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Sample records for full coupled navier-stokes

  1. Coupling Boltzmann and Navier-Stokes equations by friction

    Energy Technology Data Exchange (ETDEWEB)

    Bourgat, J.F. [INRIA, Le Chesnay (France); Le Tallec, P. [Universite Paris, Dauphine (France)]|[INRIA, Le Chesnay (France); Tidriri, M.D. [ICASE, Hampton, VA (United States)

    1996-09-01

    The aim of this paper is to introduce and validate a coupled Navier-Stokes Boltzman approach for the calculation of hypersonic rarefied flows around maneuvering vehicles. The proposed strategy uses locally a kinetic model in the boundary layer coupled through wall friction forces to a global Navier-Stokes solver. Different numerical experiments illustrate the potentialities of the method. 29 refs., 24 figs.

  2. Coupling Boltzmann and Navier-Stokes Equations by Friction

    OpenAIRE

    Bourgat, Jean-François; Le Tallec, Patrick; Tidriri, Moulay D.

    1995-01-01

    Projet MENUSIN; The aim of this paper is to introduce and validate a coupled Navier-Stokes Boltzmann approach for the calculation of hypersonic rarefied flows around manoeuvering vehicles. The proposed strategy uses locally a kinetic model in the boundary layer coupled through wall friction forces to a global Navier-Stokes solver. Different numerical experiments illustrate the potentialities of the method.

  3. Unstructured Navier-Stokes Analysis of Full TCA Configuration

    Science.gov (United States)

    Frink, Neal T.; Pirzadeh, Shahyar Z.

    1999-01-01

    This paper presents an Unstructured Navier-Stokes Analysis of Full TCA (Technology Concept Airplane) Configuration. The topics include: 1) Motivation; 2) Milestone and approach; 3) Overview of the unstructured-grid system; 4) Results on full TCA W/B/N/D/E configuration; 5) Concluding remarks; and 6) Future directions.

  4. Evaluation of micronozzle performance through DSMC, navier-stokes and coupled dsmc/navier-stokes approaches

    NARCIS (Netherlands)

    Torre, F. la; Kenjeres, S.; Kleijn, C.R.; Moerel, J.L.P.A.

    2009-01-01

    Both the particle based Direct Simulation Monte Carlo (DSMC) method and a compressible Navier-Stokes based continuum method are used to investigate the flow inside micronozzles and to predict the performance of such devices. For the Navier-Stokes approach, both slip and no-slip boundary conditions

  5. On Coupled System of Navier-Stokes Equations and Temperature

    African Journals Online (AJOL)

    Dr. Anthony Peter

    ABSTRACT. This paper deals with the coupled system of Navier-Stokes equations and temperature (Thermohydraulics) in a strip in the class of spatially non-decaying (infinite-energy) solutions belonging to the properly chosen uniformly local Sobolev spaces. The global well-posedness and dissipativity of the Navier- ...

  6. Stability of Non-constant Equilibrium Solutions for Bipolar Full Compressible Navier-Stokes-Maxwell Systems

    Science.gov (United States)

    Li, Xin; Wang, Shu; Feng, Yue-Hong

    2018-01-01

    We study the stability of smooth solutions near non-constant equilibrium states for a bipolar full compressible Navier-Stokes-Maxwell system in a three-dimensional torus T= (R/Z)^3 . This system is quasilinear hyperbolic-parabolic. In the first part, by using the maximum principle, we find a non-constant steady state solution with small amplitude for this system. In the second part, with the help of suitable choices of symmetrizers and classic energy estimates, we prove that global smooth solutions exist and converge to the non-constant steady states as the time goes to infinity. As a byproduct, we obtain the global stability for the bipolar full compressible Navier-Stokes-Poisson system.

  7. Navier-Stokes equation

    Directory of Open Access Journals (Sweden)

    Hannelore Breckner

    2000-01-01

    Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.

  8. KNOW-BLADE task-4 report: Navier-Stokes aeroelasticity

    DEFF Research Database (Denmark)

    Politis, E.S.; Nikolaou, I.G.; Chaviaropoulos, P.K.

    2004-01-01

    The problem of the aeroelastic stability of wind turbine blades is addressed in this report by advancing the aerodynamic modelling in the beam element type codes from the engineering-type empirical models to unsteady, 2D or 3D, Navier-Stokes solvers. Inthis project, structural models for the full...... wind turbine blade have been combined with 2D and 3D unsteady Navier-Stokes solvers. The relative disadvantage of the quasi-3D approach (where the elastic solver is coupled with a 2D Navier-Stokes solver) isits inability to model induced flow. The lack of a validation test case did not allow...

