entrainment ratio, respectively. The numerical results are confirmed by means of an experimental investigation. It is shown that supersonic flow conditions are induced in the ejector; resulting in the induction of a vacuum pressure in the suction channel and the subsequent recovery of the anode off-gas at the outlet of the main channel. In addition, it is shown that the mass flow rate in the suction channel increases with an increasing mass flow rate at the primary channel inlet. Finally, the results show that a higher entrainment ratio is obtained as the throat diameter of the nozzle in the ejector is reduced. Overall, the results presented in this study provide a useful source of reference for developing the ejector devices applied to fuel cell systems while simultaneously avoiding extra energy consumption.
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A. A. Bykov
2016-01-01
Full Text Available Evolution equations are derived for the contrasting-structure-type solution of the gen-eralized Kolmogorov–Petrovskii–Piskunov (GKPP equation with the small parameter with high order derivatives. The GKPP equation is a pseudoparabolic equation with third order derivatives. This equation describes numerous processes in physics, chemistry, biology, for example, magnetic ﬁeld generation in a turbulent medium and the moving front for the carriers in semiconductors. The proﬁle of the moving internal transitional layer (ITL is found, and an expression for drift speed of the ITL is derived. An adaptive mesh (AM algorithm for the numerical solution of the initial-boundary value problem for the GKPP equation is developed and rigorously substantiated. AM algorithm for the special point of the ﬁrst kind is developed, in which drift speed of the ITL in the ﬁrst order of the asymptotic expansion turns to zero. Suﬃcient conditions for ITL transitioning through the special point within ﬁnite time are formulated. AM algorithm for the special point of the second kind is developed, in which drift speed of the ITL in the ﬁrst order formally turns to inﬁnity. Substantiation of the AM method is given based on the method of diﬀerential inequalities. Upper and lower solutions are derived. The results of the numerical algorithm are presented.
Schwing, Alan Michael
For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable
Improved computational schemes for the numerical modeling of hydrothermal resources in Wyoming
Energy Technology Data Exchange (ETDEWEB)
Heasler, H.P.; George, J.H.; Allen, M.B.
1990-05-01
A new method, the Conjugate Gradient Squared (CGS) solution technique, is shown to be extremely effective when applied to the finite-difference solution of conductive and convective heat transfer in geologic systems. The CGS method is compared to the Successive Over/Under Relaxation schemes, a version of the Gaussian elimination method, and the Generalized Minimum Residual (GMRES) approach. The CGS procedure converges at least ten times faster than the nearest competitor. The model is applied to the Thermopolis hydrothermal system, located in northwestern Wyoming. Modeled results are compared with measured temperature-depth profiles and results from other studies. The temperature decrease from 72{degree}C to 54{degrees}C along the crest of the Thermopolis anticline is shown to result from cooling of the geothermal fluid as it moves to the southeast. Modeled results show correct general trends, however, a time-varying three-dimensional model will be needed to fully explain the effects of mixing within the aquifers along the crest of the anticline and thermal affects of surface surface topography. 29 refs., 18 figs., 2 tabs.
Energy Technology Data Exchange (ETDEWEB)
Lode, Axel U.J.
2013-06-03
This thesis explores the quantum many-body tunneling dynamics of open ultracold bosonic systems with the recently developed multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. The capabilities of MCTDHB to provide solutions to the full time-dependent many-body problem are assessed in a benchmark using the analytically solvable harmonic interaction Hamiltonian and a generalization of it with time-dependent both one- and two-body potentials. In a comparison with numerically exact MCTDHB results, it is shown that e.g. lattice methods fail qualitatively to describe the tunneling dynamics. A model assembling the many-body physics of the process from basic simultaneously happening single-particle processes is derived and verified with a numerically exact MCTDHB description. The generality of the model is demonstrated even for strong interactions and large particle numbers. The ejection of the bosons from the source occurs with characteristic velocities. These velocities are defined by the chemical potentials of systems with different particle numbers which are converted to kinetic energy. The tunneling process is accompanied by fragmentation: the ejected bosons lose their coherence with the source and among each other. It is shown that the various aspects of the tunneling dynamics' can be controlled well with the interaction and the potential threshold.
2011-08-01
NASA Report TM 109112, NASA Langley Research Center, Hampton, VA [4] Chapra SC, Canale RP (2006) Numerical Methods for Engineers, 5th edn. McGraw-Hill...covariances or deterministic modes, and schemes to maintain orthonormal modes at the numerical level are relevant to any system solved using the DO method ...heat transfers [49, 52]. However, the DO method has not yet been applied to Boussinesq flows, and the numerical challenges of the DO decomposition for
Modeling Small Exoplanets Interiors: a Numerical Scheme to Explore Possible Compositions
Brugger, B.; Mousis, O.; Deleuil, M.
2016-12-01
Despite the huge number of discovered exoplanets, our knowledge of their compositions remains extremely limited. Modeling the interiors of such bodies is necessary to go further than the first approximation given by their mean density. Here we present a numerical model aiming at computing the internal structure of a given exoplanet from its measured mass and radius, and providing a range of compositions compatible with these data. Our model assumes the presence of a metal core surrounded by a silicate mantle and a water layer. Depending on their respective proportions, we can model various compositions, typically from terrestrial planets to ocean or Mercury-like planets. We apply this model to the case of CoRoT-7b, whose mass and radius values have recently been updated to 4.73 ± 0.95% mearth and 1.585 ± 0.064 rearth, respectively. We show that these values are fully compatible with a solid composition, and find that CoRoT-7b may present a core mass fraction of 80% at maximum, or on the opposite, a maximum water mass fraction of 51%. If this latter composition is compatible with that of several icy moons in the solar system, a 80% core in mass is less conceivable and a lower limit can be placed from solar system formation conditions. These results confirm the Super-Earth status of CoRoT-7b, and show that an Earth-like composition may be obtained more easily compared to previous conclusions.
A numerical study of 2D detonation waves with adaptive finite volume methods on unstructured grids
Hu, Guanghui
2017-02-01
In this paper, a framework of adaptive finite volume solutions for the reactive Euler equations on unstructured grids is proposed. The main ingredients of the algorithm include a second order total variation diminishing Runge-Kutta method for temporal discretization, and the finite volume method with piecewise linear solution reconstruction of the conservative variables for the spatial discretization in which the least square method is employed for the reconstruction, and weighted essentially nonoscillatory strategy is used to restrain the potential numerical oscillation. To resolve the high demanding on the computational resources due to the stiffness of the system caused by the reaction term and the shock structure in the solutions, the h-adaptive method is introduced. OpenMP parallelization of the algorithm is also adopted to further improve the efficiency of the implementation. Several one and two dimensional benchmark tests on the ZND model are studied in detail, and numerical results successfully show the effectiveness of the proposed method.
Saad, Bilal Mohammed
2014-06-28
We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.
Kihm, J.; Park, S.; Kim, J.; SNU CO2 GEO-SEQ TEAM
2011-12-01
A series of integrated injection well and geologic formation numerical simulations was performed to evaluate the injection efficiency of carbon dioxide using a multiphase thermo-hydrological numerical model. The numerical simulation results show that groundwater flow, carbon dioxide flow, and heat transport in both injection well and sandstone formation can be simultaneously analyzed, and thus the injection efficiency (i.e., injection rate and injectivity) of carbon dioxide can be quantitatively evaluated using the integrated injection well and geologic formation numerical simulation scheme. The injection rate and injectivity of carbon dioxide increase rapidly during the early period of time (about 10 days) and then increase slightly up to about 2.07 kg/s (equivalent to 0.065 Mton/year) and about 2.84 × 10-7 kg/s/Pa, respectively, until 10 years for the base case. The sensitivity test results show that the injection pressure and temperature of carbon dioxide at the wellhead have significant impacts on its injection rate and injectivity. The vertical profile of the fluid pressure in the injection well becomes almost a hydrostatical equilibrium state within 1 month for all the cases. The vertical profile of the fluid temperature in the injection well becomes a monotonously increasing profile with the depth due to isenthalpic or adiabatic compression within 6 months for all the cases. The injection rate of carbon dioxide increases linearly with the fluid pressure difference between the well bottom and the sandstone formation far from the injection well. In contrast, the injectivity of carbon dioxide varies unsystematically with the fluid pressure difference. On the other hand, the reciprocal of the kinematic viscosity of carbon dioxide at the well bottom has an excellent linear relationship with the injectivity of carbon dioxide. It indicates that the above-mentioned variation of the injectivity of carbon dioxide can be corrected using this linear relationship. The
Doungmo Goufo, Emile Franc; Atangana, Abdon
2016-08-01
There have been numbers of conflicting and confusing situations, but also uniformity, in the application of the two most popular fractional derivatives, namely the classic Riemann-Liouville and Caputo fractional derivatives. The range of these issues is wide, including the initialization with the Caputo derivative and its observed difficulties compared to the Riemann-Liouville initialization conditions. In this paper, being aware of these issues and reacting to the newly introduced Caputo-Fabrizio fractional derivative (CFFD) without singular kernel, we introduce a new definition of fractional derivative called the new Riemann-Liouville fractional derivative (NRLFD) without singular kernel. The filtering property of the NRLFD is pointed out by showing it as the derivative of a convolution and contrary to the CFFD, it matches with the function when the order is zero. We also explore various scientific situations that may be conflicting and confusing in the applicability of both new derivatives. In particular, we show that both definitions still have some basic similarities, like not obeying the traditional chain rule. Furthermore, we provide the explicit formula for the Laplace transform of the NRLFD and we prove that, contrary to the CFFD, the NRLFD requires non-constant initial conditions and does not require the function f to be continuous or differentiable. Some simulations for the NRLFD are presented for different values of the derivative order. In the second part of this work, numerical approximations for the first- and second-order NRLFD are developped followed by a concrete application to diffusion. The stability of the numerical scheme is proved and numerical simulations are performed for different values of the derivative order α. They exhibit similar behavior for closed values of α.
Jiang, Ying; Chen, Jeff Z. Y.
2013-10-01
This paper concerns establishing a theoretical basis and numerical scheme for studying the phase behavior of AB diblock copolymers made of wormlike chains. The general idea of a self-consistent field theory is the combination of the mean-field approach together with a statistical weight that describes the configurational properties of a polymer chain. In recent years, this approach has been extensively used for structural prediction of block copolymers, based on the Gaussian-model description of a polymer chain. The wormlike-chain model has played an important role in the description of polymer systems, covering the semiflexible-to-rod crossover of the polymer properties and the highly stretching regime, which the Gaussian-chain model has difficulties to describe. Although the idea of developing a self-consistent field theory for wormlike chains could be traced back to early development in polymer physics, the solution of such a theory has been limited due to technical difficulties. In particular, a challenge has been to develop a numerical algorithm enabling the calculation of the phase diagram containing three-dimensional structures for wormlike AB diblock copolymers. This paper describes a computational algorithm that combines a number of numerical tricks, which can be used for such a calculation. A phase diagram covering major parameter areas was constructed for the wormlike-chain system and reported by us, where the ratio between the total length and the persistence length of a constituent polymer is suggested as another tuning parameter for the microphase-separated structures; all detailed technical issues are carefully addressed in the current paper.
Directory of Open Access Journals (Sweden)
Shun Takahashi
2014-01-01
Full Text Available A computational code adopting immersed boundary methods for compressible gas-particle multiphase turbulent flows is developed and validated through two-dimensional numerical experiments. The turbulent flow region is modeled by a second-order pseudo skew-symmetric form with minimum dissipation, while the monotone upstream-centered scheme for conservation laws (MUSCL scheme is employed in the shock region. The present scheme is applied to the flow around a two-dimensional cylinder under various freestream Mach numbers. Compared with the original MUSCL scheme, the minimum dissipation enabled by the pseudo skew-symmetric form significantly improves the resolution of the vortex generated in the wake while retaining the shock capturing ability. In addition, the resulting aerodynamic force is significantly improved. Also, the present scheme is successfully applied to moving two-cylinder problems.
Directory of Open Access Journals (Sweden)
Yandy G. Mayor
2015-01-01
Full Text Available This paper evaluates the sensitivity to cumulus and microphysics schemes, as represented in numerical simulations of the Weather Research and Forecasting model, in characterizing a deep convection event over the Cuban island on 1 May 2012. To this end, 30 experiments combining five cumulus and six microphysics schemes, in addition to two experiments in which the cumulus parameterization was turned off, are tested in order to choose the combination that represents the event precipitation more accurately. ERA Interim is used as lateral boundary condition data for the downscaling procedure. Results show that convective schemes are more important than microphysics schemes for determining the precipitation areas within a high-resolution domain simulation. Also, while one cumulus scheme captures the overall spatial convective structure of the event more accurately than others, it fails to capture the precipitation intensity. This apparent discrepancy leads to sensitivity related to the verification method used to rank the scheme combinations. This sensitivity is also observed in a comparison between parameterized and explicit cumulus formation when the Kain-Fritsch scheme was used. A loss of added value is also found when the Grell-Freitas cumulus scheme was activated at 1 km grid spacing.
A computationally efficient 3D finite-volume scheme for violent liquid–gas sloshing
CSIR Research Space (South Africa)
Oxtoby, Oliver F
2015-10-01
Full Text Available . The high resolution artificial compressive (HiRAC) volume-of-fluid method is used for accurate capturing of the free surface in violent flow regimes while allowing natural applicability to hybrid-unstructured meshes. The code is parallelised for solution...
Green, F. M.; Resnick, D. R.
1979-01-01
An FMP (Flow Model Processor) was designed for use in the Numerical Aerodynamic Simulation Facility (NASF). The NASF was developed to simulate fluid flow over three-dimensional bodies in wind tunnel environments and in free space. The facility is applicable to studying aerodynamic and aircraft body designs. The following general topics are discussed in this volume: (1) FMP functional computer specifications; (2) FMP instruction specification; (3) standard product system components; (4) loosely coupled network (LCN) specifications/description; and (5) three appendices: performance of trunk allocation contention elimination (trace) method, LCN channel protocol and proposed LCN unified second level protocol.
A finite-volume numerical method to calculate fluid forces and rotordynamic coefficients in seals
Athavale, M. M.; Przekwas, A. J.; Hendricks, R. C.
1992-01-01
A numerical method to calculate rotordynamic coefficients of seals is presented. The flow in a seal is solved by using a finite-volume formulation of the full Navier-Stokes equations with appropriate turbulence models. The seal rotor is perturbed along a diameter such that the position of the rotor is a sinusoidal function of time. The resulting flow domain changes with time, and the time-dependent flow in the seal is solved using a space conserving moving grid formulation. The time-varying fluid pressure reaction forces are then linked with the rotor center displacement, velocity and acceleration to yield the rotordynamic coefficients. Results for an annular seal are presented, and compared with experimental data and other more simplified numerical methods.
Institute of Scientific and Technical Information of China (English)
Wang Hua; Tao Guo; Shang Xue-Feng; Fang Xin-Ding; Daniel R. Burns
2013-01-01
In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius~27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is>30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(M-PML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d0. The optimal parameter space for the maximum value of the linear frequency-shifted factor (α0) and the scaling factor (β0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to<1%using
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Ye. S. Sherina
2014-01-01
Full Text Available This research has been aimed to carry out a study of peculiarities that arise in a numerical simulation of the electrical impedance tomography (EIT problem. Static EIT image reconstruction is sensitive to a measurement noise and approximation error. A special consideration has been given to reducing of the approximation error, which originates from numerical implementation drawbacks. This paper presents in detail two numerical approaches for solving EIT forward problem. The finite volume method (FVM on unstructured triangular mesh is introduced. In order to compare this approach, the finite element (FEM based forward solver was implemented, which has gained the most popularity among researchers. The calculated potential distribution with the assumed initial conductivity distribution has been compared to the analytical solution of a test Neumann boundary problem and to the results of problem simulation by means of ANSYS FLUENT commercial software. Two approaches to linearized EIT image reconstruction are discussed. Reconstruction of the conductivity distribution is an ill-posed problem, typically requiring a large amount of computation and resolved by minimization techniques. The objective function to be minimized is constructed of measured voltage and calculated boundary voltage on the electrodes. A classical modified Newton type iterative method and the stochastic differential evolution method are employed. A software package has been developed for the problem under investigation. Numerical tests were conducted on simulated data. The obtained results could be helpful to researches tackling the hardware and software issues for medical applications of EIT.
Yan, Jinliang; Zhang, Zhiyue
2016-04-01
Two energy-preserving schemes are proposed for the "good" Boussinesq (GBq) equation using the Hamiltonian Boundary Value and Fourier pseudospectral methods. The equation is discretized in space by Fourier pseudospectral method and in time by Hamiltonian Boundary Value methods (HBVMs). The outstanding advantages of the proposed schemes are that they can precisely conserve the global mass and energy, and provide highly accurate results. The single solitary wave, the interaction of two solitary waves and the birth of solitary waves are presented to validate the accuracy and conservation properties of the proposed schemes. In addition, we also compare our numerical results with other known studied methods in terms of numerical accuracy and conservation properties.
Energy-preserving finite volume element method for the improved Boussinesq equation
Wang, Quanxiang; Zhang, Zhiyue; Zhang, Xinhua; Zhu, Quanyong
2014-08-01
In this paper, we design an energy-preserving finite volume element scheme for solving the initial boundary problems of the improved Boussinesq equation. Theoretical analysis shows that the proposed numerical schemes can conserve the energy and mass. Numerical experiments are performed to illustrate the efficiency of the scheme and theoretical analysis. While the results demonstrate that the proposed finite volume element scheme is second-order accuracy in space and time. Moreover, the new scheme can conserve mass and energy.
Nogherotto, Rita; Tompkins, Adrian Mark; Giuliani, Graziano; Coppola, Erika; Giorgi, Filippo
2016-07-01
We implement and evaluate a new parameterization scheme for stratiform cloud microphysics and precipitation within regional climate model RegCM4. This new parameterization is based on a multiple-phase one-moment cloud microphysics scheme built upon the implicit numerical framework recently developed and implemented in the ECMWF operational forecasting model. The parameterization solves five prognostic equations for water vapour, cloud liquid water, rain, cloud ice, and snow mixing ratios. Compared to the pre-existing scheme, it allows a proper treatment of mixed-phase clouds and a more physically realistic representation of cloud microphysics and precipitation. Various fields from a 10-year long integration of RegCM4 run in tropical band mode with the new scheme are compared with their counterparts using the previous cloud scheme and are evaluated against satellite observations. In addition, an assessment using the Cloud Feedback Model Intercomparison Project (CFMIP) Observational Simulator Package (COSP) for a 1-year sub-period provides additional information for evaluating the cloud optical properties against satellite data. The new microphysics parameterization yields an improved simulation of cloud fields, and in particular it removes the overestimation of upper level cloud characteristics of the previous scheme, increasing the agreement with observations and leading to an amelioration of a long-standing problem in the RegCM system. The vertical cloud profile produced by the new scheme leads to a considerably improvement of the representation of the longwave and shortwave components of the cloud radiative forcing.
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T. Chourushi
2017-01-01
Full Text Available Viscoelastic fluids due to their non-linear nature play an important role in process and polymer industries. These non-linear characteristics of fluid, influence final outcome of the product. Such processes though look simple are numerically challenging to study, due to the loss of numerical stability. Over the years, various methodologies have been developed to overcome this numerical limitation. In spite of this, numerical solutions are considered distant from accuracy, as first-order upwind-differencing scheme (UDS is often employed for improving the stability of algorithm. To elude this effect, some works been reported in the past, where high-resolution-schemes (HRS were employed and Deborah number was varied. However, these works are limited to creeping flows and do not detail any information on the numerical stability of HRS. Hence, this article presents the numerical study of high shearing contraction flows, where stability of HRS are addressed in reference to fluid elasticity. Results suggest that all HRS show some order of undue oscillations in flow variable profiles, measured along vertical lines placed near contraction region in the upstream section of domain, at varied elasticity number E≈5. Furthermore, by E, a clear relationship between numerical stability of HRS and E was obtained, which states that the order of undue oscillations in flow variable profiles is directly proportional to E.
Yu, Guojun
2012-10-01
In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.
Zanotti, Olindo; Dumbser, Michael; Hidalgo, Arturo
2015-01-01
In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space-time adaptive Cartesian meshes (AMR) for hyperbolic conservation laws in multiple space dimensions, using a high order \\aposteriori sub-cell ADER-WENO finite volume \\emph{limiter}. Notoriously, the original DG method produces strong oscillations in the presence of discontinuous solutions and several types of limiters have been introduced over the years to cope with this problem. Following the innovative idea recently proposed in \\cite{Dumbser2014}, the discrete solution within the troubled cells is \\textit{recomputed} by scattering the DG polynomial at the previous time step onto a suitable number of sub-cells along each direction. Relying on the robustness of classical finite volume WENO schemes, the sub-cell averages are recomputed and then gathered back into the DG polynomials over the main grid. In this paper this approach is implemented for the first time within a space-time adaptive ...
Sarkadi, N.; Geresdi, I.; Thompson, G.
2016-11-01
In this study, results of bulk and bin microphysical schemes are compared in the case of idealized simulations of pre-frontal orographic clouds with enhanced embedded convection. The description graupel formation by intensive riming of snowflakes was improved compared to prior versions of each scheme. Two methods of graupel melting coincident with collisions with water drops were considered: (1) all simulated melting and collected water drops increase the amount of melted water on the surface of graupel particles with no shedding permitted; (2) also no shedding permitted due to melting, but the collision with the water drops can induce shedding from the surface of the graupel particles. The results of the numerical experiments show: (i) The bin schemes generate graupel particles more efficiently by riming than the bulk scheme does; the intense riming of snowflakes was the most dominant process for the graupel formation. (ii) The collision-induced shedding significantly affects the evolution of the size distribution of graupel particles and water drops below the melting level. (iii) The three microphysical schemes gave similar values for the domain integrated surface precipitation, but the patterns reveal meaningful differences. (iv) Sensitivity tests using the bulk scheme show that the depth of the melting layer is sensitive to the description of the terminal velocity of the melting snow. (v) Comparisons against Convair-580 flight measurements suggest that the bin schemes simulate well the evolution of the pristine ice particles and liquid drops, while some inaccuracy can occur in the description of snowflakes riming. (vi) The bin scheme with collision-induced shedding reproduced well the quantitative characteristics of the observed bright band.
Numerical study of cesium effects on negative ion production in volume sources
Energy Technology Data Exchange (ETDEWEB)
Fukumasa, Osamu; Niitani, Eiji [Yamaguchi Univ., Ube (Japan). Faculty of Engineering
1997-02-01
Effects of cesium vapor injection of H{sup -} production in a tandem negative ion source are studied numerically as a function of plasma parameters. Model calculation is done by solving a set of particle balance equations in a steady-state hydrogen discharge plasmas. Here, the results which focus on gas pressure and electron temperature dependences of H{sup -} volume production are presented and discussed. With including H{sup -} surface production processes caused by both H atoms and positive hydrogen ions, enhancement of H{sup -} production and pressure dependence of H{sup -} production observed experimentally are well reproduced in the model. To enhance H{sup -} production, however, so-called electron cooling is not so effective if plasma parameters are initially optimized with the use of magnetic filter. (author)
NUMERICAL RESEARCH ON WATER GUIDE BEARING OF HYDRO-GENERATOR UNIT USING FINITE VOLUME METHOD
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
With the consideration of the geometry of tilting pad journal bearing, a new form of the Reynolds equation was derived in this article. The film thickness, the squeeze motion of the journal and the rotation motion of the pad were explicitly contained in the equation. Based on this equation, together with the equilibrium equation of pad pivot, the water guide bearing used in the Gezhouba 10 F hydro-generator unit was numerically researched. The new Reynolds equation for the lubricating film was solved using Finite Volume (FV) discretization, Successive Over-Relaxation (SOR) iteration method and C++ code are included. According to the numerical solution, and the stability of the film and the influences of the film thickness, the journal squeeze effect and the pad rotation effect on film force were discussed. The results indicate that the squeeze effect can not be neglected, although the rotation effect is negligible for both low-speed and high-speed bearings, so the computing time could be greatly reduced.
Pan, JianHua; Ren, YuXin
2017-08-01
In this paper, a family of sub-cell finite volume schemes for solving the hyperbolic conservation laws is proposed and analyzed in one-dimensional cases. The basic idea of this method is to subdivide a control volume (main cell) into several sub-cells and the finite volume discretization is applied to each of the sub-cells. The averaged values on the sub-cells of current and face neighboring main cells are used to reconstruct the polynomial distributions of the dependent variables. This method can achieve arbitrarily high order of accuracy using a compact stencil. It is similar to the spectral volume method incorporating with PNPM technique but with fundamental differences. An elaborate utilization of these differences overcomes some shortcomings of the spectral volume method and results in a family of accurate and robust schemes for solving the hyperbolic conservation laws. In this paper, the basic formulation of the proposed method is presented. The Fourier analysis is performed to study the properties of the one-dimensional schemes. A WENO limiter based on the secondary reconstruction is constructed.
CPV边界积分的对称数值求积法%Numerical Evaluation of CPV Boundary Integrals with Symmetrical Quadrature Schemes
Institute of Scientific and Technical Information of China (English)
马杭; 徐凯宇
2003-01-01
Stemming from the definition of the Cauchy principal values (CPV) integrals, a newly developed symmetrical quadrature scheme was proposed in the paper for the accurate numerical evaluation of the singular boundary integrals in the sense of CPV encountered in the boundary element method. In the case of inner-element singularities, the CPV integrals could be evaluated in a straightforward way by dividing the element into the symmetrical part and the remainder(s). And in the case of end-singularities, the CPV integrals could be evaluated simply by taking a tangential distance transformation of the integrand after cutting out a symmetrical tiny zone around the singular point. In both cases, the operations are no longer necessary before the numerical implementation, which involves the dull routine work to separate out singularities from the integral kernels. Numerical examples were presented for both the two-and the three-dimensional boundary integrals in elasticity. Comparing the numerical results with those by other approaches demonstrates the feasibility and the effectiveness of the proposed scheme.
Energy Technology Data Exchange (ETDEWEB)
Touma, Rony [Department of Computer Science & Mathematics, Lebanese American University, Beirut (Lebanon); Zeidan, Dia [School of Basic Sciences and Humanities, German Jordanian University, Amman (Jordan)
2016-06-08
In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential of the proposed scheme.
Bernales, Jorge; Rogozhina, Irina; Greve, Ralf; Thomas, Maik
2017-01-01
The shallow ice approximation (SIA) is commonly used in ice-sheet models to simplify the force balance equations within the ice. However, the SIA cannot adequately reproduce the dynamics of the fast flowing ice streams usually found at the margins of ice sheets. To overcome this limitation, recent studies have introduced heuristic hybrid combinations of the SIA and the shelfy stream approximation. Here, we implement four different hybrid schemes into a model of the Antarctic Ice Sheet in order to compare their performance under present-day conditions. For each scheme, the model is calibrated using an iterative technique to infer the spatial variability in basal sliding parameters. Model results are validated against topographic and velocity data. Our analysis shows that the iterative technique compensates for the differences between the schemes, producing similar ice-sheet configurations through quantitatively different results of the sliding coefficient calibration. Despite this we observe a robust agreement in the reconstructed patterns of basal sliding parameters. We exchange the calibrated sliding parameter distributions between the schemes to demonstrate that the results of the model calibration cannot be straightforwardly transferred to models based on different approximations of ice dynamics. However, easily adaptable calibration techniques for the potential distribution of basal sliding coefficients can be implemented into ice models to overcome such incompatibility, as shown in this study.
The dust emission scheme of Shao (2004) has been implemented into the regional atmospheric model COSMO-ART and has been applied to a severe dust event in northeastern Germany on 8th April 2011. The model sensitivity to soil moisture and vegetation cover has been studied. Soil moisture has been found...
Directory of Open Access Journals (Sweden)
yangchun chen
2017-01-01
Full Text Available Objective(s: In this study, we aimed to evaluate the efficacy of thyroid volume measurement using 99mTc pertechnetate single-photon emission computed tomography (SPECT images, acquired by the standardized uptake value (SUV-shape scheme designed by our expert team.Methods: A total of 18 consecutive patients with Graves’ disease (GD were subjected to both ultrasonographic and 99mTc pertechnetate SPECT examinations of thyroid within a five-day interval. The volume of thyroid lobes and isthmus was measured by ultrasonography (US according to the ellipsoid volume equation. The total thyroid volume, determined as the sum of the volume of both lobes and isthmus, was recorded as TV-US (i.e., thyroid volume measured by US and set as the reference. The thyroid volume was defined according to our SUV-shape scheme and was recorded as TV-SS (i.e., thyroid volume determined by the SUV-shape scheme. The data were analyzed using the Bland-Altman plot, linear regression analysis, Spearman’s rank correlation, and paired t-test, if necessary.Results: The values of TV-SS (40.2±29.4 mL and TV-US (43.0±34.7 mL were not significantly different (t=0.813; P=0.43. The linear regression equation of the two values was determined as TV-US= 1.072 × TV-SS − 0.29(r=0.906; P
Stewart, Andrew L.; Dellar, Paul J.