  9. A convergent numerical method for the full Navier-Stokes-Fourier system in smooth physical domains

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Hošek, Radim; Michálek, Martin

    2016-01-01

    Roč. 54, č. 5 (2016), s. 3062-3082 ISSN 0036-1429 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * finite element method * finite volume method Subject RIV: BA - General Mathematics Impact factor: 1.978, year: 2016 http://epubs.siam.org/doi/abs/10.1137/15M1011809

  10. A convergent numerical method for the full Navier-Stokes-Fourier system in smooth physical domains

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Hošek, Radim; Michálek, Martin

    2016-01-01

    Roč. 54, č. 5 (2016), s. 3062-3082 ISSN 0036-1429 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes- Fourier system * finite element method * finite volume method Subject RIV: BA - General Mathematics Impact factor: 1.978, year: 2016 http://epubs.siam.org/doi/abs/10.1137/15M1011809

  11. Inviscid incompressible limits of the full Navier-Stokes-Fourier system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Novotný, A.

    2013-01-01

    Roč. 321, č. 3 (2013), s. 605-628 ISSN 0010-3616 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * inviscid limit * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 1.901, year: 2013 http://link.springer.com/article/10.1007%2Fs00220-013-1691-4

  12. The incompressible limit of the full Navier-Stokes-Fourier system on domains with rough boundaries

    Czech Academy of Sciences Publication Activity Database

    Bucur, D.; Feireisl, Eduard

    2009-01-01

    Roč. 10, č. 5 (2009), s. 3203-3229 ISSN 1468-1218 R&D Projects: GA AV ČR(CZ) IAA100190606; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : low Mach number * Navier-Stokes-Fourier system * rough boundary Subject RIV: BA - General Mathematics Impact factor: 2.381, year: 2009

  13. On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation

    KAUST Repository

    Wang, Y.

    2013-01-01

    A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy\\'s law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.

  14. Hovering of model insects: simulation by coupling equations of motion with Navier-Stokes equations.

    Science.gov (United States)

    Wu, Jiang Hao; Zhang, Yan Lai; Sun, Mao

    2009-10-01

    When an insect hovers, the centre of mass of its body oscillates around a point in the air and its body angle oscillates around a mean value, because of the periodically varying aerodynamic and inertial forces of the flapping wings. In the present paper, hover flight including body oscillations is simulated by coupling the equations of motion with the Navier-Stokes equations. The equations are solved numerically; periodical solutions representing the hover flight are obtained by the shooting method. Two model insects are considered, a dronefly and a hawkmoth; the former has relatively high wingbeat frequency (n) and small wing mass to body mass ratio, whilst the latter has relatively low wingbeat frequency and large wing mass to body mass ratio. The main results are as follows. (i) The body mainly has a horizontal oscillation; oscillation in the vertical direction is about 1/6 of that in the horizontal direction and oscillation in pitch angle is relatively small. (ii) For the hawkmoth, the peak-to-peak values of the horizontal velocity, displacement and pitch angle are 0.11 U (U is the mean velocity at the radius of gyration of the wing), 0.22 c=4 mm (c is the mean chord length) and 4 deg., respectively. For the dronefly, the corresponding values are 0.02 U, 0.05 c=0.15 mm and 0.3 deg., much smaller than those of the hawkmoth. (iii) The horizontal motion of the body decreases the relative velocity of the wings by a small amount. As a result, a larger angle of attack of the wing, and hence a larger drag to lift ratio or larger aerodynamic power, is required for hovering, compared with the case of neglecting body oscillations. For the hawkmoth, the angle of attack is about 3.5 deg. larger and the specific power about 9% larger than that in the case of neglecting the body oscillations; for the dronefly, the corresponding values are 0.7 deg. and 2%. (iv) The horizontal oscillation of the body consists of two parts; one (due to wing aerodynamic force) is proportional to

  15. Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations

    International Nuclear Information System (INIS)

    Pontaza, J.P.; Reddy, J.N.

    2004-01-01

    We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least

  16. An inexact Newton method for fully-coupled solution of the Navier-Stokes equations with heat and mass transport

    Energy Technology Data Exchange (ETDEWEB)

    Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics

    1997-02-01

    The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.