2016-05-01
We present an energy- and potential enstrophy-conserving scheme for the non-traditional shallow water equations that include the complete Coriolis force and topography. These integral conservation properties follow from material conservation of potential vorticity in the continuous shallow water equations. The latter property cannot be preserved by a discretisation on a fixed Eulerian grid, but exact conservation of a discrete energy and a discrete potential enstrophy seems to be an effective substitute that prevents any distortion of the forward and inverse cascades in quasi-two dimensional turbulence through spurious sources and sinks of energy and potential enstrophy, and also increases the robustness of the scheme against nonlinear instabilities. We exploit the existing Arakawa-Lamb scheme for the traditional shallow water equations, reformulated by Salmon as a discretisation of the Hamiltonian and Poisson bracket for this system. The non-rotating, traditional, and our non-traditional shallow water equations all share the same continuous Hamiltonian structure and Poisson bracket, provided one distinguishes between the particle velocity and the canonical momentum per unit mass. We have determined a suitable discretisation of the non-traditional canonical momentum, which includes additional coupling between the layer thickness and velocity fields, and modified the discrete kinetic energy to suppress an internal symmetric computational instability that otherwise arises for multiple layers. The resulting scheme exhibits the expected second-order convergence under spatial grid refinement. We also show that the drifts in the discrete total energy and potential enstrophy due to temporal truncation error may be reduced to machine precision under suitable refinement of the timestep using the third-order Adams-Bashforth or fourth-order Runge-Kutta integration schemes.
Qu, Mengmeng; Jiang, Dazhi; Lu, Lucy X.
2016-11-01
To address the multiscale deformation and fabric development in Earth's ductile lithosphere, micromechanics-based self-consistent homogenization is commonly used to obtain macroscale rheological properties from properties of constituent elements. The homogenization is heavily based on the solution of an Eshelby viscous inclusion in a linear viscous medium and the extension of the solution to nonlinear viscous materials. The homogenization requires repeated numerical evaluation of Eshelby tensors for constituent elements and becomes ever more computationally challenging as the elements are deformed to more elongate or flattened shapes. In this paper, we develop an optimal scheme for evaluating Eshelby tensors, using a combination of a product Gaussian quadrature and the Lebedev quadrature. We first establish, through numerical experiments, an empirical relationship between the inclusion shape and the computational time it takes to evaluate its Eshelby tensors. We then use the relationship to develop an optimal scheme for selecting the most efficient quadrature to obtain the Eshelby tensors. The optimal scheme is applicable to general homogenizations. In this paper, it is implemented in a MATLAB package for investigating the evolution of solitary rigid or deformable inclusions and the development of shape preferred orientations in multi-inclusion systems during deformation. The MATLAB package, upgrading an earlier effort written in MathCad, can be downloaded online.
Kulikov, Igor
2016-01-01
An approach for constructing a low-dissipation numerical method is described. The method is based on a combination of the operator-splitting method, Godunov method, and piecewise-parabolic method on the local stencil. Numerical method was tested on a standard suite of hydrodynamic test problems. In addition, the performance of the method is demonstrated on a global test problem showing the development of a spiral structure in a gravitationally unstable gaseous galactic disk.
Directory of Open Access Journals (Sweden)
Adam Martowicz
2015-01-01
Full Text Available The paper addresses the problem of numerical dispersion in simulations of wave propagation in solids. This characteristic of numerical models results from both spatial discretization and temporal discretization applied to carry out transient analyses. A denser mesh of degrees of freedom could be a straightforward solution to mitigate numerical dispersion, since it provides more advantageous relation between the model length scale and considered wavelengths. However, this approach also leads to higher computational effort. An alternative approach is the application of nonlocal discretization schemes, which employ a relatively sparse spatial distribution of nodes. Numerical analysis carried out to study the propagation of elastic waves in isotropic solid materials is demonstrated. Fourier-based nonlocal discretization for continuum mechanics is introduced for a two-dimensional model undergoing out-of-plane wave propagation. The results show gradual increase of the effectiveness of this approach while expanding the region of nonlocal interactions in the numerical model. A challenging case of high ratio between the model length scale and wavelength is investigated to present capability of the proposed approach. The elaborated discretization method also provides the perspective of accurate representation of any arbitrarily shaped dispersion relation based on physical properties of modelled materials.
Directory of Open Access Journals (Sweden)
M. Boumaza
2015-07-01
Full Text Available Transient convection heat transfer is of fundamental interest in many industrial and environmental situations, as well as in electronic devices and security of energy systems. Transient fluid flow problems are among the more difficult to analyze and yet are very often encountered in modern day technology. The main objective of this research project is to carry out a theoretical and numerical analysis of transient convective heat transfer in vertical flows, when the thermal field is due to different kinds of variation, in time and space of some boundary conditions, such as wall temperature or wall heat flux. This is achieved by the development of a mathematical model and its resolution by suitable numerical methods, as well as performing various sensitivity analyses. These objectives are achieved through a theoretical investigation of the effects of wall and fluid axial conduction, physical properties and heat capacity of the pipe wall on the transient downward mixed convection in a circular duct experiencing a sudden change in the applied heat flux on the outside surface of a central zone.
A reaction-based river/stream water quality model Part I: Model development and numerical schemes
Energy Technology Data Exchange (ETDEWEB)
Zhang, Fan [ORNL; Gour-Tsyh, Yeh [University of Central Florida, Orlando; Parker, Jack C. [University of Tennessee, Knoxville (UTK); Jardine, Philip M [ORNL
2008-01-01
This paper presents the conceptual and mathematical development of a numerical model of sediment and reactive chemical transport in river/streams. The distribution of mobile suspended sediments and immobile bed sediments is controlled by hydrologic transport as well as erosion and deposition processes. The fate and transport of water quality constituents involving a variety of chemical and physical processes is mathematically described by a system of reaction equations for immobile constituents and advective-dispersive-reactive transport equations for constituents. To circumvent stiffness associated with equilibrium reactions, matrix decomposition is performed via Gauss-Jordan column reduction. After matrix decomposition, the system of water quality constituent reactive transport equations is transformed into a set of thermodynamic equations representing equilibrium reactions and a set of transport equations involving no equilibrium reactions. The decoupling of equilibrium and kinetic reactions enables robust numerical integration of the partial differential equations for non-equilibrium-variables. Solving non-equilibrium-variable transport equations instead of individual water quality constituent transport equations also reduces the number of PDEs. A variety of numerical methods are investigated for solving the mixed differential and algebraic equations. Two verification examples are compared with analytical solutions to demonstrate the correctness of the code and to illustrate the importance of employing application-dependent numerical methods to solve specific problems.
Karino, S; Eriguchi, Y; Karino, Shigeyuki; Yoshida, Shin'ichirou; Yoshida, Shijun; Eriguchi, Yoshiharu
2000-01-01
We have developed a new numerical scheme to solve r-mode oscillations of {\\it rapidly rotating polytropic stars} in Newtonian gravity. In this scheme, Euler perturbations of the density, three components of the velocity are treated as four unknown quantities together with the oscillation frequency. For the basic equations of oscillations, the compatibility equations are used instead of the linearized equations of motion. By using this scheme, we have solved the classical r-mode oscillations of rotational equilibrium sequences of polytropes with the polytropic indices $N = 0.5, 1.0$ and 1.5 for $m = 2, 3$ and 4 modes. Here $m$ is the rank of the spherical harmonics $Y_l^m$. These results have been applied to investigate evolution of uniformly rotating hot young neutron stars by considering the effect of gravitational radiation and viscosity. We have found that the maximum angular velocities of neutron stars are around 10-20% of the Keplerian angular velocity irrespective of the softness of matter. This confirm...
Madavan, Nateri K.
1995-01-01
The work in this report was conducted at NASA Ames Research Center during the period from August 1993 to January 1995 deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a heated flat plate in the presence of relatively high freestream turbulence was performed. The geometry and flow conditions were chosen to match earlier experiments. The development of the momentum and thermal boundary layers was documented. Velocity and temperature profiles, as well as distributions of skin friction, surface heat transfer rate, Reynolds shear stress, and turbulent heat flux were shown to compare well with experiment. The numerical method used here can be applied to complex geometries in a straightforward manner.
Institute of Scientific and Technical Information of China (English)
WANG Yehong; ZHAO Yuchun; CUI Chunguang
2007-01-01
On the basis of the joint estimated 1-h precipitation from Changde, Jingzhou, and Yichang Doppler radars as well as Wuhan digital radar, and the retrieved wind fields from Yichang and Jingzhou Doppler radars, a series of numerical experiments with an advanced regional η-coordinate model (AREM) under different model initial schemes, i.e., Grapes-3DVAR, Barnes objective analysis, and Barnes-3DVAR, are carried out for a torrential rain process occurring along the Yangtze River in the 24-h period from 2000 BT 22 July 2002 to investigate the effects of the Doppler-radar estimated rainfall and retrieved winds on the rainfall forecast. The main results are as follows: (1) The simulations are obviously different under three initial schemes with the same data source (the radiosounding and T213L31 analysis). On the whole,Barnes-3DVAR, which combines the advantages of the Barnes objective analysis and the Grapes-3DVAR method, gives the best simulations: well-simulated rain band and clear mesoscale structures, as well as their location and intensity close to observations. (2) Both Barnes-3DVAR and Grapes-3DVAR schemes are able to assimilate the Doppler-radar estimated rainfall and retrieved winds, but differences in simulation results are very large, with Barnes-3DVAR's simulation much better than Grapes-3DVAR's. (3) Under Grapes3DVAR scheme, the simulation of 24-h rainfall is improved obviously when assimilating the Doppler-radar estimated precipitation into the model in compared with the control experiment; but it becomes a little worse when assimilating the Doppler-radar retrieved winds into the model, and it becomes worse obviously when assimilating the Doppler-radar estimated precipitation as well as retrieved winds into the model. However,the simulation is different under Barnes-3DVAR scheme. The simulation is improved to a certain degree no matter assimilating the estimated precipitation or retrieved winds, or both of them. The result is the best when assimilating both
Effects for ICBM Basing. Volume 6. Numerical Simulation and Evaluation of Non-Ideal Airblast
1990-12-01
non-rectangular grid system in the one-dimensional sense . The FCT scheme in both codes was originally implemented based on the assumption of a...MSEC) 240.0-1 1 -------- HML GENERIC MODELO .- GAGE 203 HELIUM LAYER S0 -DUST 190.0 *:P -- CLEAN 0 cooo CERF DATA @HST6-60 140.0- a 210 204 PRESSURE
de Oliveira, G L
2016-01-01
In this work we show a strategy for synchronization of three optoelectronic oscillators (OEO) operating in chaotic regime. Two applications of synchronized OEOs in secure communications are considered. In the first one the OEO is used to produce a pseudo-random bit sequence. The second application is an optical setup for secure transmission of sampled analog signals. Using numerical simulations, we calculated the bit error rate taking into account parameter mismatch noise and Gaussian noise in the input optical power. The conditions for error rate of up to 15% during key generation are shown.
Kawata, Daisuke; Gibson, Brad K.; Barnes, David J.; Grand, Robert J. J.; Rahimi, Awat
2014-02-01
To study the star formation and feedback mechanism, we simulate the evolution of an isolated dwarf irregular galaxy (dIrr) in a fixed dark matter halo, similar in size to Wolf-Lundmark-Melotte, using a new stellar feedback scheme. We use the new version of our original N-body/smoothed particle chemodynamics code, GCD+, which adopts improved hydrodynamics, metal diffusion between the gas particles and new modelling of star formation and stellar wind and supernovae feedback. Comparing the simulations with and without stellar feedback effects, we demonstrate that the collisions of bubbles produced by strong feedback can induce star formation in a more widely spread area. We also demonstrate that the metallicity in star-forming regions is kept low due to the mixing of the metal-rich bubbles and the metal-poor interstellar medium. Our simulations also suggest that the bubble-induced star formation leads to many counter-rotating stars. The bubble-induced star formation could be a dominant mechanism to maintain star formation in dIrrs, which is different from larger spiral galaxies where the non-axisymmetric structures, such as spiral arms, are a main driver of star formation.
Sman, van der R.G.M.
2006-01-01
In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the
CSIR Research Space (South Africa)
Heyns, Johan A
2012-06-01
Full Text Available combines a blended higher resolution scheme with the addition of an artificial compressive term to the volume-of-fluid equation. This reduces the numerical smearing of the interface associated with explicit higher resolution schemes while limiting...
Ciliberti, Stefania Angela; Peneva, Elisaveta; Storto, Andrea; Rostislav, Kandilarov; Lecci, Rita; Yang, Chunxue; Coppini, Giovanni; Masina, Simona; Pinardi, Nadia
2016-04-01
This study describes a new model implementation for the Black Sea, which uses data assimilation, towards operational forecasting, based on NEMO (Nucleus for European Modelling of the Ocean, Madec et al., 2012). The Black Sea domain is resolved with 1/27°×1/36° horizontal resolution (~3 km) and 31 z-levels with partial steps based on the GEBCO bathymetry data (Grayek et al., 2010). The model is forced by momentum, water and heat fluxes interactively computed by bulk formulae using high resolution atmospheric forcing provided by the European Centre for Medium-Range Forecast (ECMWF). The initial condition is calculated from long-term climatological temperature and salinity 3D fields. Precipitation field over the basin has been computed from the climatological GPCP rainfall monthly data (Adler et al., 2003; Huffman et al., 2009), while the evaporation is derived from the latent heat flux. The climatological monthly mean runoff of the major rivers in the Black Sea is computed using the hydrological dataset provided by SESAME project (Ludvig et al., 2009). The exchange with Mediterranean Sea through the Bosporus Straits is represented by a surface boundary condition taking into account the barotropic transport calculated to balance the fresh water fluxes on monthly bases (Stanev and Beckers, 1999, Peneva et al., 2001). A multi-annual run 2011-2015 has been completed in order to describe the main characteristics of the Black Sea circulation dynamics and thermohaline structure and the numerical results have been validated using in-situ (ARGO) and satellite (SST, SLA) data. The Black Sea model represents also the core of the new Black Sea Forecasting System, implemented at CMCC operationally since January 2016, which produces at daily frequency 10-day forecasts, 3-days analyses and 1-day simulation. Once a week, the system is run 15-day in the past in analysis mode to compute the new optimal initial condition for the forecast cycle. The assimilation is performed by a
Cartalade, Alain; Plapp, Mathis
2016-01-01
A lattice-Boltzmann (LB) scheme, based on the Bhatnagar-Gross-Krook (BGK) collision rules is developed for a phase-field model of alloy solidification in order to simulate the growth of dendrites. The solidification of a binary alloy is considered, taking into account diffusive transport of heat and solute, as well as the anisotropy of the solid-liquid interfacial free energy. The anisotropic terms in the phase-field evolution equation, the phenomenological anti-trapping current (introduced in the solute evolution equation to avoid spurious solute trapping), and the variation of the solute diffusion coefficient between phases, make it necessary to modify the equilibrium distribution functions of the LB scheme with respect to the one used in the standard method for the solution of advection-diffusion equations. The effects of grid anisotropy are removed by using the lattices D3Q15 and D3Q19 instead of D3Q7. The method is validated by direct comparison of the simulation results with a numerical code that uses t...
Vanzo, Davide; Siviglia, Annunziato; Toro, Eleuterio F.
2016-09-01
The purpose of this paper is twofold. First, using the Cattaneo's relaxation approach, we reformulate the system of governing equations for the pollutant transport by shallow water flows over non-flat topography and anisotropic diffusion as hyperbolic balance laws with stiff source terms. The proposed relaxation system circumvents the infinite wave speed paradox which is inherent in standard advection-diffusion models. This turns out to give a larger stability range for the choice of the time step. Second, following a flux splitting approach, we derive a novel numerical method to discretise the resulting problem. In particular, we propose a new flux splitting and study the associated two systems of differential equations, called the "hydrodynamic" and the "relaxed diffusive" system, respectively. For the presented splitting we analyse the resulting two systems of differential equations and propose two discretisation schemes of the Godunov-type. These schemes are simple to implement, robust, accurate and fast when compared with existing methods. The resulting method is implemented on unstructured meshes and is systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems including non-flat topography and wetting and drying problems. Formal second order accuracy is assessed through convergence rates studies.
Directory of Open Access Journals (Sweden)
A. Malizia
2014-01-01
Full Text Available The large volume vacuum systems are used in many industrial operations and research laboratories. Accidents in these systems should have a relevant economical and safety impact. A loss of vacuum accident (LOVA due to a failure of the main vacuum vessel can result in a fast pressurization of the vessel and consequent mobilization dispersion of hazardous internal material through the braches. It is clear that the influence of flow fields, consequence of accidents like LOVA, on dust resuspension is a key safety issue. In order to develop this analysis an experimental facility is been developed: STARDUST. This last facility has been used to improve the knowledge about LOVA to replicate a condition more similar to appropriate operative condition like to kamaks. By the experimental data the boundary conditions have been extrapolated to give the proper input for the 2D thermofluid-dynamics numerical simulations, developed by the commercial CFD numerical code. The benchmark of numerical simulation results with the experimental ones has been used to validate and tune the 2D thermofluid-dynamics numerical model that has been developed by the authors to replicate the LOVA conditions inside STARDUST. In present work, the facility, materials, numerical model, and relevant results will be presented.
Finite volume numerical solution to a blood flow problem in human artery
Wijayanti Budiawan, Inge; Mungkasi, Sudi
2017-01-01
In this paper, we solve a one dimensional blood flow model in human artery. This model is of a non-linear hyperbolic partial differential equation system which can generate either continuous or discontinuous solution. We use the Lax–Friedrichs finite volume method to solve this model. Particularly, we investigate how a pulse propagates in human artery. For this simulation, we give a single sine wave with a small time period as an impluse input on the left boundary. The finite volume method is successful in simulating how the pulse propagates in the artery. It detects the positions of the pulse for the whole time period.
Wang, Peng; Wang, Lian-Ping; Guo, Zhaoli
2016-10-01
The main objective of this work is to perform a detailed comparison of the lattice Boltzmann equation (LBE) and the recently developed discrete unified gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulence and the Kida vortex flow in a periodic box. The flow fields and key statistical quantities computed by both methods are compared with those from the pseudospectral method at both low and moderate Reynolds numbers. The results show that the LBE is more accurate and efficient than the DUGKS, but the latter has a superior numerical stability, particularly for high Reynolds number flows. In addition, we conclude that the DUGKS can adequately resolve the flow when the minimum spatial resolution parameter k_{max}η>3, where k_{max} is the maximum resolved wave number and η is the flow Kolmogorov length. This resolution requirement can be contrasted with the requirements of k_{max}η>1 for the pseudospectral method and k_{max}η>2 for the LBE. It should be emphasized that although more validations should be conducted before the DUGKS can be called a viable tool for DNS of turbulent flows, the present work contributes to the overall assessment of the DUGKS, and it provides a basis for further applications of DUGKS in studying the physics of turbulent flows.
Wang, Peng; Wang, Lian-Ping; Guo, Zhaoli
2016-10-01
The main objective of this work is to perform a detailed comparison of the lattice Boltzmann equation (LBE) and the recently developed discrete unified gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulence and the Kida vortex flow in a periodic box. The flow fields and key statistical quantities computed by both methods are compared with those from the pseudospectral method at both low and moderate Reynolds numbers. The results show that the LBE is more accurate and efficient than the DUGKS, but the latter has a superior numerical stability, particularly for high Reynolds number flows. In addition, we conclude that the DUGKS can adequately resolve the flow when the minimum spatial resolution parameter kmaxη >3 , where kmax is the maximum resolved wave number and η is the flow Kolmogorov length. This resolution requirement can be contrasted with the requirements of kmaxη >1 for the pseudospectral method and kmaxη >2 for the LBE. It should be emphasized that although more validations should be conducted before the DUGKS can be called a viable tool for DNS of turbulent flows, the present work contributes to the overall assessment of the DUGKS, and it provides a basis for further applications of DUGKS in studying the physics of turbulent flows.
Energy Technology Data Exchange (ETDEWEB)
None
1992-10-01
This appendix contains the numerically indexed bibliography for the complete group of reports on municipal solid waste management alternatives. The list references information on the following topics: mass burn technologies, RDF technologies, fluidized bed combustion, pyrolysis and gasification of MSW, materials recovery- recycling technologies, sanitary landfills, composting and anaerobic digestion of MSW.
A new numerical framework to simulate viscoelastic free-surface flows with the finite-volume method
DEFF Research Database (Denmark)
Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri
A new method for the simulation of 2D viscoelastic flow is presented. Numerical stability is obtained by the logarithmic-conformation change of variable, and a fully-implicit pure-streamfunction flow formulation, without use of any artificial diffusion. As opposed to other simulation results, our...... calculations predict a hydrodynamic instability in the 4:1 contraction geometry at a Weissenberg number of order 4. This new result is in qualitative agreement with the prediction of a non-linear subcritical elastic instability in Poiseuille flow. Our viscoelastic flow solver is coupled with a volume...
A new numerical framework to simulate viscoelastic free-surface flows with the finite-volume method
DEFF Research Database (Denmark)
Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri
2015-01-01
A new method for the simulation of 2D viscoelastic flow is presented. Numerical stability is obtained by the logarithmic-conformation change of variable, and a fully-implicit pure-streamfunction flow formulation, without use of any artificial diffusion. As opposed to other simulation results, our...... calculations predict a hydrodynamic instability in the 4:1 contraction geometry at a Weissenberg number of order 4. This new result is in qualitative agreement with the prediction of a non-linear subcritical elastic instability in Poiseuille flow. Our viscoelastic flow solver is coupled with a volume...
Fujita, Koki; Ichimura, Naoyuki; Hanada, Toshiya
2017-04-01
This paper presents a novel method to simultaneously detect multiple trajectories of space debris in an observation image sequence to establish a reliable model for space debris environment in Geosynchronous Earth Orbit (GEO). The debris in GEO often appear faintly in image sequences due to the high altitude. A simple but steady way to detect such faint debris is to decrease a threshold value of binarization applied to an image sequence during preprocessing. However, a low threshold value of binarization leads to extracting a large number of objects other than debris that become obstacles to detect debris trajectories. In order to detect debris from binarized image frames with massive obstacles, this work proposes a method that utilizes a cascade of numerical evaluations and a voting scheme to evaluate characteristics of the line segments obtained by connecting two image objects in different image frames, which are the candidates of debris trajectories. In the proposed method, the line segments corresponding to objects other than debris are filtered out using three types of characteristics, namely displacement, direction, and continuity. First, the displacement and direction of debris motion are evaluated to remove irrelevant trajectories. Then, the continuity of the remaining line segments is checked to find debris by counting the number of image objects appearing on or close to the line segments. Since checking the continuity can be regarded as a voting scheme, the proposed cascade algorithm can take advantage of the properties of voting method such as the Hough transform, i.e., the robustness against heavy noises and clutters, and ability of detecting multiple trajectories simultaneously. The experimental tests using real image sequences obtained in a past observation campaign demonstrate the effectiveness of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Fujieda, T.; Tanahashi, T.; Okada, A. [Keio University, Tokyo (Japan). Faculty of Science and Technology; Kato, Y. [Asahi Glass Co. Ltd., Tokyo (Japan)
1997-06-25
In this paper, we propose a new GSMAC-FEM (generalized simplified marker and cell-finite element method) which is suited to the numerical analysis of visco-elastic fluids. The equation of continuity and the equation of momentum are solved by the GSMAC-FEM algorithm and the constitutive equation is solved by the finite volume method. This scheme employs the third order MUSCL (Monotone Upstream-centered Schemes for Conservation Law) in order to guarantee the absence of spurious oscillation near the steep gradients of the variable. This method uses a minmod limiter in order to satisfy the TVD (Total Variation Diminishing) condition. The present method employs the simultaneous relaxation of velocity and pressure for the incompressible condition. The flows of Maxwell fluid through two-dimensional planer abrupt contraction are calculated by the present method and the effects the Weissenberg number and the Reynolds number are discussed. 13 refs., 12 figs.
Finite Volume Numerical Methods for Aeroheating Rate Calculations from Infrared Thermographic Data
Daryabeigi, Kamran; Berry, Scott A.; Horvath, Thomas J.; Nowak, Robert J.
2006-01-01
The use of multi-dimensional finite volume heat conduction techniques for calculating aeroheating rates from measured global surface temperatures on hypersonic wind tunnel models was investigated. Both direct and inverse finite volume techniques were investigated and compared with the standard one-dimensional semi-infinite technique. Global transient surface temperatures were measured using an infrared thermographic technique on a 0.333-scale model of the Hyper-X forebody in the NASA Langley Research Center 20-Inch Mach 6 Air tunnel. In these tests the effectiveness of vortices generated via gas injection for initiating hypersonic transition on the Hyper-X forebody was investigated. An array of streamwise-orientated heating striations was generated and visualized downstream of the gas injection sites. In regions without significant spatial temperature gradients, one-dimensional techniques provided accurate aeroheating rates. In regions with sharp temperature gradients caused by striation patterns multi-dimensional heat transfer techniques were necessary to obtain more accurate heating rates. The use of the one-dimensional technique resulted in differences of 20% in the calculated heating rates compared to 2-D analysis because it did not account for lateral heat conduction in the model.
Ash3d: A finite-volume, conservative numerical model for ash transport and tephra deposition
Schwaiger, Hans F.; Denlinger, Roger P.; Mastin, Larry G.
2012-01-01
We develop a transient, 3-D Eulerian model (Ash3d) to predict airborne volcanic ash concentration and tephra deposition during volcanic eruptions. This model simulates downwind advection, turbulent diffusion, and settling of ash injected into the atmosphere by a volcanic eruption column. Ash advection is calculated using time-varying pre-existing wind data and a robust, high-order, finite-volume method. Our routine is mass-conservative and uses the coordinate system of the wind data, either a Cartesian system local to the volcano or a global spherical system for the Earth. Volcanic ash is specified with an arbitrary number of grain sizes, which affects the fall velocity, distribution and duration of transport. Above the source volcano, the vertical mass distribution with elevation is calculated using a Suzuki distribution for a given plume height, eruptive volume, and eruption duration. Multiple eruptions separated in time may be included in a single simulation. We test the model using analytical solutions for transport. Comparisons of the predicted and observed ash distributions for the 18 August 1992 eruption of Mt. Spurr in Alaska demonstrate to the efficacy and efficiency of the routine.
Delaying Modified QUICK Scheme and its Application in Slug Flow
Institute of Scientific and Technical Information of China (English)
LU Yuan-Wei; HE An-Ding; WANG Yue-She; ZHOU Fang-De
2001-01-01
Calculations of several classic questions in numerical heat transfer with delaying modified QUICKscheme show good agreement with benchmark. Combining volume of fluid model with the well known SIMPLEC method, the reasonable Taylor bubble shape has been obtained by using delaying modified QUICK scheme and donoracceptor scheme of inteffacial advection respectively. At the same time the stream field and the liquid film thickness around the Taylor bubble have been well figured out.
Lee, S. S.; Sengupta, S.; Nwadike, E. V.
1982-01-01
The six-volume report: describes the theory of a three dimensional (3-D) mathematical thermal discharge model and a related one dimensional (1-D) model, includes model verification at two sites, and provides a separate user's manual for each model. The 3-D model has two forms: free surface and rigid lid. The former, verified at Anclote Anchorate (FL), allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth; e.g., estuaries and coastal regions. The latter, verified at Lake Keowee (SC), is suited for small surface wave heights compared to depth (e.g., natural or man-made inland lakes) because surface elevation has been removed as a parameter. These models allow computation of time dependent velocity and temperature fields for given initial conditions and time-varying boundary conditions.
Lee, S. S.; Sengupta, S.; Nwadike, E. V.
1982-01-01
The six-volume report: describes the theory of a three dimensional (3-D) mathematical thermal discharge model and a related one dimensional (1-D) model, includes model verification at two sites, and provides a separate user's manual for each model. The 3-D model has two forms: free surface and rigid lid. The former, verified at Anclote Anchorage (FL), allows a free air/water interface and is suited for significant surface wave heights compared to mean water depth; e.g., estuaries and coastal regions. The latter, verified at Lake Keowee (SC), is suited for small surface wave heights compared to depth (e.g., natural or man-made inland lakes) because surface elevation has been removed as a parameter.
Directory of Open Access Journals (Sweden)
M Safaei
2016-09-01
Full Text Available In the present study, first the turbulent natural convection and then laminar mixed convection of air flow was solved in a room and the calculated outcomes are compared with results of other scientists and after showing validation of calculations, aforementioned flow is solved as a turbulent mixed convection flow, using the valid turbulence models Standard k-ε, RNG k-ε and RSM. To solve governing differential equations for this flow, finite volume method was used. This method is a specific case of residual weighting method. The results show that at high Richardson Numbers, the flow is rather stationary at the center of the enclosure. Moreover, it is distinguished that when Richardson Number increases the maximum of local Nusselt decreases. Therefore, it can be said that less number of Richardson Number, more rate of heat transfer.
Numerical study of impeller-driven von Karman flows via a volume penalization method
Kreuzahler, Sebastian; Homann, Holger; Ponty, Yannick; Grauer, Rainer
2013-01-01
Simulations of impeller-driven flows in cylindrical geometry are performed via direct numerical simulations (DNS) and compared to flows obtained in the von Karman flow experiments. The geometry of rotating impellers assembled of several basic geometric objects is modeled via a penalization method and implemented in a massive parallel pseudo-spectral Navier-Stokes solver. We performed simulations of impellers with different curvature of blades, especially one resembling the so-called TM28 configuration used in water experiments. The decomposition into poloidal, toroidal components and the mean velocity fields from our simulations are quantitatively in agreement with experimental results. We analyzed the flow structure close to the impeller blades and found different vortex topologies.
An accelerated, fully-coupled, parallel 3D hybrid finite-volume fluid–structure interaction scheme
CSIR Research Space (South Africa)
Malan, AG
2012-09-01
Full Text Available . This is such that both dynamic and kinematic continuity ? i.e. continuity of forces and velocities ? are satisfied at the fluid/solid interface. So-called monolithic methods ensure this by solving the entire coupled system [22, 23, 24]. Partitioned solvers...?j ). (3) Here, S(t) denotes the surface of the volume V(t) with n being a unit vector normal to S(t); Q is a vector of source terms (e.g. body forces), u denotes velocity, p is the pressure, ? is density, ? stress, and ?ij is the Kronecker delta...
Numerical method for dam break problem using Godunov approach
Directory of Open Access Journals (Sweden)
A. Kartono
2013-03-01
Full Text Available In this study a numerical scheme was developed in order to overcome the problem of shock wave for the test case of dam break. The numerical scheme was based on Godunov approach of finite volume method to solve the shallow water equation. In order to expedite and improve the solution an approximate Roe’s Riemann solver associated with Monotone Upstream-centred Scheme for Conservation Laws (MUSCL was applied. The results were presented in one and two dimensional and verifications were made with analytical solution. The results are comparable and a good agreement is achieved between numerical and analytical.
Energy Technology Data Exchange (ETDEWEB)
Sugano, Yasutaka [Graduate School of Health Sciences, Hokkaido University, Kita-12, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-0812 (Japan); Mizuta, Masahiro [Laboratory of Advanced Data Science, Information Initiative Center, Hokkaido University, Kita-11, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-0811 (Japan); Takao, Seishin; Shirato, Hiroki; Sutherland, Kenneth L. [Department of Radiation Medicine, Graduate School of Medicine, Hokkaido University, Kita-15, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-8638 (Japan); Date, Hiroyuki, E-mail: date@hs.hokudai.ac.jp [Faculty of Health Sciences, Hokkaido University, Kita-12, Nishi-5, Kita-ku, Sapporo, Hokkaido 060-0812 (Japan)
2015-11-15
Purpose: Radiotherapy of solid tumors has been performed with various fractionation regimens such as multi- and hypofractionations. However, the ability to optimize the fractionation regimen considering the physical dose distribution remains insufficient. This study aims to optimize the fractionation regimen, in which the authors propose a graphical method for selecting the optimal number of fractions (n) and dose per fraction (d) based on dose–volume histograms for tumor and normal tissues of organs around the tumor. Methods: Modified linear-quadratic models were employed to estimate the radiation effects on the tumor and an organ at risk (OAR), where the repopulation of the tumor cells and the linearity of the dose-response curve in the high dose range of the surviving fraction were considered. The minimization problem for the damage effect on the OAR was solved under the constraint that the radiation effect on the tumor is fixed by a graphical method. Here, the damage effect on the OAR was estimated based on the dose–volume histogram. Results: It was found that the optimization of fractionation scheme incorporating the dose–volume histogram is possible by employing appropriate cell surviving models. The graphical method considering the repopulation of tumor cells and a rectilinear response in the high dose range enables them to derive the optimal number of fractions and dose per fraction. For example, in the treatment of prostate cancer, the optimal fractionation was suggested to lie in the range of 8–32 fractions with a daily dose of 2.2–6.3 Gy. Conclusions: It is possible to optimize the number of fractions and dose per fraction based on the physical dose distribution (i.e., dose–volume histogram) by the graphical method considering the effects on tumor and OARs around the tumor. This method may stipulate a new guideline to optimize the fractionation regimen for physics-guided fractionation.
Karelsky, K V; Slavin, A G
2011-01-01
The numerical method for study of hydrodynamic flows over an arbitrary bed profile in the presence of external force is proposed in this paper. This method takes into account the external force effect, it uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with consideration of features of the flow near the step. A distinctive feature of the proposed method is the consideration of the properties of the process of the waterfall, namely the fluid flow on the step in which the fluid does not wet part of the vertical wall of the step. The presence of dry zones in the vertical part of the step indicates violation of the conditions of hydrostatic flow. The quasi-two-layer approach allows to determine the size of the dry zone of the vertical component of the step. Consequently it gives an opportunity to figure out the amount of kinetic energy dissipation. There are performed the numerical simulations based on the proposed algorithm of various physical phenomena, such as a breakdown of the r...
Moon, Ji Young; Tanner, Roger I; Lee, Joon Sang
2016-07-01
A red blood cell (RBC) in a microfluidic channel is highly interesting for scientists in various fields of research on biological systems. This system has been studied extensively by empirical, analytical, and numerical methods. Nonetheless, research of predicting the behavior of an RBC in a microchannel is still an interesting area. The complications arise from deformation of an RBC and interactions among the surrounding fluid, wall, and RBCs. In this study, a pressure-driven RBC in a microchannel was simulated with a three-dimensional lattice Boltzmann method of an immersed boundary. First, the effect of boundary thickness on the interaction between the wall and cell was analyzed by measuring the time of passage through the narrow channel. Second, the effect of volume conservation stiffness was studied. Finally, the effect of global area stiffness was analyzed.
Institute of Scientific and Technical Information of China (English)
LI Xue-yan; REN Bing; WANG Guo Yu; WANG Yong-xue
2011-01-01
In the present study,a new algorithm based on the Volume Of Fluid (vOF) method is developed to simulate the hydrodynamic characteristics on an arc crown wall.Structured grids are generated by the coordinate transform method in an arbitrary complex region.The Navier-Stokes equations for two-dimensional incompressible viscous flows are discretized in the Body Fitted Coordinate (BFC) system.The transformed SIMPLE algorithm is proposed to modify the pressure-velocity field and a transformed VOF method is used to trace the free surface.Hydrodynamic characteristics on an arc crown wall are obtained by the improved numerical model based on the BFC system (BFC model).The velocity field,the pressure field and the time profiles of the water surface near the arc crown wall obtained by using the BFC model and the Cartesian model are compared.The BFC model is verified by experimental results.
Drop by drop backscattered signal of a 50 × 50 × 50 m3 volume: A numerical experiment
Gires, A.; Tchiguirinskaia, I.; Schertzer, D.
2016-09-01
The goal of this paper is to analyse the influence of individual drop positions on a backscattered radar signal. This is achieved through a numerical experiment: a 3D rain drop field generator is developed and implemented over a volume of 50 × 50 × 50 m3, and then the sum of the electromagnetic waves backscattered by its hydrometeors is computed. Finally the temporal evolution over 1 s is modelled with simplistic assumptions. For the rainfall generator, the liquid water content (LWC) distribution is represented with the help of a multiplicative cascade down to 0.5 m, below which it is considered as homogeneous. Within each 0.5 × 0.5 × 0.5 m3 patch, liquid water is distributed into drops, located randomly uniformly according to a pre-defined drop size distribution (DSD). Such configuration is compared with the one consisting of the same drops being uniformly distributed over the entire 50 × 50 × 50 m3 volume. Due to the fact that the radar wave length is much smaller than the size of a rainfall "patch", it appears that, in agreement with the theory, we retrieve an exponential distribution for potential measures on horizontal reflectivity. Much thinner dispersion is noticed for differential reflectivity. We show that a simple ballistic assumption for drop velocities does not enable the reproduction of radar observations, and turbulence should be taken into account. Finally the sensitivity of these outputs to the various model parameters is quantified.
Del Bello, Elisabetta; Taddeucci, Jacopo; de’ Michieli Vitturi, Mattia; Scarlato, Piergiorgio; Andronico, Daniele; Scollo, Simona; Kueppers, Ulrich; Ricci, Tullio
2017-01-01
Most of the current ash transport and dispersion models neglect particle-fluid (two-way) and particle-fluid plus particle-particle (four-way) reciprocal interactions during particle fallout from volcanic plumes. These interactions, a function of particle concentration in the plume, could play an important role, explaining, for example, discrepancies between observed and modelled ash deposits. Aiming at a more accurate prediction of volcanic ash dispersal and sedimentation, the settling of ash particles at particle volume fractions (ϕp) ranging 10‑7-10‑3 was performed in laboratory experiments and reproduced by numerical simulations that take into account first the two-way and then the four-way coupling. Results show that the velocity of particles settling together can exceed the velocity of particles settling individually by up to 4 times for ϕp ~ 10‑3. Comparisons between experimental and simulation results reveal that, during the sedimentation process, the settling velocity is largely enhanced by particle-fluid interactions but partly hindered by particle-particle interactions with increasing ϕp. Combining the experimental and numerical results, we provide an empirical model allowing correction of the settling velocity of particles of any size, density, and shape, as a function of ϕp. These corrections will impact volcanic plume modelling results as well as remote sensing retrieval techniques for plume parameters.
Del Bello, Elisabetta; Taddeucci, Jacopo; de’ Michieli Vitturi, Mattia; Scarlato, Piergiorgio; Andronico, Daniele; Scollo, Simona; Kueppers, Ulrich; Ricci, Tullio
2017-01-01
Most of the current ash transport and dispersion models neglect particle-fluid (two-way) and particle-fluid plus particle-particle (four-way) reciprocal interactions during particle fallout from volcanic plumes. These interactions, a function of particle concentration in the plume, could play an important role, explaining, for example, discrepancies between observed and modelled ash deposits. Aiming at a more accurate prediction of volcanic ash dispersal and sedimentation, the settling of ash particles at particle volume fractions (ϕp) ranging 10−7-10−3 was performed in laboratory experiments and reproduced by numerical simulations that take into account first the two-way and then the four-way coupling. Results show that the velocity of particles settling together can exceed the velocity of particles settling individually by up to 4 times for ϕp ~ 10−3. Comparisons between experimental and simulation results reveal that, during the sedimentation process, the settling velocity is largely enhanced by particle-fluid interactions but partly hindered by particle-particle interactions with increasing ϕp. Combining the experimental and numerical results, we provide an empirical model allowing correction of the settling velocity of particles of any size, density, and shape, as a function of ϕp. These corrections will impact volcanic plume modelling results as well as remote sensing retrieval techniques for plume parameters. PMID:28045056
Energy Technology Data Exchange (ETDEWEB)
Watanabe, Taro, E-mail: watanabe_t@qe.see.eng.osaka-u.ac.jp [Graduate School of Engineering, Osaka University, 2-1, Yamadaoka, Suita-shi, Osaka 565-7895 (Japan); Takata, Takashi, E-mail: takata.takashi@jaea.go.jp [Japan Atomic Energy Agency, 4002 Narita-chou, Oarai-machi, Higashi-Ibaraki-gun, Ibaraki 331-1393 (Japan); Yamaguchi, Akira, E-mail: yamaguchi@n.t.u-tokyo.ac.jp [Graduate School of Engineering, The University of Tokyo, 2-22 Shirakata-Shirane, Tokai-mura, Naka-gun, Ibaraki 319-1188 (Japan)
2017-03-15
Highlights: • Thin liquid film flow under CCFL was modeled and coupled with the VOF method. • The difference of the liquid flow rate in experiments of CCFL was evaluated. • The proposed VOF method can quantitatively predict CCFL with low computational cost. - Abstract: Countercurrent flow limitation (CCFL) in a heat transfer tube at a steam generator (SG) of pressurized water reactor (PWR) is one of the important issues on the core cooling under a loss of coolant accident (LOCA). In order to improve the prediction accuracy of the CCFL characteristics in numerical simulations using the volume of fluid (VOF) method with less computational cost, a thin liquid film flow in a countercurrent flow is modeled independently and is coupled with the VOF method. The CCFL characteristics is evaluated analytically in condition of a maximizing down-flow rate as a function of a void fraction or a liquid film thickness considering a critical thickness. Then, we have carried out numerical simulations of a countercurrent flow in a vertical tube so as to investigate the CCFL characteristics and compare them with the previous experimental results. As a result, it has been concluded that the effect of liquid film entrainment by upward gas flux will cause the difference in the experiments.
Česenek, Jan
The article is concerned with the numerical simulation of the compressible turbulent flow in time dependent domains. The mathematical model of flow is represented by the system of non-stationary Reynolds- Averaged Navier-Stokes (RANS) equations. The motion of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian-Eulerian) formulation of the RANS equations. This RANS system is equipped with two-equation k - ω turbulence model. These two systems of equations are solved separately. Discretization of the RANS system is carried out by the space-time discontinuous Galerkin method which is based on piecewise polynomial discontinuous approximation of the sought solution in space and in time. Discretization of the two-equation k - ω turbulence model is carried out by the implicit finite volume method, which is based on piecewise constant approximation of the sought solution. We present some numerical experiments to demonstrate the applicability of the method using own-developed code.
Homogenization scheme for acoustic metamaterials
Yang, Min
2014-02-26
We present a homogenization scheme for acoustic metamaterials that is based on reproducing the lowest orders of scattering amplitudes from a finite volume of metamaterials. This approach is noted to differ significantly from that of coherent potential approximation, which is based on adjusting the effective-medium parameters to minimize scatterings in the long-wavelength limit. With the aid of metamaterials’ eigenstates, the effective parameters, such as mass density and elastic modulus can be obtained by matching the surface responses of a metamaterial\\'s structural unit cell with a piece of homogenized material. From the Green\\'s theorem applied to the exterior domain problem, matching the surface responses is noted to be the same as reproducing the scattering amplitudes. We verify our scheme by applying it to three different examples: a layered lattice, a two-dimensional hexagonal lattice, and a decorated-membrane system. It is shown that the predicted characteristics and wave fields agree almost exactly with numerical simulations and experiments and the scheme\\'s validity is constrained by the number of dominant surface multipoles instead of the usual long-wavelength assumption. In particular, the validity extends to the full band in one dimension and to regimes near the boundaries of the Brillouin zone in two dimensions.
A cell-centered lagrangian scheme in two-dimensional cylindrical geometry
Institute of Scientific and Technical Information of China (English)
SHEN ZhiJun; YUAN GuangWei; YUE JingYan; LIU XueZhe
2008-01-01
A new Lagrangian cell-centered scheme for two-dimensional compressible flows in planar geometry is proposed by Malre et al. The main new feature of the algorithm is that the vertex velocities and the numerical fluxes through the cell interfaces are all evaluated in a coherent manner contrary to standard approaches. In this paper the method introduced by Malre et al. is extended for the equations of Lagrangian gas dynamics in cylindrical symmetry. Two different schemes are proposed, whose difference is that one uses volume weighting and the other area weighting in the discretization of the momentum equation. In the both schemes the conservation of total energy is ensured, and the nodal solver is adopted which has the same formulation as that in Cartesian coordinates. The volume weighting scheme preserves the momentum conservation and the area-weighting scheme preserves spherical symmetry. The numerical examples demonstrate our theoretical considerations and the robustness of the new method.
Institute of Scientific and Technical Information of China (English)
LIU Wei-qun; MIAO Xie-xing
2006-01-01
The overbroken rock mass of gob areas is made up of broken and accumulated rock blocks compressed to some extent by the overlying strata. The bearing pressure of the gob can directly affect the safety of mining fields, formation of road retained along the next goaf and seepage of water and methane through the gob. In this paper, the software RFPA'2000 is used to construct numerical models. Especially the Euler method of control volume is proposed to solve the simulation difficulty arising from plastically finite deformations. The results show that three characteristic regions occurred in the gob area: (1) a naturally accumulated region, 0-10 m away from unbroken surrounding rock walls, where the bearing pressure is nearly zero; (2) an overcompacted region, 10-20 m away from unbroken walls, where the bearing pressure results in the maximum value of the gob area; (3) a stable compaction region, more than 20 m away from unbroken walls and occupying absolutely most of the gob area, where the bearing pressures show basically no differences. Such a characteristic can explain the easy-seepaged "O"-ring phenomena around mining fields very well.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
New form of the constitutive equations for the Oldroyd-B model, which have physical meaning, is developed to facilitate theoretical analysis. The new equations are used to simulate planar 4∶1 contraction flow of a Maxwell fluid using a third-order upwind finite volume method. The numerical results compare well with the theoretical solutions and the results of other references to show the effectiveness of the numerical method. Numerical experiments suggest that the present method not only converges fairly rapidly, but can also generate a highly resolved approximation to an Oldroyd-B fluid flow at a high Weissenberg number.
Application of ADER Scheme in MHD Simulation
Institute of Scientific and Technical Information of China (English)
ZHANG Yanyan; FENG Xueshang; JIANG Chaowei; ZHOU Yufen
2012-01-01
The Arbitrary accuracy Derivatives Riemann problem method（ADER） scheme is a new high order numerical scheme based on the concept of finite volume integration,and it is very easy to be extended up to any order of space and time accuracy by using a Taylor time expansion at the cell interface position.So far the approach has been applied successfully to flow mechanics problems.Our objective here is to carry out the extension of multidimensional ADER schemes to multidimensional MHD systems of conservation laws by calculating several MHD problems in one and two dimensions： （ⅰ） Brio-Wu shock tube problem,（ⅱ） Dai-Woodward shock tube problem,（ⅲ） Orszag-Tang MHD vortex problem.The numerical results prove that the ADER scheme possesses the ability to solve MHD problem,remains high order accuracy both in space and time,keeps precise in capturing the shock.Meanwhile,the compared tests show that the ADER scheme can restrain the oscillation and obtain the high order non-oscillatory result.
A High Resolution Low Dissipation Hybrid Scheme for Compressible Flows
Institute of Scientific and Technical Information of China (English)
YU Jian; YAN Chao; JIANG Zhenhua
2011-01-01
In this paper,an efficient hybrid shock capturing scheme is proposed to obtain accurate results both in the smooth region and around discontinuities for compressible flows.The hybrid algorithm is based on a fifth-order weighted essentially non-oscillatory (WENO) scheme in the finite volume form to solve the smooth part of the flow field,which is coupled with a characteristic-based monotone upstream-centered scheme for conservation laws(MUSCL) to capture discontinuities.The hybrid scheme is intended to combine high resolution of MUSCL scheme and low dissipation of WENO scheme.The two ingredients in this hybrid scheme are switched with an indicator.Three typical indicators are chosen and compared.MUSCL and WENO are both shock capturing schemes making the choice of the indicator parameter less crucial.Several test cases are carried out to investigate hybrid scheme with different indicators in terms of accuracy and efficiency.Numerical results demonstrate that the hybrid scheme in the present work performs well in a broad range of problems.
Institute of Scientific and Technical Information of China (English)
胡俊; 张磊; 任坦
2012-01-01
为探究差分格式和限制器对高超声速热流密度计算结果的影响,以N-S方程为基本控制方程,采用FDS的Roe格式、FVS的van Leer格式对双椭球模型进行了数值模拟,并采用Roe格式选取min mod、van Leer、Osher_C三种限制器对双椭球进行了进一步数值模拟.研究了不同空间差分格式、不同限制器对双椭球压力、气动热数值模拟结果的影响,并对双椭球模型的流场进行了相关分析.研究结果表明:差分格式和限制器对压力系数影响不大,而对热流密度影响较大,采用minmod限制器的Roe格式计算精度最高.%In order to study the effect of difference schemes and limiters, on the basis of Navier-Stokes equation, the flow fields around double-ellipsoid were simulated numerically using Roe scheme of FDS and van Leer scheme of FVS. The limiters of min mod, van Leer, Osher_C under Roe difference scheme were also simulated. The effects of different difference schemes and limiters on the simulation results of double-ellipsoid's aerodynamics and aerothermodynamics were researched and the flow fields of double-ellipsoid were analyzed. The results indicate that the effect of difference schemes and limiters on pressure is less than heat flux and Ree scheme with minmod limitors can obtain high accuracy results.
Deen, Niels G.; Sint Annaland, van Martin; Kuipers, J.A.M.
2007-01-01
In this paper a hybrid model is presented for the numerical simulation of gas-liquid-solid flows using a combined Volume Of Fluid (VOF) and Discrete Particle (DP) approach applied for respectively dispersed gas bubbles and solid particles present in the continuous liquid phase. The hard sphere DP mo
Deen, Niels G.; Sint Annaland, van Martin; Kuipers, J.A.M.
2006-01-01
In this paper a hybrid model is presented for the numerical simulation of gas-liquid-solid flows using a combined Volume Of Fluid (VOF) and Discrete Particle (DP) approach applied for respectively dispersed gas bubbles and solid particles present in the continuous liquid phase. The hard sphere DP mo
Aoufi, A.
2017-05-01
This paper analyzes from a numerical point of view the ignition and propagation of the combustion front during the exothermic TiC combustion synthesis of a material made of pressed titanium and carbide particles when thermophysical properties are either assumed constant or temperature and conversion rate dependent. A two-dimensional cylindrical geometry is considered. The heat supply is prescribed on one, two or three sides of the physical domain. A one-step kinetics is used to describe the reaction Ti+C→TiC in a solid phase and leads to the computation of the conversion rate. A coupling with a non-linear heat equation which takes into account the heat generated by the exothermic kinetics and the two allotropic phase-changes is considered. An explicit finite-volume discretization of the coupled system is constructed and analyzed. Time-step’s stability condition is given for a general expression of the thermo-physical characteristics. A discrete maximum principle is reported. Open MP API was used to parallelize the numerical software written in C. An average speedup of three was obtained on an intel quad-core processor i7-2600. The ignition time and the fraction of unreacted material are systematically computed and compared for several heat supply scenario.
UNIFIED COMPUTATION OF FLOW WITH COMPRESSIBLE AND INCOMPRESSIBLE FLUID BASED ON ROE'S SCHEME
Institute of Scientific and Technical Information of China (English)
HUANG Dian-gui
2006-01-01
A unified numerical scheme for the solutions of the compressible and incompressible Navier-Stokes equations is investigated based on a time-derivative preconditioning algorithm. The primitive variables are pressure, velocities and temperature. The time integration scheme is used in conjunction with a finite volume discretization. The preconditioning is coupled with a high order implicit upwind scheme based on the definition of a Roe's type matrix. Computational capabilities are demonstrated through computations of high Mach number, middle Mach number, very low Mach number, and incompressible flow. It has also been demonstrated that the discontinuous surface in flow field can be captured for the implementation Roe's scheme.
Directory of Open Access Journals (Sweden)
Zhang, M. Z.
2010-12-01
Full Text Available Concrete diffusivity is a function of its microstructure on many scales, ranging from nanometres to millimetres. Multi-scale techniques are therefore needed to model this parameter. Representative elementary volume (REV, in conjunction with the homogenization principle, is one of the most common multi-scale approaches. This study aimed to establish a procedure for establishing the REV required to determine cement paste diffusivity based on a three-step, numerical-statistical approach. First, several series of 3D cement paste microstructures were generated with HYMOSTRUC3D, a cement hydration and microstructure model, for different volumes of cement paste and w/c ratios ranging from 0.30 to 0.60. Second, the finite element method was used to simulate the diffusion of tritiated water through these microstructures. Effective cement paste diffusivity values for different REVs were obtained by applying Fick’s law. Finally, statistical analysis was used to find the fluctuation in effective diffusivity with cement paste volume, from which the REV was then determined. The conclusion drawn was that the REV for measuring diffusivity in cement paste is 100x100x100 μm^{3}.
La difusividad del hormigón depende de su microestructura a numerosas escalas, desde nanómetros hasta milímetros, por lo que se precisa de técnicas multiescala para representar este parámetro. Junto con el principio de homogeneización, uno de los métodos multiescala más habituales es el volumen elemental representativo (VER. El objeto de este estudio era establecer un procedimiento que permitiera determinar el VER necesario para calcular la difusividad de la pasta de cemento, basándose en un método numéricoestadístico que consta de tres etapas. Primero, se crearon varias series de microestructuras de pasta de cemento en 3D con HYMOSTRUC3D, un programa que permite crear un modelo de la hidratación y microestructura del cemento. Luego se empleó el método de
Homographic scheme for Riccati equation
Dubois, François
2011-01-01
In this paper we present a numerical scheme for the resolution of matrix Riccati equation, usualy used in control problems. The scheme is unconditionnaly stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.
The finite volume local evolution Galerkin method for solving the hyperbolic conservation laws
Sun, Yutao; Ren, Yu-Xin
2009-07-01
This paper presents a finite volume local evolution Galerkin (FVLEG) scheme for solving the hyperbolic conservation laws. The FVLEG scheme is the simplification of the finite volume evolution Galerkin method (FVEG). In FVEG, a necessary step is to compute the dependent variables at cell interfaces at tn + τ (0 FVEG. The FVLEG scheme greatly simplifies the evaluation of the numerical fluxes. It is also well suited with the semi-discrete finite volume method, making the flux evaluation being decoupled with the reconstruction procedure while maintaining the genuine multi-dimensional nature of the FVEG methods. The derivation of the FVLEG scheme is presented in detail. The performance of the proposed scheme is studied by solving several test cases. It is shown that FVLEG scheme can obtain very satisfactory numerical results in terms of accuracy and resolution.
Institute of Scientific and Technical Information of China (English)
XIONG Chun-hui; ZHANG Li-feng; GUAN Ji-ping; PENG Jun; ZHANG Bin
2013-01-01
A fine heavy rain forecast plays an important role in the accurate flood forecast,the urban rainstorm waterlogging and the secondary hydrological disaster preventions.To improve the heavy rain forecast skills,a hybrid Breeding Growing Mode (BGM)-three-dimensional variational (3DVAR) Data Assimilation (DA) scherne is designed on running the Advanced Research WRF (ARW WRF) model using the Advanced Microwave Sounder Unit A (AMSU-A) satellite radiance data.Results show that:the BGM ensemble prediction method can provide an effective background field and a flow dependent background error covariance for the BGM-3DVAR scheme.The BGM-3DVAR scheme adds some effective mesoscale information with similar scales as the heavy rain clusters to the initial field in the heavy rain area,which improves the heavy rain forecast significantly,while the 3DVAR scheme adds information with relatively larger scales than the heavy rain clusters to the initial field outside of the heavy rain area,which does not help the heavy rain forecast improvement.Sensitive experiments demonstrate that the flow dependent background error covariance and the ensemble mean background field are both the key factors for adding effective mesoscale information to the heavy rain area,and they are both essential for improving the heavy rain forecasts.
Energy Technology Data Exchange (ETDEWEB)
Fanselau, R.W.; Thakkar, J.G.; Hiestand, J.W.; Cassell, D.
1981-03-01
The Comparative Thermal-Hydraulic Evaluation of Steam Generators program represents an analytical investigation of the thermal-hydraulic characteristics of four PWR steam generators. The analytical tool utilized in this investigation is the CALIPSOS code, a three-dimensional flow distribution code. This report presents the steady state thermal-hydraulic characteristics on the secondary side of a Westinghouse Model 51 steam generator. Details of the CALIPSOS model with accompanying assumptions, operating parameters, and transport correlations are identified. Comprehensive graphical and numerical results are presented to facilitate the desired comparison with other steam generators analyzed by the same flow distribution code.
An Explicit High Resolution Scheme for Nonlinear Shallow Water Equations
Institute of Scientific and Technical Information of China (English)
FANG Ke-zhao; ZOU Zhi-li; WANG Yan
2005-01-01
The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations (NSWE) for the wave run-up on a beach. The finite volume method (FVM) is used to solve the equations, and a second-order explicit scheme is developed to improve the computation efficiency. The numerical fluxes are obtained by the two dimensional Roe's flux function to overcome the errors caused by the use of one dimensional fluxes in dimension splitting methods. The high-resolution Godunov-type TVD upwind scheme is employed and a second-order accuracy is achieved based on monotonic upstream schemes for conservation laws (MUSCL) variable extrapolation; a nonlinear limiter is applied to prevent unwanted spurious oscillation. A simple but efficient technique is adopted to deal with the moving shoreline boundary. The verification of the solution technique is carried out by comparing the model output with documented results and it shows that the solution technique is robust.
A moving mesh unstaggered constrained transport scheme for magnetohydrodynamics
Mocz, Philip; Springel, Volker; Vogelsberger, Mark; Marinacci, Federico; Hernquist, Lars
2016-01-01
We present a constrained transport (CT) algorithm for solving the 3D ideal magnetohydrodynamic (MHD) equations on a moving mesh, which maintains the divergence-free condition on the magnetic field to machine-precision. Our CT scheme uses an unstructured representation of the magnetic vector potential, making the numerical method simple and computationally efficient. The scheme is implemented in the moving mesh code Arepo. We demonstrate the performance of the approach with simulations of driven MHD turbulence, a magnetized disc galaxy, and a cosmological volume with primordial magnetic field. We compare the outcomes of these experiments to those obtained with a previously implemented Powell divergence-cleaning scheme. While CT and the Powell technique yield similar results in idealized test problems, some differences are seen in situations more representative of astrophysical flows. In the turbulence simulations, the Powell cleaning scheme artificially grows the mean magnetic field, while CT maintains this co...
Wie, Yong-Sun
1990-01-01
A procedure for calculating 3-D, compressible laminar boundary layer flow on general fuselage shapes is described. The boundary layer solutions can be obtained in either nonorthogonal 'body oriented' coordinates or orthogonal streamline coordinates. The numerical procedure is 'second order' accurate, efficient and independent of the cross flow velocity direction. Numerical results are presented for several test cases, including a sharp cone, an ellipsoid of revolution, and a general aircraft fuselage at angle of attack. Comparisons are made between numerical results obtained using nonorthogonal curvilinear 'body oriented' coordinates and streamline coordinates.
1992-10-01
AS A RELAXATION SCHEME Consider solving Equation (61) using the Gauss- Seidel method . In Equation (61) D is a block diagonal matrix, M+ is a block...zero, the Gauss- Seidel method is D 1’m + 1.m =-Rn+1.mDX1 - [-* Xi- Im+I. (66) After completing this forward pass the Xl-m are known, and a backward
Energy Technology Data Exchange (ETDEWEB)
Gomez T, A.M.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico); Delfin L, A.; Alonso V, G. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)] e-mail: armagotorres@aol.com
2003-07-01
In this work a finite differences technique centered in mesh based on a cubic reduced nodal scheme type finite element to solve the equations of the kinetics 1 D that include the equations corresponding to the concentrations of precursors of delayed neutrons is described. The technique of finite elements used is that of Galerkin where so much the neutron flux as the concentrations of precursors its are spatially approached by means of a three grade polynomial. The matrices of rigidity and of mass that arise during this discretization process are numerically evaluated using the open quadrature non standard of Newton-Cotes and that of Radau respectively. The purpose of the application of these quadratures is the one of to eliminate in the global matrices the couplings among the values of the flow in points of the discretization with the consequent advantages as for the reduction of the order of the matrix associated to the discreet problem that is to solve. As for the time dependent part the classical integration scheme known as {theta} scheme is applied. After carrying out the one reordering of unknown and equations it arrives to a reduced system that it can be solved but quickly. With the McKin compute program developed its were solved three benchmark problems and those results are shown for the relative powers. (Author)
PERTURBATION FINITE VOLUME METHOD FOR CONVECTIVE-DIFFUSION INTEGRAL EQUATION
Institute of Scientific and Technical Information of China (English)
GAO Zhi; YANG Guowei
2004-01-01
A perturbation finite volume (PFV) method for the convective-diffusion integral equation is developed in this paper. The PFV scheme is an upwind and mixed scheme using any higher-order interpolation and second-order integration approximations, with the least nodes similar to the standard three-point schemes, that is, the number of the nodes needed is equal to unity plus the face-number of the control volume. For instance, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D linear and nonlinear problems, 2-D and 3-D flow model equations. Comparing with other standard three-point schemes, the PFV scheme has much smaller numerical diffusion than the first-order upwind scheme (UDS). Its numerical accuracies are also higher than the second-order central scheme (CDS), the power-law scheme (PLS) and QUICK scheme.
Directory of Open Access Journals (Sweden)
Nopparat Pochai
2014-01-01
Full Text Available Two mathematical models are used to simulate water quality in a nonuniform flow stream. The first model is the hydrodynamic model that provides the velocity field and the elevation of water. The second model is the dispersion model that provides the pollutant concentration field. Both models are formulated in one-dimensional equations. The traditional Crank-Nicolson method is also used in the hydrodynamic model. At each step, the flow velocity fields calculated from the first model are the input into the second model as the field data. A modified MacCormack method is subsequently employed in the second model. This paper proposes a simply remarkable alteration to the MacCormack method so as to make it more accurate without any significant loss of computational efficiency. The results obtained indicate that the proposed modified MacCormack scheme does improve the prediction accuracy compared to that of the traditional MacCormack method.
Directory of Open Access Journals (Sweden)
Szymkiewicz Adam
2015-09-01
Full Text Available Flow in unsaturated porous media is commonly described by the Richards equation. This equation is strongly nonlinear due to interrelationships between water pressure head (negative in unsaturated conditions, water content and hydraulic conductivity. The accuracy of numerical solution of the Richards equation often depends on the method used to estimate average hydraulic conductivity between neighbouring nodes or cells of the numerical grid. The present paper discusses application of the computer simulation code VS2DI to three test problems concerning infiltration into an initially dry medium, using various methods for inter-cell conductivity calculation (arithmetic mean, geometric mean and upstream weighting. It is shown that the influence of the averaging method can be very large for coarse grid, but that it diminishes as cell size decreases. Overall, the arithmetic average produced the most reliable results for coarse grids. Moreover, the difference between results obtained with various methods is a convenient indicator of the adequacy of grid refinement.
Szymkiewicz, Adam; Tisler, Witold; Burzyński, Kazimierz
2015-09-01
Flow in unsaturated porous media is commonly described by the Richards equation. This equation is strongly nonlinear due to interrelationships between water pressure head (negative in unsaturated conditions), water content and hydraulic conductivity. The accuracy of numerical solution of the Richards equation often depends on the method used to estimate average hydraulic conductivity between neighbouring nodes or cells of the numerical grid. The present paper discusses application of the computer simulation code VS2DI to three test problems concerning infiltration into an initially dry medium, using various methods for inter-cell conductivity calculation (arithmetic mean, geometric mean and upstream weighting). It is shown that the influence of the averaging method can be very large for coarse grid, but that it diminishes as cell size decreases. Overall, the arithmetic average produced the most reliable results for coarse grids. Moreover, the difference between results obtained with various methods is a convenient indicator of the adequacy of grid refinement.
Space-Time Transformation in Flux-form Semi-Lagrangian Schemes
Directory of Open Access Journals (Sweden)
Peter C. Chu Chenwu Fan
2010-01-01
Full Text Available With a finite volume approach, a flux-form semi-Lagrangian (TFSL scheme with space-time transformation was developed to provide stable and accurate algorithm in solving the advection-diffusion equation. Different from the existing flux-form semi-Lagrangian schemes, the temporal integration of the flux from the present to the next time step is transformed into a spatial integration of the flux at the side of a grid cell (space for the present time step using the characteristic-line concept. The TFSL scheme not only keeps the good features of the semi-Lagrangian schemes (no Courant number limitation, but also has higher accuracy (of a second order in both time and space. The capability of the TFSL scheme is demonstrated by the simulation of the equatorial Rossby-soliton propagation. Computational stability and high accuracy makes this scheme useful in ocean modeling, computational fluid dynamics, and numerical weather prediction.
Discrete unified gas kinetic scheme with force term for incompressible fluid flows
Wu, Chen; Chai, Zhenhua; Wang, Peng
2014-01-01
The discrete unified gas kinetic scheme (DUGKS) is a finite-volume scheme with discretization of particle velocity space, which combines the advantages of both lattice Boltzmann equation (LBE) method and unified gas kinetic scheme (UGKS) method, such as the simplified flux evaluation scheme, flexible mesh adaption and the asymptotic preserving properties. However, DUGKS is proposed for near incompressible fluid flows, the existing compressible effect may cause some serious errors in simulating incompressible problems. To diminish the compressible effect, in this paper a novel DUGKS model with external force is developed for incompressible fluid flows by modifying the approximation of Maxwellian distribution. Meanwhile, due to the pressure boundary scheme, which is wildly used in many applications, has not been constructed for DUGKS, the non-equilibrium extrapolation (NEQ) scheme for both velocity and pressure boundary conditions is introduced. To illustrate the potential of the proposed model, numerical simul...
Jin, BoCheng
2011-12-01
Organic and inorganic fiber reinforced composites with innumerable fiber orientation distributions and fiber geometries are abundantly available in several natural and synthetic structures. Inorganic glass fiber composites have been introduced to numerous applications due to their economical fabrication and tailored structural properties. Numerical characterization of such composite material systems is necessitated due to their intrinsic statistical nature, which renders extensive experimentation prohibitively time consuming and costly. To predict various mechanical behavior and characterizations of Uni-Directional Fiber Composites (UDFC) and Random Fiber Composites (RaFC), we numerically developed Representative Volume Elements (RVE) with high accuracy and efficiency and with complex fiber geometric representations encountered in uni-directional and random fiber networks. In this thesis, the numerical simulations of unidirectional RaFC fiber strand RVE models (VF>70%) are first presented by programming in ABAQUS PYTHON. Secondly, when the cross sectional aspect ratios (AR) of the second phase fiber inclusions are not necessarily one, various types of RVE models with different cross sectional shape fibers are simulated and discussed. A modified random sequential absorption algorithm is applied to enhance the volume fraction number (VF) of the RVE, which the mechanical properties represents the composite material. Thirdly, based on a Spatial Segment Shortest Distance (SSSD) algorithm, a 3-Dimentional RaFC material RVE model is simulated in ABAQUS PYTHON with randomly oriented and distributed straight fibers of high fiber aspect ratio (AR=100:1) and volume fraction (VF=31.8%). Fourthly, the piecewise multi-segments fiber geometry is obtained in MATLAB environment by a modified SSSD algorithm. Finally, numerical methods including the polynomial curve fitting and piecewise quadratic and cubic B-spline interpolation are applied to optimize the RaFC fiber geometries
FVS SCHEME FOR SEVERE TRANSIENT FLOW IN PIPE NETWORKS
Institute of Scientific and Technical Information of China (English)
GENG Yan-fen; WANG Zhi-li; JIN Sheng
2005-01-01
An efficient numerical method with first and second order accuracy is developed by the flux split technology to simulate the water hammer problem in single and multiple pipe networks under severe transient conditions. The finite volume formulation ensures that both schemes conserve mass and momentum and produces physically realizable shock fronts. The conception of the fictitious cell at the junction is developed. The typical water hammer problem and the experiment with friction and the comprehensive orbicular network with control valve and pressure relief valve and surge tank are implemented to test the numerical method. Strong numerical evidences show that the proposed scheme has several desirable properties, such as, accurate, efficient, robust, high shock resolution, conservative and stable for Courant number.
Sud, Y. C.; Mocko, David M.; Lin, S. J.
2006-01-01
An objective assessment of the impact of a new cloud scheme, called Microphysics of Clouds with Relaxed Arakawa-Schubert Scheme (McRAS) (together with its radiation modules), on the finite volume general circulation model (fvGCM) was made with a set of ensemble forecasts that invoke performance evaluation over both weather and climate timescales. The performance of McRAS (and its radiation modules) was compared with that of the National Center for Atmospheric Research Community Climate Model (NCAR CCM3) cloud scheme (with its NCAR physics radiation). We specifically chose the boreal summer months of May and June 2003, which were characterized by an anomalously wet eastern half of the continental United States as well as northern regions of Amazonia. The evaluation employed an ensemble of 70 daily 10-day forecasts covering the 61 days of the study period. Each forecast was started from the analyzed initial state of the atmosphere and spun-up soil moisture from the first-day forecasts with the model. Monthly statistics of these forecasts with up to 10-day lead time provided a robust estimate of the behavior of the simulated monthly rainfall anomalies. Patterns of simulated versus observed rainfall, 500-hPa heights, and top-of-the-atmosphere net radiation were recast into regional anomaly correlations. The correlations were compared among the simulations with each of the schemes. The results show that fvGCM with McRAS and its radiation package performed discernibly better than the original fvGCM with CCM3 cloud physics plus its radiation package. The McRAS cloud scheme also showed a reasonably positive response to the observed sea surface temperature on mean monthly rainfall fields at different time leads. This analysis represents a method for helpful systematic evaluation prior to selection of a new scheme in a global model.
A semi-implicit gas-kinetic scheme for smooth flows
Wang, Peng; Guo, Zhaoli
2016-08-01
In this paper, a semi-implicit gas-kinetic scheme (SIGKS) is derived for smooth flows based on the Bhatnagar-Gross-Krook (BGK) equation. As a finite-volume scheme, the evolution of the average flow variables in a control volume is under the Eulerian framework, whereas the construction of the numerical flux across the cell interface comes from the Lagrangian perspective. The adoption of the Lagrangian aspect makes the collision and the transport mechanisms intrinsically coupled together in the flux evaluation. As a result, the time step size is independent of the particle collision time and solely determined by the Courant-Friedrichs-Lewy (CFL) condition. An analysis of the reconstructed distribution function at the cell interface shows that the SIGKS can be viewed as a modified Lax-Wendroff type scheme with an additional term. Furthermore, the addition term coming from the implicitness in the reconstruction is expected to be able to enhance the numerical stability of the scheme. A number of numerical tests of smooth flows with low and moderate Mach numbers are performed to benchmark the SIGKS. The results show that the method has second-order spatial accuracy, and can give accurate numerical solutions in comparison with benchmark results. It is also demonstrated that the numerical stability of the proposed scheme is better than the original GKS for smooth flows.
The Meshfree Finite Volume Method with application to multi-phase porous media models
Foy, Brody H.; Perré, Patrick; Turner, Ian
2017-03-01
Numerical methods form a cornerstone of the analysis and investigation of mathematical models for physical processes. Many classical numerical schemes rely on the application of strict meshing structures to generate accurate solutions, which in some applications are an infeasible constraint. Within this paper we outline a new meshfree numerical scheme, which we call the Meshfree Finite Volume Method (MFVM). The MFVM uses interpolants to approximate fluxes in a disjoint finite volume scheme, allowing for the accurate solution of strong-form PDEs. We present a derivation of the MFVM, and give error bounds on the spatial and temporal approximations used within the scheme. We present a wide variety of applications of the method, showing key features, and advantages over traditional meshed techniques. We close with an application of the method to a non-linear multi-phase wood drying model, showing the potential for solving numerically challenging problems.
Blachère, F.; Turpault, R.
2016-06-01
The objective of this work is to design explicit finite volumes schemes for specific systems of conservations laws with stiff source terms, which degenerate into diffusion equations. We propose a general framework to design an asymptotic preserving scheme, that is stable and consistent under a classical hyperbolic CFL condition in both hyperbolic and diffusive regime, for any two-dimensional unstructured mesh. Moreover, the scheme developed also preserves the set of admissible states, which is mandatory to keep physical solutions in stiff configurations. This construction is achieved by using a non-linear scheme as a target scheme for the diffusive equation, which gives the form of the global scheme for the complete system of conservation laws. Numerical results are provided to validate the scheme in both regimes.
Katsman, R; Scher, H
2005-01-01
Porous rocks, subjected to compressive stress, often undergo mechanical compaction via grain crushing and grain rearrangement, and chemical compaction by pressure solution. Such volume reduction processes are known to spontaneously localize under certain conditions, creating compaction and compacting shear bands, solution-seams, and stylolites. However the localization process is poorly understood. The formation and propagation of compaction bands has recently been studied using an elasto-plastic Spring Network Model [Katsman, Aharonov, and Scher, 2005]. In the current paper, the same technique was employed to systematically analyze localized volume reduction (LVR) defects and their interactions with the surrounding elastic media, i. e., the stress distribution around an LVR region. Simulation results show that LVR regions experience stress concentrations at their tips, reminiscent of Mode I cracks. However, aside from this similarity point, comparison of stress around LVR regions to stress around cracks reve...
1991-05-22
Eisenberg 1987). Among other formulations, the existing models are based on the theories of elasticity, hypoelasticity , plasticity and viscoplasticity...AD-A238 158 AFOSR4R. 91 069.1 A STUDY OF THE BEHAVIOR AND MICROMECHANICAL MODELLING OF GRANULAR SOIL DTIC VOLUME mI ELECTIE A NUMERICAL INVESTIGATION...Final 1/6/ 9-5/15/91 4. nU AN SUS"Ll5. FUNDING NUMBERS A Study of the Behavior and Micromechanical Modelling of Grant AFOSR-89-0350 Granular Soil PR
Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations
Institute of Scientific and Technical Information of China (English)
Tongke
2010-01-01
This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.
Institute of Scientific and Technical Information of China (English)
杜宪亭; 夏禾; 张田
2012-01-01
Bridge and vehicle subsystems were simplified into oscillators connected with springs or a system of masses with springs in vertical direction, respectively. The numerical stabilities of iterative schemes in solving dynamic interaction of train and bridge were studied with different wheel-rail relations on the basis of the spectral radius theory. The corresponding improvement approach was proposed in term of possible causes leading to numerical divergence. The results showed that the iteration can converge if the time step is small enough for the wheel-rail separation model; for the wheel-rail non-separation model, direct iterative scheme may lead to numerical instability if the mass of a bridge node is smaller than that of the passing wheel-pair; the virtual mass approach is proposed, it can not only avoid potential divergence but also retain the advantages of direct iterative scheme.%将桥梁、车辆分别简化为竖向振动的弹簧振子、簧上质量系,应用谱半径理论研究不同轮轨关系、不同迭代格式下车桥动力相互作用的数值求解稳定性问题,针对可能引起迭代计算发散的原因,提出改进措施.研究表明,采用轮轨分离模型,时间积分步足够小,迭代过程即可收敛；轮轨密贴分析模型中,轮对质量大于所通过桥梁节点质量时采用直接迭代格式会造成数值计算发散；轮轨密贴模型迭代求解过程中应用该虚拟质量法既可避免迭代数值发散亦可保留直接迭代优点.
APPLICATION OF FDS SCHEME TO 2D DEPTH-AVERAGED FLOW-POLLUTANTS SIMULATION
Institute of Scientific and Technical Information of China (English)
Zhang Li-qiong; Zhao Di-hua; Lai Jihn-sung; Yao Qi; Xiao Jun-ying
2003-01-01
A Fulx Difference Splitting (FDS) scheme was used in a 2D depth-averaged flow-pollutant model. Within the framework of the Finite Volume Method (FVM) a 2D simulation was transferred into solving a series of local 1D problems based on the rotational invariance property of the flux. The FDS scheme was employed to estimate the normal numerical flux of variables including water mass, momentum and pollutant concentration across the interface between cells. The scheme was checked with exact solutions and verified by observations in the Nantong reach of the Yangtze River. Calculated results well match both exact solutions and observations.
DEFF Research Database (Denmark)
van Leeuwen, Theo
2013-01-01
This chapter presents a framework for analysing colour schemes based on a parametric approach that includes not only hue, value and saturation, but also purity, transparency, luminosity, luminescence, lustre, modulation and differentiation....
TIME-DOMAIN VOLUME INTEGRAL EQUATION FOR TRANSIENT SCATTERING FROM INHOMOGENEOUS OBJECTS-2D TM CASE
Institute of Scientific and Technical Information of China (English)
Wang Jianguo; Fan Ruyu
2001-01-01
This letter proposes a time-domain volume integral equation based method for analyzing the transient scattering from a 2D inhomogeneous cylinder by involking the volume equivalence principle for the transverse magnetic case. This integral equation is solved by using an MOT scheme. Numerical results obtained using this method agree very well with those obtained using the FDTD method.
TIME-DOMAIN VOLUME INTEGRAL EQUATION FOR TRANSIENT SCATTERING FROM INHOMOGENEOUS OBJECTS-2D TE CASE
Institute of Scientific and Technical Information of China (English)
Wang Jianguo; Fan Ruyu
2001-01-01
This letter proposes a time-domain volume integral equation based method for analyzing the transient scattering from a 2D inhomogeneous cylinder by involking the volume equivalence principle for the transverse electric case. This integral equation is solved by using an MOT scheme. Numerical results obtained using this method agree very well with those obtained using the FDTD method.
A RANS/DES Numerical Procedure for Axisymmetric Flows with and without Strong Rotation
Energy Technology Data Exchange (ETDEWEB)
Andrade, Andrew Jacob [Univ. of California, Davis, CA (United States)
2007-01-01
A RANS/DES numerical procedure with an extended Lax-Wendroff control-volume scheme and turbulence model is described for the accurate simulation of internal/external axisymmetric flow with and without strong rotation. This new procedure is an extension, from Cartesian to cylindrical coordinates, of (1) a second order accurate multi-grid, control-volume integration scheme, and (2) a k-ω turbulence model. This paper outlines both the axisymmetric corrections to the mentioned numerical schemes and the developments of techniques pertaining to numerical dissipation, multi-block connectivity, parallelization, etc. Furthermore, analytical and experimental case studies are presented to demonstrate accuracy and computational efficiency. Notes are also made toward numerical stability of highly rotational flows.
Kröger, Tim; Lukáčová-Medvid'ová, Mária
2005-06-01
In this paper we propose a new finite volume evolution Galerkin (FVEG) scheme for the shallow water magnetohydrodynamic (SMHD) equations. We apply the exact integral equations already used in our earlier publications to the SMHD system. Then, we approximate these integral equation in a general way which does not exploit any particular property of the SMHD equations and should thus be applicable to arbitrary systems of hyperbolic conservation laws in two space dimensions. In particular, we investigate more deeply the approximation of the spatial derivatives which appear in the integral equations. The divergence free condition is satisfied discretely, i.e. at each vertex. First numerical results confirm reliability of the numerical scheme.
Energy Technology Data Exchange (ETDEWEB)
BLUM,T.
1999-09-14
The RIKEN BNL Research Center hosted its 19th workshop April 27th through May 1, 1999. The topic was Numerical Algorithms at Non-Zero Chemical Potential. QCD at a non-zero chemical potential (non-zero density) poses a long-standing unsolved challenge for lattice gauge theory. Indeed, it is the primary unresolved issue in the fundamental formulation of lattice gauge theory. The chemical potential renders conventional lattice actions complex, practically excluding the usual Monte Carlo techniques which rely on a positive definite measure for the partition function. This ''sign'' problem appears in a wide range of physical systems, ranging from strongly coupled electronic systems to QCD. The lack of a viable numerical technique at non-zero density is particularly acute since new exotic ''color superconducting'' phases of quark matter have recently been predicted in model calculations. A first principles confirmation of the phase diagram is desirable since experimental verification is not expected soon. At the workshop several proposals for new algorithms were made: cluster algorithms, direct simulation of Grassman variables, and a bosonization of the fermion determinant. All generated considerable discussion and seem worthy of continued investigation. Several interesting results using conventional algorithms were also presented: condensates in four fermion models, SU(2) gauge theory in fundamental and adjoint representations, and lessons learned from strong; coupling, non-zero temperature and heavy quarks applied to non-zero density simulations.
Institute of Scientific and Technical Information of China (English)
H.SAGHI; M.J.KETABDARI; S.BOOSHI
2012-01-01
A two-dimensional (2D) numerical model is developed for the wave simulation and propagation in a wave flume.The fluid flow is assumed to be viscous and incompressible,and the Navier-Stokes and continuity equations are used as the governing equations.The standard κ-ε model is used to model the turbulent flow.The NavierStokes equations are discretized using the staggered grid finite difference method and solved by the simplified marker and cell (SMAC) method. Waves are generated and propagated using a piston type wave maker. An open boundary condition is used at the end of the numerical flume.Some standard tests,such as the lid-driven cavity,the constant unidirectional velocity field,the shearing flow,and the dam-break on the dry bed,are performed to valid the model.To demonstrate the capability and accuracy of the present method,the results of generated waves are compared with available wave theories.Finally,the clustering technique (CT) is used for the mesh generation,and the best condition is suggested.
Directory of Open Access Journals (Sweden)
Mun Jang
2017-09-01
Full Text Available Background: Volume overload results in higher mortality rates in patients on continuous ambulatory peritoneal dialysis (CAPD. The ratio of bioimpedance (RBI might be a helpful parameter in adjusting dry body weight in CAPD patients. This study examined whether it is possible to distinguish between non-hypervolemic status and hypervolemic status in CAPD patients by using only RBI. Methods: RBI was calculated as follows: RBI = impedance at 50 kHz/impedance at 500 kHz. Based on the experts’ judgements, a total of 64 CAPD patients were divided into two groups, a non-hypervolemic group and a hypervolemic group. The RBI was measured from right wrist to right ankle (rw-raRBI by bioimpedance spectroscopy (BCM®, Fresenius Medical Care before and after the peritosol was emptied. Other RBIs were measured from the right side of the anterior superior iliac spine to the ipsilateral ankle (rasis-raRBI to control for the electro-physiological effects of peritoneal dialysate. Results: The mean rw-raRBI of non-hypervolemic patients was higher than that of hypervolemic patients in the presence (1.141 ± 0.022 vs. 1.121 ± 0.021, P < 0.001 of a peritosol. Likewise, the mean rasis-raRBI of non-hypervolemic patients was higher than that of hypervolemic patients (presence of peritosol: 1.136 ± 0.026 vs. 1.109 ± 0.022, P < 0.001; absence of peritosol: 1.131 ± 0.022 vs. 1.107 ± 0.022, P < 0.001. Conclusion: The volume status of CAPD patients was able to be simply expressed by RBI. Therefore, this study suggests that when patients cannot be analyzed using BCM, RBI could be an alternative.
DEVELOPMENT AND APPLICATIONS OF WENO SCHEMES IN CONTINUUM PHYSICS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper briefly presents the general ideas of high order accurate weighted essentially non-oscillatory (WENO) schemes, and describes the similarities and differences of the two classes of WENO schemes: finite volume schemes and finite difference schemes. We also briefly mention a recent development of WENO schemes,namely an adaptive approach within the finite difference framework using smooth time dependent curvilinear coordinates.``
Chimera: A hybrid approach to numerical loop quantum cosmology
Diener, Peter; Singh, Parampreet
2013-01-01
The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosi...
Dehghan, Mehdi; Mohammadi, Vahid
2017-08-01
In this research, we investigate the numerical solution of nonlinear Schrödinger equations in two and three dimensions. The numerical meshless method which will be used here is RBF-FD technique. The main advantage of this method is the approximation of the required derivatives based on finite difference technique at each local-support domain as Ωi. At each Ωi, we require to solve a small linear system of algebraic equations with a conditionally positive definite matrix of order 1 (interpolation matrix). This scheme is efficient and its computational cost is same as the moving least squares (MLS) approximation. A challengeable issue is choosing suitable shape parameter for interpolation matrix in this way. In order to overcome this matter, an algorithm which was established by Sarra (2012), will be applied. This algorithm computes the condition number of the local interpolation matrix using the singular value decomposition (SVD) for obtaining the smallest and largest singular values of that matrix. Moreover, an explicit method based on Runge-Kutta formula of fourth-order accuracy will be applied for approximating the time variable. It also decreases the computational costs at each time step since we will not solve a nonlinear system. On the other hand, to compare RBF-FD method with another meshless technique, the moving kriging least squares (MKLS) approximation is considered for the studied model. Our results demonstrate the ability of the present approach for solving the applicable model which is investigated in the current research work.
A modified Rusanov scheme for shallow water equations with topography and two phase flows
Mohamed, Kamel; Benkhaldoun, F.
2016-06-01
In this work, we introduce a finite volume method for numerical simulation of shallow water equations with source terms in one and two space dimensions, and one-pressure model of two-phase flows in one space dimension. The proposed method is composed of two steps. The first, called predictor step, depends on a local parameter allowing to control the numerical diffusion. A strategy based on limiters theory enables to control this parameter. The second step recovers the conservation equation. The scheme can thus be turned to order 1 in the regions where the flow has a strong variation, and order 2 in the regions where the flow is regular. The numerical scheme is applied to several test cases in one and two space dimensions. This scheme demonstrates its well-balanced property, and that it is an efficient and accurate approach for solving shallow water equations with and without source terms, and water faucet problem.
ON DISPERSION-CONTROLLED PRINCIPLES FOR NON-OSCILLATORY SHOCK-CAPTURING SCHEMES
Institute of Scientific and Technical Information of China (English)
JIANG Zonglin
2004-01-01
The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time. It is only during the last two decades that extensive studies on the dispersion-controlled dissipative (DCD) schemes were reported. The studies have demonstrated that this kind of the schemes is distinct from conventional dissipation-based schemes in which the dispersion term of the modified equation is not considered in scheme construction to avoid nonphysical oscillation occurring in shock wave simulations. The principle of the dispersion controlled aims at removing nonphysical oscillations by making use of dispersion characteristics instead of adding artificial viscosity to dissipate the oscillation as the conventional schemes do. Research progresses on the dispersioncontrolled principles are reviewed in this paper, including the exploration of the role of dispersions in numerical simulations, the development of the dispersion-controlled principles, efforts devoted to high-order dispersion-controlled dissipative schemes, the extension to both the finite volume and the finite element methods, scheme verification and solution validation, and comments on several aspects of the schemes from author's viewpoint.
A new semi-Lagrangian difference scheme
Institute of Scientific and Technical Information of China (English)
季仲贞; 陈嘉滨
2001-01-01
A new completely energy-conserving semi-Lagrangian scheme is constructed. The numerical solution of shallow water equation shows that this conservative scheme preserves the total energy in twelve significant digits, while the traditional scheme does only in five significant digits.
Institute of Scientific and Technical Information of China (English)
陈同庆; 张庆河
2013-01-01
Based on the modified three-dimensional non-hydrostatic ocean model, SUNTANS, simulation of inter-nal solitary waves is carried out for the idealized case and the northeastern South China Sea to investigate the in-fluence of four flux limiters of TVD (total variance diminishing) scheme on the calculated results. The TVD scheme is used to solve the equations of salinity and temperature, and the considered flux limiters are superbee, minmod, van Leer, and MUSCL limiters. Analysis of the calculated results indicates that MUSCL limiter exhibits the best performance among the four considered limiters. It is recommended to use MUSCL limiter in the numerical simula-tion of internal solitary waves in the northeastern South China Sea.% 为了研究不同TVD格式对内孤立波模拟结果的影响,利用改进后的SUNTANS三维非静压海洋模型,通过理想算例和南海东北部海域内孤立波的模拟,比较分析了求解温盐方程TVD格式的4种经典通量限制函数(superbee, minmod, van Leer和MUSCL)对计算结果的影响。综合理想算例和南海东北部海域模拟结果,在所讨论的4种通量限制函数中,利用MUSCL限制函数所得模拟结果最优,建议在南海东北部海域内孤立波模拟中采用MUSCL限制函数。
Nonstandard finite difference schemes for differential equations
Directory of Open Access Journals (Sweden)
Mohammad Mehdizadeh Khalsaraei
2014-12-01
Full Text Available In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs. Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with standard methods.
Unconditionnally stable scheme for Riccati equation
Dubois, François; 10.1051/proc:2000003
2011-01-01
We present a numerical scheme for the resolution of matrix Riccati equation used in control problems. The scheme is unconditionnally stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.
Energy Technology Data Exchange (ETDEWEB)
Chien, T.H.; Domanus, H.M.; Sha, W.T.
1993-02-01
The COMMIX-PPC computer pregrain is an extended and improved version of earlier COMMIX codes and is specifically designed for evaluating the thermal performance of power plant condensers. The COMMIX codes are general-purpose computer programs for the analysis of fluid flow and heat transfer in complex Industrial systems. In COMMIX-PPC, two major features have been added to previously published COMMIX codes. One feature is the incorporation of one-dimensional equations of conservation of mass, momentum, and energy on the tube stile and the proper accounting for the thermal interaction between shell and tube side through the porous-medium approach. The other added feature is the extension of the three-dimensional conservation equations for shell-side flow to treat the flow of a multicomponent medium. COMMIX-PPC is designed to perform steady-state and transient. Three-dimensional analysis of fluid flow with heat transfer tn a power plant condenser. However, the code is designed in a generalized fashion so that, with some modification, it can be used to analyze processes in any heat exchanger or other single-phase engineering applications. Volume I (Equations and Numerics) of this report describes in detail the basic equations, formulation, solution procedures, and models for a phenomena. Volume II (User`s Guide and Manual) contains the input instruction, flow charts, sample problems, and descriptions of available options and boundary conditions.
Energy Technology Data Exchange (ETDEWEB)
Bellivier, A.
2004-05-15
For 3D modelling of thermo-aeraulics in building using field codes, it is necessary to reduce the computing time in order to model increasingly larger volumes. The solution suggested in this study is to couple two modelling: a zonal approach and a CFD approach. The first part of the work that was carried out is the setting of a simplified CFD modelling. We propose rules for use of coarse grids, a constant effective viscosity law and adapted coefficients for heat exchange in the framework of building thermo-aeraulics. The second part of this work concerns the creation of fluid Macro-Elements and their coupling with a calculation of CFD finite volume type. Depending on the boundary conditions of the problem, a local description of the driving flow is proposed via the installation and use of semi-empirical evolution laws. The Macro-Elements is then inserted in CFD computation: the values of velocity calculated by the evolution laws are imposed on the CFD cells corresponding to the Macro-Element. We use these two approaches on five cases representative of thermo-aeraulics in buildings. The results are compared with experimental data and with traditional RANS simulations. We highlight the significant gain of time that our approach allows while preserving a good quality of numerical results. (author)
NUMERICAL SIMULATION OF SHOCK WAVE REFRACTION ON INCLINED CONTACT DISCONTINUITY
Directory of Open Access Journals (Sweden)
P. V. Bulat
2016-05-01
Full Text Available We consider numerical simulation of shock wave refraction on plane contact discontinuity, separating two gases with different density. Discretization of Euler equations is based on finite volume method and WENO finite difference schemes, implemented on unstructured meshes. Integration over time is performed with the use of the third-order Runge–Kutta stepping procedure. The procedure of identification and classification of gas dynamic discontinuities based on conditions of dynamic consistency and image processing methods is applied to visualize and interpret the results of numerical calculations. The flow structure and its quantitative characteristics are defined. The results of numerical and experimental visualization (shadowgraphs, schlieren images, and interferograms are compared.
Explicit and implicit finite difference schemes for fractional Cattaneo equation
Ghazizadeh, H. R.; Maerefat, M.; Azimi, A.
2010-09-01
In this paper, the numerical solution of fractional (non-integer)-order Cattaneo equation for describing anomalous diffusion has been investigated. Two finite difference schemes namely an explicit predictor-corrector and totally implicit schemes have been developed. In developing each scheme, a separate formulation approach for the governing equations has been considered. The explicit predictor-corrector scheme is the fractional generalization of well-known MacCormack scheme and has been called Generalized MacCormack scheme. This scheme solves two coupled low-order equations and simultaneously computes the flux term with the main variable. Fully implicit scheme however solves a single high-order undecomposed equation. For Generalized MacCormack scheme, stability analysis has been studied through Fourier method. Through a numerical test, the experimental order of convergency of both schemes has been found. Then, the domain of applicability and some numerical properties of each scheme have been discussed.
WENO SCHEMES FOR SOLUTION OF UNSTEADY ONE-DIMENSIONAL GAS DYNAMICS TEST PROBLEMS
Directory of Open Access Journals (Sweden)
P. V. Bulat
2016-01-01
Full Text Available Creation of test solutions is an essential element in the general design contents for numerical methods aimed at integration of Euler equations. We consider numerical solution of Euler equations describing flows of inviscid compressible gas and allowing continuous and discontinuous solutions. Discretization of Euler equations is based on finite volume method and WENO finite difference schemes. The numerical solutions computed are compared with the exact solutions of Riemann problem. Monotonic correction of derivatives makes it possible to avoid new extremes and ensures monotonicity of the numerical solution near the discontinuity, but it leads to the smoothness of the existing minimums and maximums and to the loss of accuracy. Calculations with the use of WENO schemes allow obtaining accurate and monotonic solution with the presence of both weak and strong gas dynamical discontinuities.
Institute of Scientific and Technical Information of China (English)
蔡丽婧
2015-01-01
The analysis of flow pattern and flow velocity is the essential prerequisite of the diversion dike design. In this paper, the numerical simulation is used as tools to design the diversion dike reinforcement scheme, a comparative analysis has been made and a reasonable diversion dike structure and length has been preferred. This paper can provide a theoreti-cal reference for the engineering design.%流态和流速分析是导流堤设计的先决问题。以某沿海水利枢纽导流堤为研究对象，采用有限元数值模拟的手段及平面二维水流数学模型，对其加长加固方案进行对比分析，优选出合理的导流堤结构型式和长度，为工程设计提供理论参考。
Simplification of the unified gas kinetic scheme
Chen, Songze; Guo, Zhaoli; Xu, Kun
2016-08-01
The unified gas kinetic scheme (UGKS) is an asymptotic preserving (AP) scheme for kinetic equations. It is superior for transition flow simulation and has been validated in the past years. However, compared to the well-known discrete ordinate method (DOM), which is a classical numerical method solving the kinetic equations, the UGKS needs more computational resources. In this study, we propose a simplification of the unified gas kinetic scheme. It allows almost identical numerical cost as the DOM, but predicts numerical results as accurate as the UGKS. In the simplified scheme, the numerical flux for the velocity distribution function and the numerical flux for the macroscopic conservative quantities are evaluated separately. The equilibrium part of the UGKS flux is calculated by analytical solution instead of the numerical quadrature in velocity space. The simplification is equivalent to a flux hybridization of the gas kinetic scheme for the Navier-Stokes (NS) equations and the conventional discrete ordinate method. Several simplification strategies are tested, through which we can identify the key ingredient of the Navier-Stokes asymptotic preserving property. Numerical tests show that, as long as the collision effect is built into the macroscopic numerical flux, the numerical scheme is Navier-Stokes asymptotic preserving, regardless the accuracy of the microscopic numerical flux for the velocity distribution function.
WEIGHTED COMPACT SCHEME FOR SHOCK CAPTURING
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A new class of finite difference schemes--the weighted compact schemes are proposed. According to the idea of the WENO schemes, the weighted compact scheme is constructed by a combination of the approximations of derivatives on candidate stencils with properly assigned weights so that the non-oscillatory property is achieved when discontinuities appear. The primitive function reconstruction method of ENO schemes is applied to obtain the conservative form of the weighted compact scheme. This new scheme not only preserves the characteristic of standard compact schemes and achieves high order accuracy and high resolution using a compact stencil,but also can accurately capture shock waves and discontinuities without oscillation, Numerical examples show that the new scheme is very promising and successful.``
Brezinski, C
2012-01-01
Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.html<
Energy Technology Data Exchange (ETDEWEB)
Abu Saleem, Rabie A., E-mail: raabusaleem@just.edu.jo [Nuclear Engineering Department, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110 (Jordan); Kozlowski, Tomasz, E-mail: txk@illinois.edu [Department of Nuclear, Plasma and Radiological Engineering, University of Illinois at Urbana-Champaign, 216 Talbot Laboratory, 104 S. Wright St., Urbana, IL 61801 (United States); Shrestha, Rijan, E-mail: rijan.shrestha@intel.com [Portland Technology Development, Intel Corporation, 2501 NW 229th Ave Hillsboro OR 97124 (United States)
2016-05-15
Highlights: • The two-fluid model and the challenges associated with its numerical modeling are investigated. • A high-order solver based on flux limiter schemes and the theta method was developed. • The solver was compared to existing thermal hydraulics codes used in nuclear industry. • The solver was shown to handle fast transients with discontinuities and phase change. - Abstract: Finite volume techniques with staggered mesh are used to develop a new numerical solver for the one-dimensional two-phase two-fluid model using a high-resolution, Total Variation Diminishing (TVD) scheme. The solver is implemented to analyze numerical benchmark problems for verification and testing its abilities to handle discontinuities and fast transients with phase change. Convergence rates are investigated by comparing numerical results to analytical solutions available in literature for the case of the faucet flow problem. The solver based on a new TVD scheme is shown to exhibit higher-order of accuracy compared to other numerical schemes. Mass errors are also examined when phase change occurs for the shock tube problem, and compared to those of the 1st-order upwind scheme implemented in the nuclear thermal-hydraulics code TRACE. The solver is shown to exhibit numerical stability when applied to problems with discontinuous solutions and results of the new solver are free of spurious oscillations.
Constructing of constraint preserving scheme for Einstein equations
Tsuchiya, Takuya
2016-01-01
We propose a new numerical scheme of evolution for the Einstein equations using the discrete variational derivative method (DVDM). We derive the discrete evolution equation of the constraint using this scheme and show the constraint preserves in the discrete level. In addition, to confirm the numerical stability using this scheme, we perform some numerical simulations by discretized equations with the Crank-Nicolson scheme and with the new scheme, and we find that the new discretized equations have better stability than that of the Crank-Nicolson scheme.
Discrete unified gas kinetic scheme for all Knudsen number flows: low-speed isothermal case.
Guo, Zhaoli; Xu, Kun; Wang, Ruijie
2013-09-01
Based on the Boltzmann-BGK (Bhatnagar-Gross-Krook) equation, in this paper a discrete unified gas kinetic scheme (DUGKS) is developed for low-speed isothermal flows. The DUGKS is a finite-volume scheme with the discretization of particle velocity space. After the introduction of two auxiliary distribution functions with the inclusion of collision effect, the DUGKS becomes a fully explicit scheme for the update of distribution function. Furthermore, the scheme is an asymptotic preserving method, where the time step is only determined by the Courant-Friedricks-Lewy condition in the continuum limit. Numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current DUGKS. The comparison between the DUGKS and the well-defined lattice Boltzmann equation method (D2Q9) is presented as well.
Zhang, Xiangxiong
2017-01-01
We construct a local Lax-Friedrichs type positivity-preserving flux for compressible Navier-Stokes equations, which can be easily extended to multiple dimensions for generic forms of equations of state, shear stress tensor and heat flux. With this positivity-preserving flux, any finite volume type schemes including discontinuous Galerkin (DG) schemes with strong stability preserving Runge-Kutta time discretizations satisfy a weak positivity property. With a simple and efficient positivity-preserving limiter, high order explicit Runge-Kutta DG schemes are rendered preserving the positivity of density and internal energy without losing local conservation or high order accuracy. Numerical tests suggest that the positivity-preserving flux and the positivity-preserving limiter do not induce excessive artificial viscosity, and the high order positivity-preserving DG schemes without other limiters can produce satisfying non-oscillatory solutions when the nonlinear diffusion in compressible Navier-Stokes equations is accurately resolved.
A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation
Energy Technology Data Exchange (ETDEWEB)
Banks, J W; Hittinger, J A
2009-11-24
Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.
Institute of Scientific and Technical Information of China (English)
高伟; 耿建华
2013-01-01
介绍一种基于离散粒子理论地震波传播数值模拟的网格剖分计算方法.根据离散粒子理论,将研究区域划分为由一系列相互作用的粒子组成的正六边形网格,这些粒子在它们的接触点处发生相互作用,并用Hooke定律和Newton定律描述.为解决六边形网格带来的网格交错而难以计算以及波场输出问题,将横向网格进行加密,加密处赋予假想的粒子,输出波场时选取偶数行偶数列点或奇数行奇数列点的波场值.均匀介质和层状介质模型的数值模拟结果表明,该网格剖分计算方法能够将离散粒子理论用于模拟弹性波在非均匀各向同性介质中地震波的传播.%A mesh generation calculation method based on discrete particle scheme for numerical modeling seismic waves is presented.According to the discrete particle theory,the study area can be divided into regular hexagon grid composed of a series of interacting particles.These particles interact at their contact points and the motion of particles in space is described by Hook's Law and Newton's Law.To solve the problem of the grid crisscross brought by hexagon grids which may lead to difficulty in calculation and output wave field's value,we encrypt the imaginary particles at the horizontal grids and output the wave field value of the even lines＇ points in the even column or odd lines＇ points in odd column.The numerical simulation results of homogeneous model and layer model proved that this mesh generation calculation method based on discrete particle theory is capable of modeling the propagation of elastic waves through heterogeneous isotropic media.
A cell-centered lagrangian scheme in two-dimensional cylindrical geometry
Institute of Scientific and Technical Information of China (English)
2008-01-01
A new Lagrangian cell-centered scheme for two-dimensional compressible flows in planar geometry is proposed by Maire et al.The main new feature of the algorithm is that the vertex velocities and the numerical fluxes through the cell interfaces are all evaluated in a coherent manner contrary to standard approaches.In this paper the method introduced by Maire et al.is extended for the equations of Lagrangian gas dynamics in cylindrical symmetry.Two different schemes are proposed,whose difference is that one uses volume weighting and the other area weighting in the discretization of the momentum equation.In the both schemes the conservation of total energy is ensured,and the nodal solver is adopted which has the same formulation as that in Cartesian coordinates.The volume weighting scheme preserves the momentum conservation and the area-weighting scheme preserves spherical symmetry.The numerical examples demonstrate our theoretical considerations and the robustness of the new method.
Numerical modeling of shallow flows including bottom topography and friction effects
Lukácová-Medvid'ová, Maria
2004-01-01
The aim of the paper is numerical modeling of the shallow water equation with source terms by genuinely multdimensional finite volume evolution Galerkin schemes. The shallow water system, or its one-dimensional analogy the Saint-Venant equation, is used extensively for numerical simulation of natural rivers. Mathematically the shallow water system belongs to the class of balance laws. A special treatment of the source terms describing the bottom topography as well as frictions effects is nece...
Good governance for pension schemes
Thornton, Paul
2011-01-01
Regulatory and market developments have transformed the way in which UK private sector pension schemes operate. This has increased demands on trustees and advisors and the trusteeship governance model must evolve in order to remain fit for purpose. This volume brings together leading practitioners to provide an overview of what today constitutes good governance for pension schemes, from both a legal and a practical perspective. It provides the reader with an appreciation of the distinctive characteristics of UK occupational pension schemes, how they sit within the capital markets and their social and fiduciary responsibilities. Providing a holistic analysis of pension risk, both from the trustee and the corporate perspective, the essays cover the crucial role of the employer covenant, financing and investment risk, developments in longevity risk hedging and insurance de-risking, and best practice scheme administration.
Modification of QUICK scheme by skew points
Energy Technology Data Exchange (ETDEWEB)
Mirzaei, M.; Mohammadi, R.; Malekzadeh, M. [K.N. Toosi Univ. of Technology, Aerospace Engineering Dept., Tehran (Iran, Islamic Republic of)]. E-mail: Mirzaei@kntu.ac.ir
2005-07-01
This paper presents a new method for convective flux approximation based on inclusions of skew points. The scheme uses the truncated terms of QUICK scheme and with the aid of an equation extracted from momentum equations, the skew points will appear in the convective flux formula. The results show that the presented scheme has better accuracy than the other schemes. Diffusion fluxes are approximated using power law scheme and for evaluation of the performance of the presented method several test cases were carried out and the results are compared with the results of other numerical works and experimental data. (author)
Numerical Modeling of Ablation Heat Transfer
Ewing, Mark E.; Laker, Travis S.; Walker, David T.
2013-01-01
A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.
7th International Conference on Hyperbolic Problems Theory, Numerics, Applications
Jeltsch, Rolf
1999-01-01
These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phe...
Subramanian, S. V.; Bozzola, R.
1987-01-01
Numerical solutions of the unsteady Euler equations are obtained using the classical fourth order Runge Kutta time marching scheme. This method is fully explicit and is applied to the governing equations in the finite volume, conservation law form. In order to determine the efficiency of this scheme for solving turbomachinery flows, steady blade-to-blade solutions are obtained for compressor and turbine cascades under subsonic and transonic flow conditions. Computed results are compared with other numerical methods and wind tunnel measurements. The study also focuses on other important numerical aspects influencing the performance of the algorithm and the solution accuracy such as grid types, boundary conditions and artificial viscosity. For this purpose, H, O, and C type computational grids as well as characteristic and extrapolation type boundary conditions are included in solution procedures.
Subramanian, S. V.; Bozzola, R.
1985-01-01
Numerical solutions of the unsteady Euler equations are obtained using the classical fourth order Runge Kutta time marching scheme. This method is fully explicit and is applied to the governing equations in the finite volume, conservation law form. In order to determine the efficiency of this scheme for solving turbomachinery flows, steady blade-to-blade solutions are obtained for compressor and turbine cascades under subsonic and transonic flow conditions. Computed results are compared with other numerical methods and wind tunnel measurements. The present study also focuses on other important numerical aspects influencing the performance of the algorithm and the solution accuracy such as grid types, boundary conditions, and artificial viscosity. For this purpose, H, O, and C type computational grids as well as characteristic and extrapolation type boundary conditions are included in the solution procedure.
Development and Comparison of Numerical Fluxes for LWDG Methods
Institute of Scientific and Technical Information of China (English)
Jianxian Qiu
2008-01-01
The discontinuous Galerkin (DG) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The Lax-Wendroff time discretization procedure is an alternative method for time discretization to the popular total variation diminishing (TVD) Runge-Kutta time discretizations. In this paper, we develop fluxes for the method of DG with Lax-Wendroff time discretization procedure (LWDG) based on different numerical fluxes for finite volume or finite difference schemes, including the first-order monotone fluxes such as the Lax-Friedrichs flux, Godunov flux, the Engquist-Osher flux etc. And the second-order TVD fluxes. We systematically investigate the performance of the LWDG methods based on these differ-ent numerical fluxes for convection terms with the objective of obtaining better perfor-mance by choosing suitable numerical fluxes. The detailed numerical study is mainly performed for the one-dimensional system case, addressing the issues of CPU cost, ac-curacy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two dimensional systems.
Central upwind scheme for a compressible two-phase flow model.
Directory of Open Access Journals (Sweden)
Munshoor Ahmed
Full Text Available In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.
Upscaling scheme for long-term ion diffusion in charged porous media
Yang, Yuankai; Wang, Moran
2017-08-01
Description of long-term (over years) ion diffusion at the pore scale is a huge challenge since the characteristic time of diffusion in a typical representative elementary volume is around microseconds, generally ten orders of magnitude lower than the time we were concerned with. This paper presents a numerical upscaling scheme for ion diffusion with electrical double-layer effects (electrodiffusion) considered in charged porous media. After a scaling analysis for the nondimensional governing equations of ion transport at the pore scale, we identify the conditions for decoupling of electrical effect and diffusion, and therefore are able to choose apposite temporal and spatial scales for corresponding directions of the electrodiffusion process. The upscaling scheme is therefore proposed based on a numerical framework for governing equations using a lattice Boltzmann method. The electrical potential or concentration profiles from steady- or unsteady-state electrodiffusion in the long, straight channel, calculated by this upscaling scheme, are compared with the well-meshed full-sized simulations with good agreement. Furthermore, this scheme is used to predict tracer-ion throughdiffusion and outdiffusion in hardened cement pastes. All numerical results show good agreement with the full-sized simulations or experiment data without any fitting parameters. This upscaling scheme bridges the ion diffusion behaviors in different time scales, and may help to improve the understanding of long-term ion transport mechanisms in charged porous media.
White, Jeffrey A.; Baurle, Robert A.; Fisher, Travis C.; Quinlan, Jesse R.; Black, William S.
2012-01-01
The 2nd-order upwind inviscid flux scheme implemented in the multi-block, structured grid, cell centered, finite volume, high-speed reacting flow code VULCAN has been modified to reduce numerical dissipation. This modification was motivated by the desire to improve the codes ability to perform large eddy simulations. The reduction in dissipation was accomplished through a hybridization of non-dissipative and dissipative discontinuity-capturing advection schemes that reduces numerical dissipation while maintaining the ability to capture shocks. A methodology for constructing hybrid-advection schemes that blends nondissipative fluxes consisting of linear combinations of divergence and product rule forms discretized using 4th-order symmetric operators, with dissipative, 3rd or 4th-order reconstruction based upwind flux schemes was developed and implemented. A series of benchmark problems with increasing spatial and fluid dynamical complexity were utilized to examine the ability of the candidate schemes to resolve and propagate structures typical of turbulent flow, their discontinuity capturing capability and their robustness. A realistic geometry typical of a high-speed propulsion system flowpath was computed using the most promising of the examined schemes and was compared with available experimental data to demonstrate simulation fidelity.
Finite volume hydromechanical simulation in porous media.
Nordbotten, Jan Martin
2014-05-01
Cell-centered finite volume methods are prevailing in numerical simulation of flow in porous media. However, due to the lack of cell-centered finite volume methods for mechanics, coupled flow and deformation is usually treated either by coupled finite-volume-finite element discretizations, or within a finite element setting. The former approach is unfavorable as it introduces two separate grid structures, while the latter approach loses the advantages of finite volume methods for the flow equation. Recently, we proposed a cell-centered finite volume method for elasticity. Herein, we explore the applicability of this novel method to provide a compatible finite volume discretization for coupled hydromechanic flows in porous media. We detail in particular the issue of coupling terms, and show how this is naturally handled. Furthermore, we observe how the cell-centered finite volume framework naturally allows for modeling fractured and fracturing porous media through internal boundary conditions. We support the discussion with a set of numerical examples: the convergence properties of the coupled scheme are first investigated; second, we illustrate the practical applicability of the method both for fractured and heterogeneous media.
Numerical study on multiphase flows induced by wall adhesion
Energy Technology Data Exchange (ETDEWEB)
Myong, Hyon Kook [Kookmin Univ., Seoul (Korea, Republic of)
2012-07-15
The present paper presents a numerical study on multiphase flows induced by wall adhesion. The continuum surface force (CSF) model with the wall adhesion boundary condition model is used for calculating the surface tension force; this model is implemented in an in house solution code (PowerCFD). The present method (code) employs an unstructured cell centered method based on a conservative pressure based finite volume method with a volume capturing method (CICSAM) in a volume of fluid (VOF) scheme for phase interface capturing. The effects of wall adhesion are then numerically simulated by using the present method for a shallow pool of water located at the bottom of a cylindrical tank with no external forces such as gravity. Two different cases are computed, one it which the water wets the wall and one in which the water does not wet the wall. It is found that the present method efficiently simulates the surface tension dominant multiphase flows induced by wall adhesion.
Directory of Open Access Journals (Sweden)
P. V. Bulat
2015-07-01
Full Text Available One-dimensional unsteady gas dynamics problems are revealing tests for the accuracy estimation of numerical solution with respect to simulation of supersonic flows of inviscid compressible gas. Numerical solution of Euler equations describing flows of inviscid compressible gas and conceding continuous and discontinuous solutions is considered. Discretization of Euler equations is based on finite volume method and WENO finite difference schemes. The numerical solutions computed are compared with the exact solution of Riemann problem. Monotonic correction of derivatives makes possible avoiding new extremes and ensures monotonicity of the numerical solution near the discontinuity, but it leads to the smoothness of the existing minimums and maximums and to the accuracy loss. Calculations with the use of WENO schemes give the possibility for obtaining accurate and monotonic solution with the presence of weak and strong gas dynamical discontinuities.
High-Order Energy Stable WENO Schemes
Yamaleev, Nail K.; Carpenter, Mark H.
2008-01-01
A new third-order Energy Stable Weighted Essentially NonOscillatory (ESWENO) finite difference scheme for scalar and vector linear hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. A rigorous truncation error analysis is presented showing that the accuracy of the 3rd-order ESWENO scheme is drastically improved if the tuning parameters of the weight functions satisfy certain criteria. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO finite difference scheme of Jiang and Shu in terms of accuracy, while providing essentially nonoscillatory solutions near strong discontinuities.
Gassner, Gregor J.; Winters, Andrew R.; Kopriva, David A.
2016-12-01
Fisher and Carpenter (2013) [12] found a remarkable equivalence of general diagonal norm high-order summation-by-parts operators to a subcell based high-order finite volume formulation. This equivalence enables the construction of provably entropy stable schemes by a specific choice of the subcell finite volume flux. We show that besides the construction of entropy stable high-order schemes, a careful choice of subcell finite volume fluxes generates split formulations of quadratic or cubic terms. Thus, by changing the subcell finite volume flux to a specific choice, we are able to generate, in a systematic way, all common split forms of the compressible Euler advection terms, such as the Ducros splitting and the Kennedy and Gruber splitting. Although these split forms are not entropy stable, we present a systematic way to prove which of those split forms are at least kinetic energy preserving. With this, we construct a unified high-order split form DG framework. We investigate with three dimensional numerical simulations of the inviscid Taylor-Green vortex and show that the new split forms enhance the robustness of high-order simulations in comparison to the standard scheme when solving turbulent vortex dominated flows. In fact, we show that for certain test cases, the novel split form discontinuous Galerkin schemes are more robust than the discontinuous Galerkin scheme with over-integration.
Electrical Injection Schemes for Nanolasers
DEFF Research Database (Denmark)
Lupi, Alexandra; Chung, Il-Sug; Yvind, Kresten
2014-01-01
Three electrical injection schemes based on recently demonstrated electrically pumped photonic crystal nanolasers have been numerically investigated: 1) a vertical p-i-n junction through a post structure; 2) a lateral p-i-n junction with a homostructure; and 3) a lateral p-i-n junction....... For this analysis, the properties of different schemes, i.e., electrical resistance, threshold voltage, threshold current, and internal efficiency as energy requirements for optical interconnects are compared and the physics behind the differences is discussed....
Institute of Scientific and Technical Information of China (English)
Wei-zhong Dai; Raja Nassar
2000-01-01
A finite difference scheme for the generalized nonlinear Schrodinger equation with variable coefficients is developed. The scheme is shown to satisfy two conser vation laws. Numerical results show that the scheme is accurate and efficient.
Institute of Scientific and Technical Information of China (English)
罗蒋梅; 潘静; 杨支中
2011-01-01
To compare the effects of different sea surface wind stress drag coefficient parameterization schemes,nine kinds of schemes were used in numerical simulation of fifteen storm surges induced by tropical cyclones near Zhanjiang Sea. The result indicates that the effects of numerical simulation are not completely same in different parameterization schemes and it is necessary that the proper scheme is selected in numerical simulating storm surge. The simulation errors of storm surge maximum are smaller in Sm80 and YT98 schemes, and it also indicates it is feasible to extraplant in high wind speed of tropical cyclone in the two schemes. Additionally, under the conditions of selecting proper parameterization schemes of sea surface wind stress drag coefficient, the simulating effect of stronger storm surges are better in using the storm surge model.%为了比较不同的海面风应力拖曳系数参数化方案在风暴潮数值模拟中的效果,采用9种不同的风应力拖曳系数参数化方案对湛江附近海域15个热带气旋风暴潮进行数值模拟.模拟结果表明,不同风应力拖曳系数参数化方案对热带气旋风暴潮增水最大值的数值模拟效果不完全相同,在风暴潮数值模拟中要选择合适的风应力拖曳系数参数化方案;文中Smith(1980)、Yelland和Taylor(1998)风应力拖曳系数参数化方案增水最大值模拟的误差较小,这也说明两种参数化方案在风暴潮数值模拟中外推到热带气旋高风速范围内是可行的.另外,数值模拟结果也表明,在选择合适海面风应力参数化方案情况下,文中采用的风暴潮模式对强热带气旋增水的数值模拟效果较好.
A semi-Lagrangian gas-kinetic scheme for smooth flows
Wang, Peng
2014-01-01
In this paper, a semi-Lagrangian gas-kinetic scheme is developed for smooth flows based on the Bhatnagar-Gross-Krook (BGK) equation. As a finite-volume scheme, the evolution of the average flow variables in a control volume is under the Eulerian framework, whereas the construction of the numerical flux across the cell interface comes from the Lagrangian perspective. The adoption of the Lagrangian aspect makes the collision and the transport mechanisms intrinsically coupled together in the flux evaluation. As a result, the time step is independent of the particle collision time and solely determined by the Courant-Friedrichs-Lewy (CFL) conditions. A set of simulations are carried out to validate the performance of the new scheme. The results show that with second-order spatial accuracy, the scheme exhibits low numerical dissipation, and can accurately capture the Navier-Stokers solutions for the smooth flows with viscous heat dissipation from the low-speed incompressible to hypersonic compressible regimes.
Institute of Scientific and Technical Information of China (English)
高文华; 赵凤生; 胡志晋; 周青
2012-01-01
本文在中国气象科学研究院(CAMS)双参数云微物理方案的基础上,增加气溶胶粒子的活化过程,改进原方案中的水汽混合比、云水混合比及云滴数浓度的预报方程,实现对各种水成物(包括云水)的混合比和数浓度的预报.此外,改进后的CAMS云方案被成功耦合到了WRF v3.1中尺度模式,本文利用耦合模式对2009年4月23～24日发生在我国北方地区的一次降水天气过程进行了模拟,将新方案的模拟结果与WRF自带的3个微物理方案进行了比较.结果显示,新方案能够合理地描述地面降水特征,其模拟的雨带分布范围与实测接近,降水中心的强度和位置优于其他3个方案.新方案模拟的云滴数浓度与WDM6方案基本一致,表明加入的气溶胶活化过程是合理的.新方案模拟的其他水成物粒子数浓度与Morrison方案相比有时会有量级的差别,说明粒子数浓度的模拟目前还存在着很大的不确定性,这也是云微物理模式进一步发展的难点.%The Chinese Academy of Meteorological Sciences (CAMS) two-moment bulk microphysics scheme was employed in this study, and a new parameterization approach to simulate the heterogeneous droplet activation was introduced into the scheme. The proposed scheme predicts both the mixing ratio and the number concentration for five hydrometeor species (cloud water, rain, cloud ice, snow, and graupel). Moreover, the improved CAMS scheme was coupled with the Weather Research and Forecasting model (WRF v3. 1), which makes it possible to investigate the effects of aerosol on clouds and precipitation. The rain event occurring on 23~ 24 April 2009 in north China was simulated using the coupled CAMS scheme and threesophisticated microphysics schemes in the WRF model. Results showed that the new scheme performed reasonably well in describing the characteristic of precipitation and the microphysics structure of cloud. The spatial pattern of precipitation, the
Engwirda, Darren; Marshall, John
2016-01-01
The development of a set of high-order accurate finite-volume formulations for evaluation of the pressure gradient force in layered ocean models is described. A pair of new schemes are presented, both based on an integration of the contact pressure force about the perimeter of an associated momentum control-volume. The two proposed methods differ in their choice of control-volume geometries. High-order accurate numerical integration techniques are employed in both schemes to account for non-linearities in the underlying equation-of-state definitions and thermodynamic profiles, and details of an associated vertical interpolation and quadrature scheme are discussed in detail. Numerical experiments are used to confirm the consistency of the two formulations, and it is demonstrated that the new methods maintain hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer-wise geometry, non-linear equation-of-state definitions and non-uniform vertical stratification profiles. Additionally, one...
Hybrid scheme for Brownian semistationary processes
DEFF Research Database (Denmark)
Bennedsen, Mikkel; Lunde, Asger; Pakkanen, Mikko S.
the asymptotics of the mean square error of the hybrid scheme and we observe that the scheme leads to a substantial improvement of accuracy compared to the ordinary forward Riemann-sum scheme, while having the same computational complexity. We exemplify the use of the hybrid scheme by two numerical experiments......, where we examine the finite-sample properties of an estimator of the roughness parameter of a Brownian semistationary process and study Monte Carlo option pricing in the rough Bergomi model of Bayer et al. (2015), respectively....
Yamaleev, Nail K.; Carpenter, Mark H.
2017-02-01
High-order numerical methods that satisfy a discrete analog of the entropy inequality are uncommon. Indeed, no proofs of nonlinear entropy stability currently exist for high-order weighted essentially nonoscillatory (WENO) finite volume or weak-form finite element methods. Herein, a new family of fourth-order WENO spectral collocation schemes is developed, that are nonlinearly entropy stable for the one-dimensional compressible Navier-Stokes equations. Individual spectral elements are coupled using penalty type interface conditions. The resulting entropy stable WENO spectral collocation scheme achieves design order accuracy, maintains the WENO stencil biasing properties across element interfaces, and satisfies the summation-by-parts (SBP) operator convention, thereby ensuring nonlinear entropy stability in a diagonal norm. Numerical results demonstrating accuracy and nonoscillatory properties of the new scheme are presented for the one-dimensional Euler and Navier-Stokes equations for both continuous and discontinuous compressible flows.
Implementation of the high-order schemes QUICK and LECUSSO in the COMMIX-1C Program
Energy Technology Data Exchange (ETDEWEB)
Sakai, K.; Sun, J.G.; Sha, W.T. [Argonne National Lab., IL (United States). Energy Technology Div.
1995-08-01
Multidimensional analysis computer programs based on the finite volume method, such as COMMIX-1C, have been commonly used to simulate thermal-hydraulic phenomena in engineering systems such as nuclear reactors. In COMMIX-1C, the first-order schemes with respect to both space and time are used. In many situations such as flow recirculations and stratifications with steep gradient of velocity and temperature fields, however, high-order difference schemes are necessary for an accurate prediction of the fields. For these reasons, two second-order finite difference numerical schemes, QUICK (Quadratic Upstream Interpolation for Convective Kinematics) and LECUSSO (Local Exact Consistent Upwind Scheme of Second Order), have been implemented in the COMMIX-1C computer code. The formulations were derived for general three-dimensional flows with nonuniform grid sizes. Numerical oscillation analyses for QUICK and LECUSSO were performed. To damp the unphysical oscillations which occur in calculations with high-order schemes at high mesh Reynolds numbers, a new FRAM (Filtering Remedy and Methodology) scheme was developed and implemented. To be consistent with the high-order schemes, the pressure equation and the boundary conditions for all the conservation equations were also modified to be of second order. The new capabilities in the code are listed. Test calculations were performed to validate the implementation of the high-order schemes. They include the test of the one-dimensional nonlinear Burgers equation, two-dimensional scalar transport in two impinging streams, von Karmann vortex shedding, shear driven cavity flow, Couette flow, and circular pipe flow. The calculated results were compared with available data; the agreement is good.
Shen, Hua
2016-10-19
A maximum-principle-satisfying space-time conservation element and solution element (CE/SE) scheme is constructed to solve a reduced five-equation model coupled with the stiffened equation of state for compressible multifluids. We first derive a sufficient condition for CE/SE schemes to satisfy maximum-principle when solving a general conservation law. And then we introduce a slope limiter to ensure the sufficient condition which is applicative for both central and upwind CE/SE schemes. Finally, we implement the upwind maximum-principle-satisfying CE/SE scheme to solve the volume-fraction-based five-equation model for compressible multifluids. Several numerical examples are carried out to carefully examine the accuracy, efficiency, conservativeness and maximum-principle-satisfying property of the proposed approach.
An hybrid finite volume finite element method for variable density incompressible flows
Calgaro, Caterina; Creusé, Emmanuel; Goudon, Thierry
2008-04-01
This paper is devoted to the numerical simulation of variable density incompressible flows, modeled by the Navier-Stokes system. We introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint. The breakthrough relies on the definition of a suitable footbridge between the two methods, through the design of compatibility condition. In turn, the method is very flexible and allows to deal with unstructured meshes. Several numerical tests are performed to show the scheme capabilities. In particular, the viscous Rayleigh-Taylor instability evolution is carefully investigated.
Dudzinski, M.; Lukáčová-Medvid'ová, M.
2013-02-01
The aim of this paper is to present a new well-balanced finite volume scheme for two-dimensional multilayer shallow water flows including wet/dry fronts. The ideas, presented here for the two-layer model, can be generalized to a multilayer case in a straightforward way. The method developed here is constructed in the framework of the Finite Volume Evolution Galerkin (FVEG) schemes. The FVEG methods couple a finite volume formulation with evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems. However, in the case of multilayer shallow water flows the required eigenstructure of the underlying equations is not readily available. Thus we approximate the evolution operators numerically. This approximation procedure can be used for arbitrary hyperbolic systems. We derive a well-balanced approximation of the evolution operators and prove that the FVEG scheme is well-balanced for the multilayer lake at rest states even in the presence of wet/dry fronts. Several numerical experiments confirm the reliability and efficiency of the new well-balanced FVEG scheme.
On Optimal Designs of Some Censoring Schemes
Directory of Open Access Journals (Sweden)
Dr. Adnan Mohammad Awad
2016-03-01
Full Text Available The main objective of this paper is to explore suitability of some entropy-information measures for introducing a new optimality censoring criterion and to apply it to some censoring schemes from some underlying life-time models. In addition, the paper investigates four related issues namely; the effect of the parameter of parent distribution on optimal scheme, equivalence of schemes based on Shannon and Awad sup-entropy measures, the conjecture that the optimal scheme is one stage scheme, and a conjecture by Cramer and Bagh (2011 about Shannon minimum and maximum schemes when parent distribution is reflected power. Guidelines for designing an optimal censoring plane are reported together with theoretical and numerical results and illustrations.
Finite Volume Evolution Galerkin Methods for Nonlinear Hyperbolic Systems
Lukáčová-Medvid'ová, M.; Saibertová, J.; Warnecke, G.
2002-12-01
We present new truly multidimensional schemes of higher order within the frame- work of finite volume evolution Galerkin (FVEG) methods for systems of nonlinear hyperbolic conservation laws. These methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of the multidimensional hyperbolic system, such that all of the infinitely many directions of wave propagation are taken into account. Following our previous results for the wave equation system, we derive approximate evolution operators for the linearized Euler equations. The integrals along the Mach cone and along the cell interfaces are evaluated exactly, as well as by means of numerical quadratures. The influence of these numerical quadratures will be discussed. Second-order resolution is obtained using a conservative piecewise bilinear recovery and the midpoint rule approximation for time integration. We prove error estimates for the finite volume evolution Galerkin scheme for linear systems with constant coefficients. Several numerical experiments for the nonlinear. Euler equations, which confirm the accuracy and good multidimensional behavior of the FVEG schemes, are presented as well.
Phonon Boltzmann equation-based discrete unified gas kinetic scheme for multiscale heat transfer
Guo, Zhaoli
2016-01-01
Numerical prediction of multiscale heat transfer is a challenging problem due to the wide range of time and length scales involved. In this work a discrete unified gas kinetic scheme (DUGKS) is developed for heat transfer in materials with different acoustic thickness based on the phonon Boltzmann equation. With discrete phonon direction, the Boltzmann equation is discretized with a second-order finite-volume formulation, in which the time-step is fully determined by the Courant-Friedrichs-Lewy (CFL) condition. The scheme has the asymptotic preserving (AP) properties for both diffusive and ballistic regimes, and can present accurate solutions in the whole transition regime as well. The DUGKS is a self-adaptive multiscale method for the capturing of local transport process. Numerical tests for both heat transfers with different Knudsen numbers are presented to validate the current method.
Multiuser switched diversity scheduling schemes
Shaqfeh, Mohammad
2012-09-01
Multiuser switched-diversity scheduling schemes were recently proposed in order to overcome the heavy feedback requirements of conventional opportunistic scheduling schemes by applying a threshold-based, distributed, and ordered scheduling mechanism. The main idea behind these schemes is that slight reduction in the prospected multiuser diversity gains is an acceptable trade-off for great savings in terms of required channel-state-information feedback messages. In this work, we characterize the achievable rate region of multiuser switched diversity systems and compare it with the rate region of full feedback multiuser diversity systems. We propose also a novel proportional fair multiuser switched-based scheduling scheme and we demonstrate that it can be optimized using a practical and distributed method to obtain the feedback thresholds. We finally demonstrate by numerical examples that switched-diversity scheduling schemes operate within 0.3 bits/sec/Hz from the ultimate network capacity of full feedback systems in Rayleigh fading conditions. © 2012 IEEE.
Numerical Modeling of Supercavitating Flows
2001-02-01
scheme was designed in accordance with the numerical stability analysis of Vada and Nakos (1993). A key result of that analysis was the demonstration...Carderock Division, Carderock, MD. Vada, T., and D.E. Nakos (1993) "Time-Marching Schemes for Ship Motion Simulations," 8 th Int’l Workshop on Water Waves
Taxonomic scheme for the identification of marine bacteria
Oliver, James D.
1982-06-01
A recently developed taxonomic scheme for the identification of marine bacteria is presented. The scheme is based on numerous reviews and monographs on marine bacteria, as well as Bergey's Manual of Determinative Bacteriology. While fairly extensive, the scheme is designed to identify marine bacteria using relatively few tests.
Numerical discretization for nonlinear diffusion filter
Mustaffa, I.; Mizuar, I.; Aminuddin, M. M. M.; Dasril, Y.
2015-05-01
Nonlinear diffusion filters are famously used in machine vision for image denoising and restoration. This paper presents a study on the effects of different numerical discretization of nonlinear diffusion filter. Several numerical discretization schemes are presented; namely semi-implicit, AOS, and fully implicit schemes. The results of these schemes are compared by visual results, objective measurement e.g. PSNR and MSE. The results are also compared to a Daubechies wavelet denoising method. It is acknowledged that the two preceding scheme have already been discussed in literature, however comparison to the latter scheme has not been made. The semi-implicit scheme uses an additive operator splitting (AOS) developed to overcome the shortcoming of the explicit scheme i.e., stability for very small time steps. Although AOS has proven to be efficient, from the nonlinear diffusion filter results with different discretization schemes, examples shows that implicit schemes are worth pursuing.
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Lukáčová-Medvid'ová, M.; Noelle, S.; Kraft, M.
2007-01-01
We present a new well-balanced finite volume method within the framework of the finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for the shallow water equations with source terms modelling the bottom topography and Coriolis forces. Results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are taken into account explicitly. We derive a well-balanced approximation of the integral equations and prove that the FVEG scheme is well-balanced for the stationary steady states as well as for the steady jets in the rotational frame. Several numerical experiments for stationary and quasi-stationary states as well as for steady jets confirm the reliability of the well-balanced FVEG scheme.
Fourth order accurate compact scheme with group velocity control (GVC)
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
For solving complex flow field with multi-scale structure higher order accurate schemes are preferred. Among high order schemes the compact schemes have higher resolving efficiency. When the compact and upwind compact schemes are used to solve aerodynamic problems there are numerical oscillations near the shocks. The reason of oscillation production is because of non-uniform group velocity of wave packets in numerical solutions. For improvement of resolution of the shock a parameter function is introduced in compact scheme to control the group velocity. The newly developed method is simple. It has higher accuracy and less stencil of grid points.
Multisymplectic five-point scheme for the nonlinear wave equation
Institute of Scientific and Technical Information of China (English)
WANG Yushun; WANG Bin; YANG Hongwei; WANG Yunfeng
2003-01-01
In this paper, we introduce the multisymplectic structure of the nonlinear wave equation, and prove that the classical five-point scheme for the equation is multisymplectic. Numerical simulations of this multisymplectic scheme on highly oscillatory waves of the nonlinear Klein-Gordon equation and the collisions between kink and anti-kink solitons of the sine-Gordon equation are also provided. The multisymplectic schemes do not need to discrete PDEs in the space first as the symplectic schemes do and preserve not only the geometric structure of the PDEs accurately, but also their first integrals approximately such as the energy, the momentum and so on. Thus the multisymplectic schemes have better numerical stability and long-time numerical behavior than the energy-conserving scheme and the symplectic scheme.
Indian Academy of Sciences (India)
M R Bhajantri; T I Eldho; P B Deolalikar
2006-12-01
Spillway ﬂow, a classical problem of hydraulics, is generally a gravity-driven free surface ﬂow. Spillway ﬂows are essentially rapidly varying ﬂows near the crest with pronounced curvature of the streamlines in the vertical direction. Two processes simultaneously occur in the ﬂow over the crest, that is, formation and gradual thickening of the turbulent boundary layer along the proﬁle, and gradual increase in the velocity and decrease in the depth of main ﬂow. Spillway hydrodynamics can be obtained through physical modelling or numerical modelling. physical modelling of spillways is expensive, cumbersome and time-consuming. The main difﬁculties in solving the spillway problem numerically are: rapidly varying ﬂow, existence of both subcritical and supercritical ﬂows, development of turbulent boundary layers, unknown free surface and air entrainment. Numerical simulation of such ﬂows over spillways in all ﬂow regimes is a challenging task. This paper describes a numerical model and its application to a case study to investigate the hydraulic characteristics of ﬂow over spillway crest proﬁles by simulating the velocity distribution, pressure distribution and discharge characteristics. Results of the numerical modelling are compared with those from the physical modelling and found to be satisfactory.
Institute of Scientific and Technical Information of China (English)
赵明; 曹义华
2011-01-01
A numerical method based on solutions of 3-D Euler/N-S equations is used for calculating the rotor flowfield in hover. Jameson central scheme, Van Leer scheme and AUSM scheme are implemented for spatial discretisation, and Van Albada limiter is also applied. Simultaneously, overset grids are adopted. Hole-Map method is utilized to identify intergrid boundary points (IGBPs). Furthermore, aiming at identification issue of donor elements, Inverse-Map method is implemented. Finally, blade surface pressure distributions derived from numerical simulation are validated compared with the experimental data. Results show that all the schemes mentioned above can accurately simulate the rotor flowfield.%给出了三维Euler/N-S方程数值模拟悬停状态旋翼流场的方法和模型.在空间离散方法上分别采用Jameson中心差分格式、Van Leer矢通量分裂格式、AUSM格式3种方法,同时加入了Van Albada限制器,并应用了嵌套网格方法.文中采用Hole-Map方法来确定洞边界,采用Inverse-Map方法来搜寻贡献单元.最后给出了旋翼桨叶表面压力分布的计算结果,并与实验数据进行了对比,证明以上3种空间离散格式在旋翼流场计算中的准确性.
An efficient explicit marching on in time solver for magnetic field volume integral equation
Sayed, Sadeed Bin
2015-07-25
An efficient explicit marching on in time (MOT) scheme for solving the magnetic field volume integral equation is proposed. The MOT system is cast in the form of an ordinary differential equation and is integrated in time using a PE(CE)m multistep scheme. At each time step, a system with a Gram matrix is solved for the predicted/corrected field expansion coefficients. Depending on the type of spatial testing scheme Gram matrix is sparse or consists of blocks with only diagonal entries regardless of the time step size. Consequently, the resulting MOT scheme is more efficient than its implicit counterparts, which call for inversion of fuller matrix system at lower frequencies. Numerical results, which demonstrate the efficiency, accuracy, and stability of the proposed MOT scheme, are presented.
DEFF Research Database (Denmark)
Larsen, Tine Steen; Nikolopoulos, N.; Nikolopoulos, A.
2011-01-01
anemometers across the openings, whilst the numerical methodology is based on the time-dependant solution of the governing Navier-Stokes equations. The experimental data are compared to the corresponding numerical results, revealing the unsteady character of the flow field especially at large incidence angles......The paper presents an extensive experimental and numerical study on a cross-ventilated building providing important features of the induced flow patterns at the two openings as a function of the free stream wind velocity’s magnitude and its incidence angle. The experimental data are measured via....... Furthermore, additional information regarding the flow field near the opening edges, not easily extracted by experimental methods, provide an in depth sight in the main characteristics of the flow field both at the openings but also inside the building. Finally, a new methodology for the approximation...
Binary Schemes of Vapor Bubble Growth
Zudin, Yu. B.
2015-05-01
A problem on spherically symmetric growth of a vapor bubble in an infi nite volume of a uniformly superheated liquid is considered. A description of the limiting schemes of bubble growth is presented. A binary inertial-thermal bubble growth scheme characterized by such specifi c features as the "three quarters" growth law and the effect of "pressure blocking" in a vapor phase is considered.
Numerical solution of non-isothermal non-adiabatic flow of real gases in pipelines
Bermúdez, Alfredo; López, Xián; Vázquez-Cendón, M. Elena
2016-10-01
A finite volume scheme for the numerical solution of a mathematical model for non-isothermal non-adiabatic compressible flow of a real gas in a pipeline is introduced. In order to make an upwind discretization of the flux, the Q-scheme of van Leer is used. Unlike standard Euler equations, the model takes into account wall friction, variable height and heat transfer between the pipe and the environment. Since all these terms are sources, in order to get a well-balanced scheme they are discretized by making a similar upwinding to the one in the flux term. The performance of the overall method has been shown for some usual numerical tests. The final goal, which is beyond the scope of this paper, is to consider a network including several pipelines connected at junctions, as those employed for natural gas transport.
Two Conservative Difference Schemes for Rosenau-Kawahara Equation
Directory of Open Access Journals (Sweden)
Jinsong Hu
2014-01-01
Full Text Available Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference schemes are of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.
Conservative Linear Difference Scheme for Rosenau-KdV Equation
Directory of Open Access Journals (Sweden)
Jinsong Hu
2013-01-01
Full Text Available A conservative three-level linear finite difference scheme for the numerical solution of the initial-boundary value problem of Rosenau-KdV equation is proposed. The difference scheme simulates two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference scheme is of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.
PERTURBATIONAL FINITE DIFFERENCE SCHEME OF CONVECTION-DIFFUSION EQUATION
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The Perturbational Finite Difference (PFD) method is a kind of high-order-accurate compact difference method, But its idea is different from the normal compact method and the multi-nodes method. This method can get a Perturbational Exact Numerical Solution (PENS) scheme for locally linearlized Convection-Diffusion (CD) equation. The PENS scheme is similar to the Finite Analytical (FA) scheme and Exact Difference Solution (EDS) scheme, which are all exponential schemes, but PENS scheme is simpler and uses only 3, 5 and 7 nodes for 1-, 2- and 3-dimensional problems, respectively. The various approximate schemes of PENS scheme are also called Perturbational-High-order-accurate Difference (PHD) scheme. The PHD schemes can be got by expanding the exponential terms in the PENS scheme into power series of grid Renold number, and they are all upwind schemes and remain the concise structure form of first-order upwind scheme. For 1-dimensional (1-D) CD equation and 2-D incompressible Navier-Stokes equation, their PENS and PHD schemes were constituted in this paper, they all gave highly accurate results for the numerical examples of three 1-D CD equations and an incompressible 2-D flow in a square cavity.
Energy Technology Data Exchange (ETDEWEB)
Ansanay-Alex, G.
2009-06-17
The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)
A simplification of the unified gas kinetic scheme
Chen, Songze; Xu, Kun
2016-01-01
Unified gas kinetic scheme (UGKS) is an asymptotic preserving scheme for the kinetic equations. It is superior for transition flow simulations, and has been validated in the past years. However, compared to the well known discrete ordinate method (DOM) which is a classical numerical method solving the kinetic equations, the UGKS needs more computational resources. In this study, we propose a simplification of the unified gas kinetic scheme. It allows almost identical numerical cost as the DOM, but predicts numerical results as accurate as the UGKS. Based on the observation that the equilibrium part of the UGKS fluxes can be evaluated analytically, the equilibrium part in the UGKS flux is not necessary to be discretized in velocity space. In the simplified scheme, the numerical flux for the velocity distribution function and the numerical flux for the macroscopic conservative quantities are evaluated separately. The simplification is equivalent to a flux hybridization of the gas kinetic scheme for the Navier-S...
Experimental and numerical investigation of the internal kinetics of a surf-zone plunging breaker
DEFF Research Database (Denmark)
Emarat, Narumon; Forehand, David I.M.; Christensen, Erik Damgaard
2012-01-01
Over the last couple of decades both the qualitative and quantitative understanding of breaking waves in the surf zone have greatly increased. This is due to the advances in experimental and numerical techniques. However, few comparisons between these two different investigative techniques...... for surfzone breaking waves have been reported. In this study, a comparison is made between the experimental and numerical investigation of the internal kinematics of a surf-zone plunging breaker. The full-field velocity measuring technique known as Particle Image Velocimetry (PIV) is used in the experiments....... In the hybrid numerical scheme, the main model solves the Navier–Stokes equations using a Finite Volume method and the free-surface is simulated using a Volume of Fluid (VOF) method. An important feature of this work is that, unlike in most other comparisons between numerical and experimental results, the exact...
An interface capturing scheme for modeling atomization in compressible flows
Garrick, Daniel P.; Hagen, Wyatt A.; Regele, Jonathan D.
2017-09-01
The study of atomization in supersonic flow is critical to ensuring reliable ignition of scramjet combustors under startup conditions. Numerical methods incorporating surface tension effects have largely focused on the incompressible regime as most atomization applications occur at low Mach numbers. Simulating surface tension effects in compressible flow requires robust numerical methods that can handle discontinuities caused by both shocks and material interfaces with high density ratios. In this work, a shock and interface capturing scheme is developed that uses the Harten-Lax-van Leer-Contact (HLLC) Riemann solver while a Tangent of Hyperbola for INterface Capturing (THINC) interface reconstruction scheme retains the fluid immiscibility condition in the volume fraction and phasic densities in the context of the five equation model. The approach includes the effects of compressibility, surface tension, and molecular viscosity. One and two-dimensional benchmark problems demonstrate the desirable interface sharpening and conservation properties of the approach. Simulations of secondary atomization of a cylindrical water column after its interaction with a shockwave show good qualitative agreement with experimentally observed behavior. Three-dimensional examples of primary atomization of a liquid jet in a Mach 2 crossflow demonstrate the robustness of the method.
A SUBDIVISION SCHEME FOR VOLUMETRIC MODELS
Institute of Scientific and Technical Information of China (English)
GhulamMustafa; LiuXuefeng
2005-01-01
In this paper, a subdivision scheme which generalizes a surface scheme in previous papers to volume meshes is designed. The scheme exhibits significant control over shrink-age/size of volumetric models. It also has the ability to conveniently incorporate boundaries and creases into a smooth limit shape of models. The method presented here is much simpler and easier as compared to MacCracken and Joy's. This method makes no restrictions on the local topology of meshes. Particularly, it can be applied without any change to meshes of nonmanifold topology.
Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids
Directory of Open Access Journals (Sweden)
Sudi Mungkasi
2016-01-01
Full Text Available This paper presents a numerical entropy production (NEP scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.
Generalized Group Signature Scheme
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The concept of generalized group signature scheme will bepresent. Based on the generalized secret sharing scheme proposed by Lin and Ha rn, a non-interactive approach is designed for realizing such generalized group signature scheme. Using the new scheme, the authorized subsets of the group in w hich the group member can cooperate to produce the valid signature for any messa ge can be randomly specified
Frenod, Emmanuel
2013-01-01
In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.
DEFF Research Database (Denmark)
Nørmark, Kurt
2010-01-01
A Scheme representation of Standard MIDI Files is proposed. The Scheme expressions are defined and constrained by an XML-language, which in the starting point is inspired by a MIDI XML event language made by the MIDI Manufactures Association. The representation of Standard MIDI Files in Scheme ma...
DEFF Research Database (Denmark)
Nørmark, Kurt
2010-01-01
A Scheme representation of Standard MIDI Files is proposed. The Scheme expressions are defined and constrained by an XML-language, which in the starting point is inspired by a MIDI XML event language made by the MIDI Manufactures Association. The representation of Standard MIDI Files in Scheme ma...
GROUP VELOCITY CONTROL SCHEME WITH LOW DISSIPATION
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In order to prevent smearing the discontinuity, a modified term is added to the third order Upwind Compact Difference scheme to lower the dissipation error. Moreover, the dispersion error is controled to hold back the non-physical oscillation by means of the group velocity control. The scheme is used to simulate the interactions of shock-density stratified interface and the disturbed interface developing to vortex rollers. Numerical results are satisfactory.
Improvement of Mixing Function for Modified Upwinding Compact Scheme
Fu, Huankun; Liu, Chaoqun
2014-01-01
The compact scheme has high order accuracy and high resolution, but cannot be used to capture the shock. WENO is a great scheme for shock capturing, but is too dissipative for turbulence and small length scales. We developed a modified upwinding compact scheme which uses an effective shock detector to block compact scheme to cross the shock and a control function to mix the flux with WENO scheme near the shock. The new scheme makes the original compact scheme able to capture the shock sharply and, more important, keep high order accuracy and high resolution in the smooth area, which is particularly important for shock boundary layer and shock acoustic interactions. This work is a continuation to modify the control function for the modified up-winding compact scheme (MUCS). Numerical results show the scheme is successful for 2-D Euler.
Rompas, P. T. D.; Taunaumang, H.; Sangari, F. J.
2017-03-01
One of equipment as prime movers in the marine current power plant is turbine. Marine current turbines require a data of marine currents velocity in its design. The objective of this study was to get the velocities distribution of marine currents in the Bangka strait. The method used survey, observation, and measurement in the Bangka strait. The data of seawater density conducted measurement in the Bangka strait. The data of width and depth of the strait collected from the map of Bangka strait and its depth of the sea. Problem solving of the study used a numerical model. The velocities distribution of marine current obtained from a numerical model in the form of numerical program. The results showed that the velocities distribution at seawater column when low and high tide currents which the maximum happened at 0.1 Sv were 0-0.9 and 0-1.0 m/s respectively, while at 0.3 Sv were 0-2.7 and 0-3.0 m/s respectively. The results will be a product in analyzing the potential kinetic energy that used to design profile of the turbines as prime mover for marine currents power plant in the Bangka strait, North Sulawesi, Indonesia.
Testing hydrodynamics schemes in galaxy disc simulations
Few, C. G.; Dobbs, C.; Pettitt, A.; Konstandin, L.
2016-08-01
We examine how three fundamentally different numerical hydrodynamics codes follow the evolution of an isothermal galactic disc with an external spiral potential. We compare an adaptive mesh refinement code (RAMSES), a smoothed particle hydrodynamics code (SPHNG), and a volume-discretized mesh-less code (GIZMO). Using standard refinement criteria, we find that RAMSES produces a disc that is less vertically concentrated and does not reach such high densities as the SPHNG or GIZMO runs. The gas surface density in the spiral arms increases at a lower rate for the RAMSES simulations compared to the other codes. There is also a greater degree of substructure in the SPHNG and GIZMO runs and secondary spiral arms are more pronounced. By resolving the Jeans length with a greater number of grid cells, we achieve more similar results to the Lagrangian codes used in this study. Other alterations to the refinement scheme (adding extra levels of refinement and refining based on local density gradients) are less successful in reducing the disparity between RAMSES and SPHNG/GIZMO. Although more similar, SPHNG displays different density distributions and vertical mass profiles to all modes of GIZMO (including the smoothed particle hydrodynamics version). This suggests differences also arise which are not intrinsic to the particular method but rather due to its implementation. The discrepancies between codes (in particular, the densities reached in the spiral arms) could potentially result in differences in the locations and time-scales for gravitational collapse, and therefore impact star formation activity in more complex galaxy disc simulations.
Testing Hydrodynamics Schemes in Galaxy Disc Simulations
Few, C G; Pettitt, A; Konstandin, L
2016-01-01
We examine how three fundamentally different numerical hydrodynamics codes follow the evolution of an isothermal galactic disc with an external spiral potential. We compare an adaptive mesh refinement code (RAMSES), a smoothed particle hydrodynamics code (sphNG), and a volume-discretised meshless code (GIZMO). Using standard refinement criteria, we find that RAMSES produces a disc that is less vertically concentrated and does not reach such high densities as the sphNG or GIZMO runs. The gas surface density in the spiral arms increases at a lower rate for the RAMSES simulations compared to the other codes. There is also a greater degree of substructure in the sphNG and GIZMO runs and secondary spiral arms are more pronounced. By resolving the Jeans' length with a greater number of grid cells we achieve more similar results to the Lagrangian codes used in this study. Other alterations to the refinement scheme (adding extra levels of refinement and refining based on local density gradients) are less successful i...
Multiphase flow through porous media: an adaptive control volume finite element formulation
Mostaghimi, P.; Tollit, B.; Gorman, G.; Neethling, S.; Pain, C.
2012-12-01
Accurate modeling of multiphase flow in porous media is of great importance in a wide range of applications in science and engineering. We have developed a numerical scheme which employs an implicit pressure explicit saturation (IMPES) algorithm for the temporal discretization of the governing equations. The saturation equation is spatially discretized using a node centered control volume method on an unstructured finite element mesh. The face values are determined through an upwind scheme. The pressure equation is spatially discretized using a continuous control volume finite element method (CV-FEM) to achieve consistency with the discrete saturation equation. The numerical simulation is implemented in Fluidity, an open source and general purpose fluid simulator capable of solving a number of different governing equations for fluid flow and accompanying field equations on arbitrary unstructured meshes. The model is verified against the Buckley-Leverett problem where a quasi-analytical solution is available. We discuss the accuracy and the order of convergence of the scheme. We demonstrate the scheme for modeling multiphase flow in a synthetic heterogeneous porous medium along with the use of anisotropic mesh adaptivity to control local solution errors and increase computational efficiency. The adaptive method is also used to simulate two-phase flow in heap leaching, an industrial mining process, where the flow of the leaching solution is gravitationally dominated. Finally we describe the extension of the developed numerical scheme for simulation of flow in multiscale fractured porous media and its capability to model the multiscale characterization of flow in full scale.
Scheme Program Documentation Tools
DEFF Research Database (Denmark)
Nørmark, Kurt
2004-01-01
This paper describes and discusses two different Scheme documentation tools. The first is SchemeDoc, which is intended for documentation of the interfaces of Scheme libraries (APIs). The second is the Scheme Elucidator, which is for internal documentation of Scheme programs. Although the tools...... are separate and intended for different documentation purposes they are related to each other in several ways. Both tools are based on XML languages for tool setup and for documentation authoring. In addition, both tools rely on the LAML framework which---in a systematic way---makes an XML language available...
RELAP5/MOD3 code manual. Volume 4, Models and correlations
Energy Technology Data Exchange (ETDEWEB)
NONE
1995-08-01
The RELAP5 code has been developed for best-estimate transient simulation of light water reactor coolant systems during postulated accidents. The code models the coupled behavior of the reactor coolant system and the core for loss-of-coolant accidents and operational transients such as anticipated transient without scram, loss of offsite power, loss of feedwater, and loss of flow. A generic modeling approach is used that permits simulating a variety of thermal hydraulic systems. Control system and secondary system components are included to permit modeling of plant controls, turbines, condensers, and secondary feedwater systems. RELAP5/MOD3 code documentation is divided into seven volumes: Volume I presents modeling theory and associated numerical schemes; Volume II details instructions for code application and input data preparation; Volume III presents the results of developmental assessment cases that demonstrate and verify the models used in the code; Volume IV discusses in detail RELAP5 models and correlations; Volume V presents guidelines that have evolved over the past several years through the use of the RELAP5 code; Volume VI discusses the numerical scheme used in RELAP5; and Volume VII presents a collection of independent assessment calculations.
Footbridge between finite volumes and finite elements with applications to CFD
Pascal, Frédéric; Ghidaglia, Jean-Michel
2001-12-01
The aim of this paper is to introduce a new algorithm for the discretization of second-order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier-Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright
A simple extension of Roe's scheme for real gases
Arabi, Sina; Trépanier, Jean-Yves; Camarero, Ricardo
2017-01-01
The purpose of this paper is to develop a highly accurate numerical algorithm to model real gas flows in local thermodynamic equilibrium (LTE). The Euler equations are solved using a finite volume method based on Roe's flux difference splitting scheme including real gas effects. A novel algorithm is proposed to calculate the Jacobian matrix which satisfies the flux difference splitting exactly in the average state for a general equation of state. This algorithm increases the robustness and accuracy of the method, especially around the contact discontinuities and shock waves where the gas properties jump appreciably. The results are compared with an exact solution of the Riemann problem for the shock tube which considers the real gas effects. In addition, the method is applied to a blunt cone to illustrate the capability of the proposed extension in solving two dimensional flows.
A finite volume method for fluctuating hydrodynamics of simple fluids
Narayanan, Kiran; Samtaney, Ravi; Moran, Brian
2015-11-01
Fluctuating hydrodynamics accounts for stochastic effects that arise at mesoscopic and macroscopic scales. We present a finite volume method for numerical solutions of the fluctuating compressible Navier Stokes equations. Case studies for simple fluids are demonstrated via the use of two different equations of state (EOS) : a perfect gas EOS, and a Lennard-Jones EOS for liquid argon developed by Johnson et al. (Mol. Phys. 1993). We extend the fourth order conservative finite volume scheme originally developed by McCorquodale and Colella (Comm. in App. Math. & Comput. Sci. 2011), to evaluate the deterministic and stochastic fluxes. The expressions for the cell-centered discretizations of the stochastic shear stress and stochastic heat flux are adopted from Espanol, P (Physica A. 1998), where the discretizations were shown to satisfy the fluctuation-dissipation theorem. A third order Runge-Kutta scheme with weights proposed by Delong et al. (Phy. Rev. E. 2013) is used for the numerical time integration. Accuracy of the proposed scheme will be demonstrated. Comparisons of the numerical solution against theory for a perfect gas as well as liquid argon will be presented. Regularizations of the stochastic fluxes in the limit of zero mesh sizes will be discussed. Supported by KAUST Baseline Research Funds.
Numerical approximation for a degenerate parabolic-elliptic system modeling flows in porous media
Directory of Open Access Journals (Sweden)
Rabah-Hacene Bellout
2012-11-01
Full Text Available We present a numerical scheme for the approximation of the system of partial differential equations of the Peaceman model for the miscible displacement of one fluid by another in a two dimensional porous medium. In this scheme, the velocity-pressure equations are treated by a mixed finite element discretization using the Raviart-Thomas element, and the concentration equation is approximated by a finite volume discretization using the Upstream scheme, knowing that the Raviart-Thomas element gives good approximations for fluids velocities and that the Upstream scheme is well suited for convection dominated equations. We prove a maximum principle for our approximate concentration more precisely $ 0leq c_h(x,tleq 1$ a.e. in $Omega_T $ as long as some grid conditions are satisfied - at the difference of Chainais and Droniou [6]who have only observed that their approximate concentration remains in $[0;1]$ (and such is the case for other proposed numerical methods; e.g., [21,22]. Moreover our grid conditions are satisfied even with very large time steps and spatial steps. Finally we prove the consistency of the proposed scheme and thus are assured of convergence. A numerical test is reported.
Convertible Proxy Signcryption Scheme
Institute of Scientific and Technical Information of China (English)
李继国; 李建中; 曹珍富; 张亦辰
2004-01-01
In 1996, Mambo et al introduced the concept of proxy signature. However, proxy signature can only provide the delegated authenticity and cannot provide confidentiality. Recently, Gamage et al and Chan and Wei proposed different proxy signcryption schemes respectively, which extended the concept of proxy signature.However, only the specified receiver can decrypt and verify the validity of proxy signcryption in their schemes.To protect the receiver' s benefit in case of a later dispute, Wu and Hsu proposed a convertible authenticated encryption scheme, which carn enable the receiver to convert signature into an ordinary one that can be verified by anyone. Based on Wu and Hsu' s scheme and improved Kim' s scheme, we propose a convertible proxy signcryption scheme. The security of the proposed scheme is based on the intractability of reversing the one-way hash function and solving the discrete logarithm problem. The proposed scheme can satisfy all properties of strong proxy signature and withstand the public key substitution attack and does not use secure channel. In addition, the proposed scheme can be extended to convertible threshold proxy signcryption scheme.
A moving mesh unstaggered constrained transport scheme for magnetohydrodynamics
Mocz, Philip; Pakmor, Rüdiger; Springel, Volker; Vogelsberger, Mark; Marinacci, Federico; Hernquist, Lars
2016-11-01
We present a constrained transport (CT) algorithm for solving the 3D ideal magnetohydrodynamic (MHD) equations on a moving mesh, which maintains the divergence-free condition on the magnetic field to machine-precision. Our CT scheme uses an unstructured representation of the magnetic vector potential, making the numerical method simple and computationally efficient. The scheme is implemented in the moving mesh code AREPO. We demonstrate the performance of the approach with simulations of driven MHD turbulence, a magnetized disc galaxy, and a cosmological volume with primordial magnetic field. We compare the outcomes of these experiments to those obtained with a previously implemented Powell divergence-cleaning scheme. While CT and the Powell technique yield similar results in idealized test problems, some differences are seen in situations more representative of astrophysical flows. In the turbulence simulations, the Powell cleaning scheme artificially grows the mean magnetic field, while CT maintains this conserved quantity of ideal MHD. In the disc simulation, CT gives slower magnetic field growth rate and saturates to equipartition between the turbulent kinetic energy and magnetic energy, whereas Powell cleaning produces a dynamically dominant magnetic field. Such difference has been observed in adaptive-mesh refinement codes with CT and smoothed-particle hydrodynamics codes with divergence-cleaning. In the cosmological simulation, both approaches give similar magnetic amplification, but Powell exhibits more cell-level noise. CT methods in general are more accurate than divergence-cleaning techniques, and, when coupled to a moving mesh can exploit the advantages of automatic spatial/temporal adaptivity and reduced advection errors, allowing for improved astrophysical MHD simulations.
Numerical methods for incompressible viscous flows with engineering applications
Rose, M. E.; Ash, R. L.
1988-01-01
A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.
Optimization-based mesh correction with volume and convexity constraints
D'Elia, Marta; Ridzal, Denis; Peterson, Kara J.; Bochev, Pavel; Shashkov, Mikhail
2016-05-01
We consider the problem of finding a mesh such that 1) it is the closest, with respect to a suitable metric, to a given source mesh having the same connectivity, and 2) the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh. This volume correction problem arises in important simulation contexts, such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi-Lagrangian transport schemes. In this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective, while the prescribed cell volumes, mesh validity and/or cell convexity specify the constraints. We solve this problem numerically using a sequential quadratic programming (SQP) method whose performance scales with the mesh size. To achieve scalable performance we develop a specialized multigrid-based preconditioner for optimality systems that arise in the application of the SQP method to the volume correction problem. Numerical examples illustrate the importance of volume correction, and showcase the accuracy, robustness and scalability of our approach.
Martyushev, S. G.; Miroshnichenko, I. V.; Sheremet, M. A.
2014-01-01
Unsteady regimes of convective-radiative heat transfer in a cubic enclosure with finitely thick heat-conducting walls in the presence of a constant-temperature energy source have been modeled mathematically under the conditions of convective heat exchange with the environment. A mathematical model has been formulated in dimensionless variables "vector potential-vorticity vector-temperature;" the model was realized numerically by the finite-difference method. An analysis of radiative heat transfer has been made on the basis of the surface-radiation approximation with the balance method in Polyak's version. Three-dimensional temperature and velocity fields and dependences for the average Nusselt number have been obtained; they reflect the influence of the reduced emissivity factor of interior surfaces of enclosing walls, of the relative thermal conductivity, and of the unsteadiness factor on the flow regimes and heat transfer.
Third-order modified coefficient scheme based on essentially non-oscillatory scheme
Institute of Scientific and Technical Information of China (English)
LI Ming-jun; YANG Yu-yue; SHU Shi
2008-01-01
A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory (MCENO) scheme without increasing the base points during construction of the scheme.The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially non oscillatory (ENO) scheme for its essential non-oscillation,total variation bounded (TVB),etc.The new scheme improves accuracy by one order compared to the original one.The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor (RT) instability with densities 1:3 and 1:100,and solve the Lax shock-wave tube numerically.The ratio of CPU time used to implement MCENO,the third-order ENO and fifth-order weighed ENO (WENO) schemes is 0.62:1:2.19.This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme.
Asynchronous discrete event schemes for PDEs
Stone, D.; Geiger, S.; Lord, G. J.
2017-08-01
A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.
Difference Schemes and Applications
2015-02-06
of the shallow water equations that is well suited for complex geometries and moving boundaries. Another (similar) regularization of...the solid wall extrapolation followed by the interpolation in the phase space (by solving the Riemann problem between the internal cell averages and...scheme. This Godunov-type scheme enjoys all major advantages of Riemann -problem-solver-free, non-oscillatory central schemes and, at the same time, have
Efficient Threshold Signature Scheme
Directory of Open Access Journals (Sweden)
Sattar J Aboud
2012-01-01
Full Text Available In this paper, we introduce a new threshold signature RSA-typed scheme. The proposed scheme has the characteristics of un-forgeable and robustness in random oracle model. Also, signature generation and verification is entirely non-interactive. In addition, the length of the entity signature participate is restricted by a steady times of the length of the RSA signature modulus. Also, the signing process of the proposed scheme is more efficient in terms of time complexity and interaction.
Stateless Transitive Signature Schemes
Institute of Scientific and Technical Information of China (English)
MA Chun-guang; CAI Man-chun; YANG Yi-xian
2004-01-01
A new practical method is introduced to transform the stateful transitive signature scheme to stateless one without the loss of security. According to the approach, two concrete stateless transitive signature schemes based on Factoring and RSA are presented respectively. Under the assumption of the hardness of factoring and one-more- RSA-inversion problem, both two schemes are secure under the adaptive chosen-message attacks in random oracle model.
Arun, K. R.; Kraft, M.; Lukáčová-Medvid'ová, M.; Prasad, Phoolan
2009-02-01
We present a generalization of the finite volume evolution Galerkin scheme [M. Lukáčová-Medvid'ová, J. Saibertov'a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533- 562; M. Lukáčová-Medvid'ová, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1-30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor-corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.
Numerical computations with GPUs
Kindratenko, Volodymyr
2014-01-01
This book brings together research on numerical methods adapted for Graphics Processing Units (GPUs). It explains recent efforts to adapt classic numerical methods, including solution of linear equations and FFT, for massively parallel GPU architectures. This volume consolidates recent research and adaptations, covering widely used methods that are at the core of many scientific and engineering computations. Each chapter is written by authors working on a specific group of methods; these leading experts provide mathematical background, parallel algorithms and implementation details leading to
Lu, Xinhua; Xie, Shengbai
2016-05-01
In the existing literature, various forms of governing equations have been proposed to solve the shallow-water equations (SWEs). Recently, attention has been dedicated to the so-called "pre-balanced" form, because finite-volume schemes that are designed on this basis satisfy the well-balanced property. In this study, we theoretically investigate the relationship between numerical schemes devised using approximate Riemann solvers in the framework of finite-volume methods for solving the conventional form of the SWEs and its "pre-balanced" variant. We find that the numerical schemes for solving these two forms of the SWEs turn out to be identical when some widely employed upwind or centered approximate Riemann solvers are adopted for the numerical flux evaluations, such as the HLL (Harten, Lax, and van Leer), HLLC (HLL solver with restoring the contact surface), FORCE (first-order centered), and SLIC (slope limited centered) schemes. Some numerical experiments are performed, which verify the validity of the result of our theoretical analysis. The theoretical and numerical results suggest that the "pre-balanced" SWEs variant is not superior to the conventional one for solving the SWEs using approximate Riemann solvers.
SMD-based numerical stochastic perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Dalla Brida, Mattia [Universita di Milano-Bicocca, Dipartimento di Fisica, Milan (Italy); INFN, Sezione di Milano-Bicocca (Italy); Luescher, Martin [CERN, Theoretical Physics Department, Geneva (Switzerland); AEC, Institute for Theoretical Physics, University of Bern (Switzerland)
2017-05-15
The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schroedinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit. (orig.)
Anisotropic Diffusion in Mesh-Free Numerical Magnetohydrodynamics
Hopkins, Philip F
2016-01-01
We extend recently-developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect), and turbulent 'eddy diffusion.' We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV) as well as smoothed-particle hydrodynamics (SPH). We show the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behavior even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators ...
Numerical investigation of shock induced bubble collapse in water
Apazidis, N.
2016-04-01
A semi-conservative, stable, interphase-capturing numerical scheme for shock propagation in heterogeneous systems is applied to the problem of shock propagation in liquid-gas systems. The scheme is based on the volume-fraction formulation of the equations of motion for liquid and gas phases with separate equations of state. The semi-conservative formulation of the governing equations ensures the absence of spurious pressure oscillations at the material interphases between liquid and gas. Interaction of a planar shock in water with a single spherical bubble as well as twin adjacent bubbles is investigated. Several stages of the interaction process are considered, including focusing of the transmitted shock within the deformed bubble, creation of a water-hammer shock as well as generation of high-speed liquid jet in the later stages of the process.
Hybrid undulator numerical optimization
Energy Technology Data Exchange (ETDEWEB)
Hairetdinov, A.H. [Kurchatov Institute, Moscow (Russian Federation); Zukov, A.A. [Solid State Physics Institute, Chernogolovka (Russian Federation)
1995-12-31
3D properties of the hybrid undulator scheme arc studied numerically using PANDIRA code. It is shown that there exist two well defined sets of undulator parameters which provide either maximum on-axis field amplitude or minimal higher harmonics amplitude of the basic undulator field. Thus the alternative between higher field amplitude or pure sinusoidal field exists. The behavior of the undulator field amplitude and harmonics structure for a large set of (undulator gap)/(undulator wavelength) values is demonstrated.
Bagci, Hakan
2010-08-01
A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well-posed even when applied to densely discretized volumes, a classically formulated S-EFIE operator is ill-posed when applied to densely discretized surfaces. This renders the discretized coupled S-EFIE and V-EFIE system ill-conditioned, and its iterative solution inefficient or even impossible. The proposed scheme regularizes the coupled set of S-EFIE and V-EFIE using a Calderón multiplicative preconditioner (CMP)-based technique. The resulting scheme enables the efficient analysis of electromagnetic interactions with composite structures containing fine/subwavelength geometric features. Numerical examples demonstrate the efficiency of the proposed scheme. © 2006 IEEE.
ON THE CENTRAL RELAXING SCHEMES I:SINGLE CONSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
Hua-zhong Tang
2000-01-01
In this first paper we present a central relaxing scheme for scalar conservation laws, based on using the local relaxation approximation. Our scheme is obtained without using linear or nonlinear Riemann solvers. A cell entropy inequality is studied for the semidiscrete central relaxing scheme, and a second order MUSCL scheme is shown to be TVD in the zero relaxation limit. The next paper will extend the central relaxing scheme to multi-dimensional systems of conservation laws in curvilinear coordinates, including numerical experiments for 1D and 2D problems.
On the monotonicity of multidimensional finite difference schemes
Kovyrkina, O.; Ostapenko, V.
2016-10-01
The classical concept of monotonicity, introduced by Godunov for linear one-dimensional difference schemes, is extended to multidimensional case. Necessary and sufficient conditions of monotonicity are obtained for linear multidimensional difference schemes of first order. The constraints on the numerical viscosity are given that ensure the monotonicity of a difference scheme in the multidimensional case. It is proposed a modification of the second order multidimensional CABARET scheme that preserves the monotonicity of one-dimensional discrete solutions and, as a result, ensures higher smoothness in the computation of multidimensional discontinuous solutions. The results of two-dimensional test computations illustrating the advantages of the modified CABARET scheme are presented.
Institute of Scientific and Technical Information of China (English)
程俊霞; 任健
2011-01-01
在非结构四边形网格上,含曲率的水平集方程采用伽辽金等参有限元方法空间离散,时间离散采用半隐格式.离散形成的线性方程组的系数矩阵是对称的稀疏矩阵,采用共轭梯度法求解.数值算例表明,在笛卡儿网格和随机网格上,含曲率的水平集方程离散格式可达到近似二阶精度.重新初始化方程的离散格式精度可达到近似一阶精度.给出了非结构四边形网格上不光滑界面以曲率收缩的运动过程.在不采用重新初始化的情况下,收缩过程未出现不稳定现象.%Level set equations containing curvature are solved on unstructured quadrilateral meshes. We use spatial discretization by the Galerkin isoparametric finite element method, and semi-implicit time stepping. Conjugate gradient method solves the linear system of equations, whose coefficient matrix is symmetric and sparse. On Cartesian meshes and random meshes, the scheme of level set equations containing curvature is nearly second order accuracy in L2 and L∝ norms. Example is given of nonsmooth level sets shortening stably without reinitialization by local curvature on unstructured quadrilateral meshes.
Energy Technology Data Exchange (ETDEWEB)
Thompson, Kelly Glen [Texas A & M Univ., College Station, TX (United States)
2000-11-01
In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness
High-Resolution Numerical Model for Shallow Water Flows and Pollutant Diffusions
Institute of Scientific and Technical Information of China (English)
王嘉松; 何友声
2002-01-01
A finite-volume high-resolution numerical model for coupling the shallow water flows and pollutant diffusions was presented based on using a hybrid TVD scheme in space discretization and a Runge-Kutta method in time discretization. Numerical simulations for modelling dam- break, enlarging open channel flow and pollutant dispersion were implemented and compared with experimental data or other published computations. The validation of this method shows that it can not only deal with the problem involving discontinuities and unsteady flows, but also solve the general shallow water flows and pollutant diffusions.
Directory of Open Access Journals (Sweden)
D. S. Moreira
2013-08-01
Full Text Available This article presents the coupling of the JULES surface model to the CCATT-BRAMS atmospheric chemistry model. This new numerical system is denominated JULES-CCATT-BRAMS. We demonstrate the performance of this new model system in relation to several meteorological variables and the CO2 mixing ratio over a large part of South America, focusing on the Amazon basin. The evaluation was conducted for two time periods, the wet (March and dry (September seasons of 2010. The model errors were calculated in relation to meteorological observations at conventional stations in airports and automatic stations. In addition, CO2 mixing ratios in the first model level were compared with meteorological tower measurements and vertical CO2 profiles were compared with observations obtained with airborne instruments. The results of this study show that the JULES-CCATT-BRAMS modeling system provided a significant gain in performance for the considered atmospheric fields relative to those simulated by the LEAF (version 3 surface model originally employed by CCATT-BRAMS. In addition, the new system significantly increases the ability to simulate processes involving air–surface interactions, due to the ability of JULES to simulate photosynthesis, respiration and dynamic vegetation, among other processes. We also discuss a wide range of numerical studies involving coupled atmospheric, land surface and chemistry processes that could be done with the system introduced here. Thus, this work presents to the scientific community a free modeling tool, with good performance in comparison with observational data and reanalysis model data, at least for the region and time period discussed here. Therefore, in principle, this model is able to produce atmospheric hindcast/forecast simulations at different spatial resolutions for any time period and any region of the globe.
Moreira, D. S.; Freitas, S. R.; Bonatti, J. P.; Mercado, L. M.; Rosário, N. M. É.; Longo, K. M.; Miller, J. B.; Gloor, M.; Gatti, L. V.
2013-01-01
This article presents the development of a new numerical system denominated JULES-CCATT-BRAMS, which resulted from the coupling of the JULES surface model to the CCATT-BRAMS atmospheric chemistry model. The performance of this system in relation to several meteorological variables (wind speed at 10 m, air temperature at 2 m, dew point temperature at 2 m, pressure reduced to mean sea level and 6 h accumulated precipitation) and the CO2 concentration above an extensive area of South America is also presented, focusing on the Amazon basin. The evaluations were conducted for two periods, the wet (March) and dry (September) seasons of 2010. The statistics used to perform the evaluation included bias (BIAS) and root mean squared error (RMSE). The errors were calculated in relation to observations at conventional stations in airports and automatic stations. In addition, CO2 concentrations in the first model level were compared with meteorological tower measurements and vertical CO2 profiles were compared with aircraft data. The results of this study show that the JULES model coupled to CCATT-BRAMS provided a significant gain in performance in the evaluated atmospheric fields relative to those simulated by the LEAF (version 3) surface model originally utilized by CCATT-BRAMS. Simulations of CO2 concentrations in Amazonia and a comparison with observations are also discussed and show that the system presents a gain in performance relative to previous studies. Finally, we discuss a wide range of numerical studies integrating coupled atmospheric, land surface and chemistry processes that could be produced with the system described here. Therefore, this work presents to the scientific community a free tool, with good performance in relation to the observed data and re-analyses, able to produce atmospheric simulations/forecasts at different resolutions, for any period of time and in any region of the globe.
Directory of Open Access Journals (Sweden)
D. S. Moreira
2013-01-01
Full Text Available This article presents the development of a new numerical system denominated JULES-CCATT-BRAMS, which resulted from the coupling of the JULES surface model to the CCATT-BRAMS atmospheric chemistry model. The performance of this system in relation to several meteorological variables (wind speed at 10 m, air temperature at 2 m, dew point temperature at 2 m, pressure reduced to mean sea level and 6 h accumulated precipitation and the CO2 concentration above an extensive area of South America is also presented, focusing on the Amazon basin. The evaluations were conducted for two periods, the wet (March and dry (September seasons of 2010. The statistics used to perform the evaluation included bias (BIAS and root mean squared error (RMSE. The errors were calculated in relation to observations at conventional stations in airports and automatic stations. In addition, CO2 concentrations in the first model level were compared with meteorological tower measurements and vertical CO2 profiles were compared with aircraft data. The results of this study show that the JULES model coupled to CCATT-BRAMS provided a significant gain in performance in the evaluated atmospheric fields relative to those simulated by the LEAF (version 3 surface model originally utilized by CCATT-BRAMS. Simulations of CO2 concentrations in Amazonia and a comparison with observations are also discussed and show that the system presents a gain in performance relative to previous studies. Finally, we discuss a wide range of numerical studies integrating coupled atmospheric, land surface and chemistry processes that could be produced with the system described here. Therefore, this work presents to the scientific community a free tool, with good performance in relation to the observed data and re-analyses, able to produce atmospheric simulations/forecasts at different resolutions, for any period of time and in any region of the globe.
Lee, S. S.; Sengupta, S.; Nwadike, E. V.
1980-01-01
A one dimensional model for studying the thermal dynamics of cooling lakes was developed and verified. The model is essentially a set of partial differential equations which are solved by finite difference methods. The model includes the effects of variation of area with depth, surface heating due to solar radiation absorbed at the upper layer, and internal heating due to the transmission of solar radiation to the sub-surface layers. The exchange of mechanical energy between the lake and the atmosphere is included through the coupling of thermal diffusivity and wind speed. The effects of discharge and intake by power plants are also included. The numerical model was calibrated by applying it to Cayuga Lake. The model was then verified through a long term simulation using Lake Keowee data base. The comparison between measured and predicted vertical temperature profiles for the nine years is good. The physical limnology of Lake Keowee is presented through a set of graphical representations of the measured data base.
Ulku, Huseyin Arda
2015-02-01
An explicit marching on-in-time (MOT) based time domain electric field volume integral equation (TDVIE) solver for characterizing electromagnetic wave interactions on scatterers with nonlinear material properties is proposed. Discretization of the unknown electric field intensity and flux density is carried out by half and full Schaubert-Wilton-Glisson basis functions, respectively. Coupled system of spatially discretized TDVIE and the nonlinear constitutive relation between the field intensity and the flux density is integrated in time to compute the samples of the unknowns. An explicit PE(CE)m scheme is used for this purpose. Explicitness allows for \\'easy\\' incorporation of the nonlinearity as a function only to be evaluated on the right hand side of the coupled system of equations. A numerical example that demonstrates the applicability of the proposed MOT scheme to analyzing electromagnetic interactions on Kerr-nonlinear scatterers is presented. © 2015 IEEE.
A low-dissipation monotonicity-preserving scheme for turbulent flows in hydraulic turbines
Yang, L.; Nadarajah, S.
2016-11-01
The objective of this work is to improve the inherent dissipation of the numerical schemes under the framework of a Reynolds-averaged Navier-Stokes (RANS) simulation. The governing equations are solved by the finite volume method with the k-ω SST turbulence model. Instead of the van Albada limiter, a novel eddy-preserving limiter is employed in the MUSCL reconstructions to minimize the dissipation of the vortex. The eddy-preserving procedure inactivates the van Albada limiter in the swirl plane and reduces the artificial dissipation to better preserve vortical flow structures. Steady and unsteady simulations of turbulent flows in a straight channel and a straight asymmetric diffuser are demonstrated. Profiles of velocity, Reynolds shear stress and turbulent kinetic energy are presented and compared against large eddy simulation (LES) and/or experimental data. Finally, comparisons are made to demonstrate the capability of the eddy-preserving limiter scheme.
Martyr-Koller, R.C.; Kernkamp, H.W.J.; Van Dam, Anne A.; Mick van der Wegen,; Lucas, Lisa; Knowles, N.; Jaffe, B.; Fregoso, T.A.
2017-01-01
A linked modeling approach has been undertaken to understand the impacts of climate and infrastructure on aquatic ecology and water quality in the San Francisco Bay-Delta region. The Delft3D Flexible Mesh modeling suite is used in this effort for its 3D hydrodynamics, salinity, temperature and sediment dynamics, phytoplankton and water-quality coupling infrastructure, and linkage to a habitat suitability model. The hydrodynamic model component of the suite is D-Flow FM, a new 3D unstructured finite-volume model based on the Delft3D model. In this paper, D-Flow FM is applied to the San Francisco Bay-Delta to investigate tidal, seasonal and annual dynamics of water levels, river flows and salinity under historical environmental and infrastructural conditions. The model is driven by historical winds, tides, ocean salinity, and river flows, and includes federal, state, and local freshwater withdrawals, and regional gate and barrier operations. The model is calibrated over a 9-month period, and subsequently validated for water levels, flows, and 3D salinity dynamics over a 2 year period.Model performance was quantified using several model assessment metrics and visualized through target diagrams. These metrics indicate that the model accurately estimated water levels, flows, and salinity over wide-ranging tidal and fluvial conditions, and the model can be used to investigate detailed circulation and salinity patterns throughout the Bay-Delta. The hydrodynamics produced through this effort will be used to drive affiliated sediment, phytoplankton, and contaminant hindcast efforts and habitat suitability assessments for fish and bivalves. The modeling framework applied here will serve as a baseline to ultimately shed light on potential ecosystem change over the current century.
Multiresolution signal decomposition schemes
J. Goutsias (John); H.J.A.M. Heijmans (Henk)
1998-01-01
textabstract[PNA-R9810] Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This report proposes a general axiomatic pyramid decomposition scheme for signal analysis
Multiresolution signal decomposition schemes
Goutsias, J.; Heijmans, H.J.A.M.
1998-01-01
[PNA-R9810] Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This report proposes a general axiomatic pyramid decomposition scheme for signal analysis and synthes
High order compact schemes for gradient approximation
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we propose three gradient recovery schemes of higher order for the linear interpolation. The first one is a weighted averaging method based on the gradients of the linear interpolation on the uniform mesh, the second is a geometric averaging method constructed from the gradients of two cubic interpolation on macro element, and the last one is a local least square method on the nodal patch with cubic polynomials. We prove that these schemes can approximate the gradient of the exact solution on the symmetry points with fourth order. In particular, for the uniform mesh, we show that these three schemes are the same on the considered points. The last scheme is more robust in general meshes. Consequently, we obtain the superconvergence results of the recovered gradient by using the aforementioned results and the supercloseness between the finite element solution and the linear interpolation of the exact solution. Finally, we provide several numerical experiments to illustrate the theoretical results.
A HIGH RESOLUTION FINITE VOLUME METHOD FOR SOLVING SHALLOW WATER EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A high-resolution finite volume numerical method for solving the shallow water equations is developed in this paper. In order to extend finite difference TVD scheme to finite volume method, a new geometry and topology of control bodies is defined by considering the corresponding relationships between nodes and elements. This solver is implemented on arbitrary quadrilateral meshes and their satellite elements, and based on a second-order hybrid type of TVD scheme in space discretization and a two-step Runge-Kutta method in time discretization. Then it is used to deal with two typical dam-break problems and very satisfactory results are obtained comparied with other numerical solutions. It can be considered as an efficient implement for the computation of shallow water problems, especially concerning those having discontinuities, subcritical and supercritical flows and complex geometries.
FINITE VOLUME METHOD FOR SIMULATION OF VISCOELASTIC FLOW THROUGH A EXPANSION CHANNEL
Institute of Scientific and Technical Information of China (English)
FU Chun-quan; JIANG Hai-mei; YIN Hong-jun; SU Yu-chi; ZENG Ye-ming
2009-01-01
A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell (UCM) fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the Finite Volume Method (FVM) in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number (We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweep efficiency.
Singh, Devraj
2015-01-01
Numerical Problems in Physics, Volume 1 is intended to serve the need of the students pursuing graduate and post graduate courses in universities with Physics and Materials Science as subject including those appearing in engineering, medical, and civil services entrance examinations. KEY FEATURES: * 29 chapters on Optics, Wave & Oscillations, Electromagnetic Field Theory, Solid State Physics & Modern Physics * 540 solved numerical problems of various universities and ompetitive examinations * 523 multiple choice questions for quick and clear understanding of subject matter * 567 unsolved numerical problems for grasping concepts of the various topic in Physics * 49 Figures for understanding problems and concept
Second-order accurate finite volume method for well-driven flows
Dotlić, Milan; Pokorni, Boris; Pušić, Milenko; Dimkić, Milan
2013-01-01
We consider a finite volume method for a well-driven fluid flow in a porous medium. Due to the singularity of the well, modeling in the near-well region with standard numerical schemes results in a completely wrong total well flux and an inaccurate hydraulic head. Local grid refinement can help, but it comes at computational cost. In this article we propose two methods to address well singularity. In the first method the flux through well faces is corrected using a logarithmic function, in a way related to the Peaceman correction. Coupling this correction with a second-order accurate two-point scheme gives a greatly improved total well flux, but the resulting scheme is still not even first order accurate on coarse grids. In the second method fluxes in the near-well region are corrected by representing the hydraulic head as a sum of a logarithmic and a linear function. This scheme is second-order accurate.
2004-01-01
J.P. CROISILLEF. DUBOISJ.F. MAITREM. MOUSSAOUIA. REZGUIA.M. ZINEF. SIDOROFF; Part one is cocerned with numerical analysis. starting from a mixed finite element interpretation of basic finite volume (F.V.) schemes, a posteriori error estimation is analysed in the hirarchy of Raviart-Thomas elements. An explicit compatible estimator is given for these F.V. schemes.Part two introduces a family of F.V.. schemes of finite differences type, for a rectangular mesh and a more general structured one. ...
The salivary testosterone and cortisol response to three loading schemes.
Crewther, Blair; Cronin, John; Keogh, Justin; Cook, Christian
2008-01-01
This aim of this study was to examine the free hormone (in saliva) responses to squat workouts performed by recreationally weight-trained males, using either a power (8 sets of 6 reps, 45% 1 repetition maximum [1RM], 3-minute rest periods, ballistic movements), hypertrophy (10 sets of 10 reps, 75% 1RM, 2-minute rest periods, controlled movements), or maximal strength scheme (6 sets of 4 reps, 88% 1RM, 4-minute rest periods, explosive intent). To determine the relative importance of the different training variables, these schemes were equated by workout duration with the power and strength schemes also equated by load volume. Salivary testosterone (T) and cortisol (C) both increased following the hypertrophy scheme (P hormonal change across the power and maximal strength schemes (P > 0.05). In general, the postexercise T and C responses to the hypertrophy scheme exceeded the other two schemes (P workout duration may explain the endocrine differences observed. The similar T and C responses to the power and maximal strength schemes (of equal volume) support such a view and suggest that differences in load intensity, rest periods, and technique are secondary to volume. Because the acute hormonal responses to resistance exercise contribute to protein metabolism, then load volume may be the most important workout variable activating the endocrine system and stimulating muscle growth.
Martin, R.; Gonzalez Ortiz, A.
In the industry as well as in the geophysical community, multiphase flows are mod- elled using a finite volume approach and a multicorrector algorithm in time in order to determine implicitly the pressures, velocities and volume fractions for each phase. Pressures, and velocities are generally determined at mid-half mesh step from each other following the staggered grid approach. This ensures stability and prevents os- cillations in pressure. It allows to treat almost all the Reynolds number ranges for all speeds and viscosities. The disadvantages appear when we want to treat more complex geometries or if a generalized curvilinear formulation of the conservation equations is considered. Too many interpolations have to be done and accuracy is then lost. In order to overcome these problems, we use here a similar algorithm in time and a Rhie and Chow interpolation (1983) of the collocated variables and essentially the velocities at the interface. The Rhie and Chow interpolation of the velocities at the finite volume interfaces allows to have no oscillatons of the pressure without checkerboard effects and to stabilize all the algorithm. In a first predictor step, fluxes at the interfaces of the finite volumes are then computed using 2nd and 3rd order shock capturing schemes of MUSCL/TVD or Van Leer type, and the orthogonal stress components are treated implicitly while cross viscous/diffusion terms are treated explicitly. A pentadiagonal system in 2D or a septadiagonal in 3D must be solve but here we have chosen to solve 3 tridiagonal linear systems (the so called Alternate Direction Implicit algorithm), one in each spatial direction, to reduce the cost of computation. Then a multi-correction of interpolated velocities, pressures and volumic fractions of each phase are done in the cartesian frame or the deformed local curvilinear coordinate system till convergence and mass conservation. At the end the energy conservation equations are solved. In all this process the
Sayed, Sadeed Bin
2016-11-02
An explicit marching on-in-time scheme for analyzing transient electromagnetic wave interactions on ferromagnetic scatterers is described. The proposed method solves a coupled system of time domain magnetic field volume integral and Landau-Lifshitz-Gilbert (LLG) equations. The unknown fluxes and fields are discretized using full and half Schaubert-Wilton-Glisson functions in space and bandlimited temporal interpolation functions in time. The coupled system is cast in the form of an ordinary differential equation and integrated in time using a PE(CE)m type linear multistep method to obtain the unknown expansion coefficients. Numerical results demonstrating the stability and accuracy of the proposed scheme are presented.
Energy Technology Data Exchange (ETDEWEB)
D' Ambros, Alder C.; Vitorassi, Pedro H.; Franco, Admilson T.; Morales, Rigoberto E.M. [Universidade Tecnologica Federal do Parana (UTFPR), Curitiba, PR (Brazil); Matins, Andre Leibsohn [PETROBRAS S.A., Rio de Janeiro, RJ (Brazil). Centro de Pesquisas (CENPES). Tecnologia de Engenharia de Perfuracao
2008-07-01
The success of oil well drilling process depends on the correct prediction of the velocities and stresses fields inside the gap between the drill string and the rock formation. Using CFD is possible to predict the behavior of the drilling fluid flow along the annular space, from the bottom to the top of the well. Commonly the drilling fluid is modeled as a Herschel-Bulkley fluid. An alternative is to employ a non-linear viscoelastic model, like the one developed by Phan-Thien-Tanner (PTT). In the present work the PTT constitutive equation is used to model the drilling fluid flow along the annular space. Thus, this work investigates the influence of the Deborah number on the laminar flow pattern through the numerical solution of the equations formed by the coupled velocity-pressure-stress fields. The results are analyzed and validated against the analytical solution for the fully developed annular pipe flow. The relation between the Deborah number (De) and the entry length is investigated, along with the influence of high values of Deborah number on the friction factor, stress and velocity fields. (author)
Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system
Lukácová-Medvid'ová, Maria; Warnecke, Gerald; Zahaykah, Yousef
2003-01-01
The subject of the paper is the derivation and analysis of third order finite volume evolution Galerkin schemes for the two-dimensional wave equation system. To achieve this the first order approximate evolution operator is considered. A recovery stage is carried out at each level to generate a piecewise polynomial approximation from the piecewise constants, to feed into the calculation of the fluxes. We estimate the truncation error and give numerical examples to demonstrate the higher order...
Finite volume evolution Galerkin (FVEG) methods for three-dimensional wave equation system
Lukácová-Medvid'ová, Maria; Warnecke, Gerald; Zahaykah, Yousef
2004-01-01
The subject of the paper is the derivation of finite volume evolution Galerkin schemes for three-dimensional wave equation system. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The idea is to evolve the initial function using the characteristic cone and then to project onto a finite element space. Numerical experiments are presented to demonstrate the accuracy and the multidimensional behaviour of the solutio...
A novel approach to construct numerical methods for stochastic differential equations
Halidias, Nikolaos
2013-01-01
In this paper we propose a new numerical method for solving stochastic differential equations (SDEs). As an application of this method we propose an explicit numerical scheme for a super linear SDE for which the usual Euler scheme diverges.
AN EXPLICIT MULTI-CONSERVATION FINITE-DIFFERENCE SCHEME FOR SHALLOW-WATER-WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
Bin Wang
2008-01-01
An explicit multi-conservation finite-difference scheme for solving the spherical shallowwater-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete form of the equations that conserves four basic physical integrals including the total energy, total mass, total potential vorticity and total enstrophy. Numerical tests show that the new scheme performs closely like but is much more time-saving than the implicit multi-conservation scheme.
Al-saggaf, Alawi A
2008-01-01
This paper attempt has been made to explain a fuzzy commitment scheme. In the conventional Commitment schemes, both committed string m and valid opening key are required to enable the sender to prove the commitment. However there could be many instances where the transmission involves noise or minor errors arising purely because of the factors over which neither the sender nor the receiver have any control. The fuzzy commitment scheme presented in this paper is to accept the opening key that is close to the original one in suitable distance metric, but not necessarily identical. The concept itself is illustrated with the help of simple situation.
A survey of Strong Convergent Schemes for the Simulation of ...
African Journals Online (AJOL)
PROF. OLIVER OSUAGWA
2014-12-01
Dec 1, 2014 ... scheme as well as the error between the analytic result and the numerical approximation. The error appeared ... financial mathematics and economics to model the .... is a standard m-dimensional Wiener process adapted to ...
On the novel chaotic secure communication scheme design
Wang, B.; Zhong, S. M.; Dong, X. C.
2016-10-01
In this paper, the problem on the chaotic secure communication is discussed. First a new dual channel transmission mechanism is presented and used in secure communication scheme design, then the channel-switching techniques are adopted to further improve the security of information transmission. Finally some typical numerical simulations are carried out to demonstrate the effectiveness of the proposed secure communication scheme.
General Projective Synchronization and Fractional Order Chaotic Masking Scheme
Institute of Scientific and Technical Information of China (English)
Shi-Quan Shao
2008-01-01
In this paper, a fractional order chaotic masking scheme used for secure communication is introduced. Based on the general projective synchronization of two coupled fractional Chert systems, a popular masking scheme is designed. Numerical example is given to demonstrate the effectiveness of the proposed method.
Boundary-volume integral equation numerical modeling for complex near surface%复杂地表边界元-体积元波动方程数值模拟
Institute of Scientific and Technical Information of China (English)
管西竹; 符力耘; 陶毅; 于更新
2011-01-01
复杂近地表引起来自深部构造的地震反射信号振幅和相位的异常变化,是影响复杂近地表地区地震资料品质的主要原因.本文采用边界元-体积元方法,通过求解含复杂地表的波动积分方程,来模拟地震波在复杂近地表构造中的传播.其中,边界元法模拟地形起伏和表层地质结构对地震波传播的影响；体积元法模拟起伏地表下非均质低降速层的影响.与其他数值模拟方法比较,其主要优点为几何上精确描述不规则地表界面,实现精确模拟自由表面对地震波的边界散射；显式应用近地表地层界面的连续边界条件,实现半解析的数值模拟；分区处理近地表复杂结构,有效模拟复杂地表下非均匀介质对地震波场的体散射.数值试验结果表明了该方法的实用性和有效性.%Complex near surface causes the anomalous variation of the amplitude and phase of seismic reflection signal from deep structures, and it is the most important factor to degrade the quality of seismic data. In this paper, we use the boundary-volume integral equation technique to simulate the seismic wave propagation in the complex near surface structure by solving the wave propagation equation with complex near surface condition. In the boundary-volume integral equation technique, the boundary element method can simulate irregular surface and geological structure for seismic wave propagation, and the volume element method can simulate the effect of the heterogeneous medium in low subweathered zone for the seismic wave propagation. Compared with other numerical simulation methods, the main advantage of the boundary-volume integral equation technique is its accurate geometric description of irregular surface and interface to simulate the boundary scattering waves by the free surface; it explicitly applies the continuous boundary conditions of the complex near surface to implement the semi-analytical numerical simulation; it
Energy Technology Data Exchange (ETDEWEB)
Masella, J.M.
1997-05-29
This thesis is devoted to the numerical simulation of some two-fluid models describing gas-liquid two-phase flow in pipes. The numerical models developed here can be more generally used in the modelling of a wide class of physical models which can be put under an hyperbolic form. We introduce first two isothermal two-fluid models, composed of a mass balance equation and a momentum equation written in each phase, describing respectively a stratified two-phase flow and a dispersed two-phase flow. These models are hyperbolic under some physical assumptions and can be written under a nonconservative vectorial system. We define and analyse a new numerical finite volume scheme (v{integral}Roe) founded on a linearized Riemann solver. This scheme does not need any analytical calculation and gives good results in the tracking of shocks. We compare this new scheme with the classical Roe scheme. Then we propose and study some numerical models, with and without flux splitting method, which are adapted to the discretization of the two-fluid models. This numerical models are given by a finite volume integration of the equations, and lean on the v{integral} scheme. In order to reducing cpu time, due to the low Mach number of two-phase flows, acoustic waves are implicit. Afterwards we proposed a discretization of boundary conditions, which allows the generation of transient flows in pipe. Some numerical academic and more physical tests show the good behaviour of the numerical methods. (author) 77 refs.
DEFF Research Database (Denmark)
Pötz, Katharina Anna; Haas, Rainer; Balzarova, Michaela
2013-01-01
Purpose – The rise of CSR followed a demand for CSR standards and guidelines. In a sector already characterized by a large number of standards, the authors seek to ask what CSR schemes apply to agribusiness, and how they can be systematically compared and analysed. Design....../methodology/approach – Following a deductive-inductive approach the authors develop a model to compare and analyse CSR schemes based on existing studies and on coding qualitative data on 216 CSR schemes. Findings – The authors confirm that CSR standards and guidelines have entered agribusiness and identify a complex landscape...... of schemes that can be categorized on focus areas, scales, mechanisms, origins, types and commitment levels. Research limitations/implications – The findings contribute to conceptual and empirical research on existing models to compare and analyse CSR standards. Sampling technique and depth of analysis limit...
Energy Technology Data Exchange (ETDEWEB)
Willcock, J J; Lumsdaine, A; Quinlan, D J
2008-08-19
Tabled execution is a generalization of memorization developed by the logic programming community. It not only saves results from tabled predicates, but also stores the set of currently active calls to them; tabled execution can thus provide meaningful semantics for programs that seemingly contain infinite recursions with the same arguments. In logic programming, tabled execution is used for many purposes, both for improving the efficiency of programs, and making tasks simpler and more direct to express than with normal logic programs. However, tabled execution is only infrequently applied in mainstream functional languages such as Scheme. We demonstrate an elegant implementation of tabled execution in Scheme, using a mix of continuation-passing style and mutable data. We also show the use of tabled execution in Scheme for a problem in formal language and automata theory, demonstrating that tabled execution can be a valuable tool for Scheme users.
Assessment of shock capturing schemes for discontinuous Galerkin method
Institute of Scientific and Technical Information of China (English)
于剑; 阎超; 赵瑞
2014-01-01
This paper carries out systematical investigations on the performance of several typical shock-capturing schemes for the discontinuous Galerkin (DG) method, including the total variation bounded (TVB) limiter and three artificial diffusivity schemes (the basis function-based (BF) scheme, the face residual-based (FR) scheme, and the element residual-based (ER) scheme). Shock-dominated flows (the Sod problem, the Shu-Osher problem, the double Mach reflection problem, and the transonic NACA0012 flow) are considered, addressing the issues of accuracy, non-oscillatory property, dependence on user-specified constants, resolution of discontinuities, and capability for steady solutions. Numerical results indicate that the TVB limiter is more eﬃcient and robust, while the artificial diffusivity schemes are able to preserve small-scale flow structures better. In high order cases, the artificial diffusivity schemes have demonstrated superior performance over the TVB limiter.
Khabaza, I M
1960-01-01
Numerical Analysis is an elementary introduction to numerical analysis, its applications, limitations, and pitfalls. Methods suitable for digital computers are emphasized, but some desk computations are also described. Topics covered range from the use of digital computers in numerical work to errors in computations using desk machines, finite difference methods, and numerical solution of ordinary differential equations. This book is comprised of eight chapters and begins with an overview of the importance of digital computers in numerical analysis, followed by a discussion on errors in comput
A new numerical method on unstructured grids
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A new numerical method-basic function method is proposed. This method can directly discrete differential operators on unstructured grids. By using the expansion of basic function to approach the exact function,the central and upwind schemes of derivative are constructed. By using the polynomial as basic function,applying the technique of flux splitting method and the combination of central and upwind schemes,the non-physical fluctuation near the shock wave is suppressed. The first-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper. Several numerical results of many typical examples for one-,two-and three-dimensional inviscid compressible steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave. Especially,combining with the adaptive remeshing technique,the satisfactory results can be obtained by these schemes.
Ashyralyev, Allaberen; Okur, Ulker
2016-08-01
In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.
The element-based finite volume method applied to petroleum reservoir simulation
Energy Technology Data Exchange (ETDEWEB)
Cordazzo, Jonas; Maliska, Clovis R.; Silva, Antonio F.C. da; Hurtado, Fernando S.V. [Universidade Federal de Santa Catarina (UFSC), Florianopolis, SC (Brazil). Dept. de Engenharia Mecanica
2004-07-01
In this work a numerical model for simulating petroleum reservoirs using the Element-based Finite Volume Method (EbFVM) is presented. The method employs unstructured grids using triangular and/or quadrilateral elements, such that complex reservoir geometries can be easily represented. Due to the control-volume approach, local mass conservation is enforced, permitting a direct physical interpretation of the resulting discrete equations. It is demonstrated that this method can deal with the permeability maps without averaging procedures, since this scheme assumes uniform properties inside elements, instead inside of control volumes, avoiding the need of weighting the permeability values at the control volumes interfaces. Moreover, it is easy to include the full permeability tensor in this method, which is an important issue in simulating heterogeneous and anisotropic reservoirs. Finally, a comparison among the results obtained using the scheme proposed in this work in the EbFVM framework with those obtained employing the scheme commonly used in petroleum reservoir simulation is presented. It is also shown that the scheme proposed is less susceptible to the grid orientation effect with the increasing of the mobility ratio. (author)
An Iterative Implicit Scheme for Nanoparticles Transport with Two-Phase Flow in Porous Media
El-Amin, Mohamed
2016-06-01
In this paper, we introduce a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium including gravity, capillary forces and Brownian diffusion. Nonlinear iterative IMPES scheme is used to solve the flow equation, and saturation and pressure are calculated at the current iteration step and then the transport equation is solved implicitly. Therefore, once the nanoparticles concentration is computed, the two equations of volume of the nanoparticles available on the pore surfaces and the volume of the nanoparticles entrapped in pore throats are solved implicitly. The porosity and the permeability variations are updated at each time step after each iteration loop. Numerical example for regular heterogenous permeability is considered. We monitor the changing of the fluid and solid properties due to adding the nanoparticles. Variation of water saturation, water pressure, nanoparticles concentration and porosity are presented graphically.
Numerical experiments modelling turbulent flows
Directory of Open Access Journals (Sweden)
Trefilík Jiří
2014-03-01
Full Text Available The work aims at investigation of the possibilities of modelling transonic flows mainly in external aerodynamics. New results are presented and compared with reference data and previously achieved results. For the turbulent flow simulations two modifications of the basic k – ω model are employed: SST and TNT. The numerical solution was achieved by using the MacCormack scheme on structured non-ortogonal grids. Artificial dissipation was added to improve the numerical stability.
Institute of Scientific and Technical Information of China (English)
DING XIU-HUAN; FU ZHI-GUO; ZHANG SHU-GONG
2009-01-01
This paper proposes an XTR version of the Kurosawa-Desmedt scheme. Our scheme is secure against adaptive choeen-ciphertext attack under the XTR version of the Decisional Diffie-Hellman assumption in the standard model. Comparing efficiency between the Kurosawa-Desmedt scheme and the proposed XTR-Kurosawa-Desmedt scheme, we find that the proposed scheme is more efficient than the Kurosawa-Desmedt scheme both in communication and computation without compromising security.
Advanced numerical methods for three dimensional two-phase flow calculations
Energy Technology Data Exchange (ETDEWEB)
Toumi, I. [Laboratoire d`Etudes Thermiques des Reacteurs, Gif sur Yvette (France); Caruge, D. [Institut de Protection et de Surete Nucleaire, Fontenay aux Roses (France)
1997-07-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.