  17. A numerical study of hypersonic flows using the full Navier-Stokes equations with different air models

    Science.gov (United States)

    Kim, Moon-Sang

    A two-dimensional, axisymmetric, full Navier-Stokes solver has been developed with equilibrium and nonequilibrium air models. The effects of a real gas are investigated numerically in the hypersonic flow regime. The code employs several different upwind schemes to examine their effect on the accuracy and stability of the numerical solutions. A finite volume method is used with curvilinear coordinates, and the first-order, up wind schemes are extended to second-order accuracy in space. The steady-state solutions are obtained using an approximately factorized implicit scheme, including fully implicit boundary conditions, to accelerate the convergence. The numerical accuracy is improved by introducing the closed-control-volume concept in the metric quantity calculations. This idea is verified by a blunt-nosed flow case with a scrambled grid. In general, the fastest convergence in an implicit scheme is obtained when the same residual and correction operators are applied. A new simplified Jacobian matrix is derived for Roe's flux difference splitting scheme because of the complexity involved in deriving the full Jacobian matrix, and which yields a faster convergence compared to the use of a different correction operator such as Steger-Warming's.

  18. Modelling of arc jet plasma flow in transitional regime by Navier Stokes and state-to-state coupling

    International Nuclear Information System (INIS)

    Alexandrova, T.; Izrar, B.; Lino da Silva, M.; Dudeck, M.

    2005-01-01

    The combination of 2D Navier-Stokes and state-to-state approaches has been used to describe the air plasma flow in an arc-jet. The gas dynamic parameters were calculated in Navier-Stokes approximation in a steady state description without chemical reaction and vibrational exchanges. And then, the set of equations of vibrational level densities and atomic species densities was locally solved. Experimental validations have been performed

  19. Navier-Stokes computer

    International Nuclear Information System (INIS)

    Hayder, M.E.

    1988-01-01

    A new scientific supercomputer, known as the Navier-Stokes Computer (NSC), has been designed. The NSC is a multi-purpose machine, and for applications in the field of computational fluid dynamics (CFD), this supercomputer is expected to yield a computational speed far exceeding that of the present-day super computers. This computer has a few very powerful processors (known as nodes) connected by an internodal network. There are three versions of the NSC nodes: micro-, mini- and full-node. The micro-node was developed to prove, to demonstrate and to refine the key architectural features of the NSC. Architectures of the two recent versions of the NSC nodes are presented, with the main focus on the full-node. At a clock speed of 20 MHz, the mini- and the full-node have peak computational speeds of 200 and 640 MFLOPS, respectively. The full-node is the final version for the NSC nodes and an NSC is expected to have 128 full-nodes. To test the suitability of different algorithms on the NSC architecture, an NSC simulator was developed. Some of the existing computational fluid dynamics codes were placed on this simulator to determine important and relevant issues relating to the efficient use of the NSC architecture

  20. Design Optimization of a Transonic-Fan Rotor Using Numerical Computations of the Full Compressible Navier-Stokes Equations and Simplex Algorithm

    Directory of Open Access Journals (Sweden)

    M. A. Aziz

    2014-01-01

    Full Text Available The design of a transonic-fan rotor is optimized using numerical computations of the full three-dimensional Navier-Stokes equations. The CFDRC-ACE multiphysics module, which is a pressure-based solver, is used for the numerical simulation. The code is coupled with simplex optimization algorithm. The optimization process is started from a suitable design point obtained using low fidelity analytical methods that is based on experimental correlations for the pressure losses and blade deviation angle. The fan blade shape is defined by its stacking line and airfoil shape which are considered the optimization parameters. The stacking line is defined by lean, sweep, and skews, while blade airfoil shape is modified considering the thickness and camber distributions. The optimization has been performed to maximize the rotor total pressure ratio while keeping the rotor efficiency and surge margin above certain required values. The results obtained are verified with the experimental data of Rotor 67. In addition, the results of the optimized fan indicate that the optimum design is found to be leaned in the direction of rotation and has a forward sweep from the hub to mean section and backward sweep to the tip. The pressure ratio increases from 1.427 to 1.627 at the design speed and mass flow rate.

  1. A finite element method for the numerical solution of the coupled Cahn-Hilliard and Navier-Stokes system for moving contact line problems

    KAUST Repository

    Bao, Kai

    2012-10-01

    In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples. © 2012 Elsevier Inc..

  2. Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration

    KAUST Repository

    Vignal, Philippe

    2015-06-01

    In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higher- order operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a two- dimensional annulus, and model spinodal decomposition under shear flow.

  3. Navier Stokes Theorem in Hydrology

    Science.gov (United States)

    Narayanan, M.

    2005-12-01

    In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time

  4. Numerical Approach of a Water Flow in an Unsaturated Porous Medium by Coupling Between the Navier-Stokes and Darcy-Forchheimer Equations

    Science.gov (United States)

    Hami, K.; Zeroual, I.

    2017-12-01

    In the present research, simulations have been conducted to determine numerically the dynamic behaviour of the flow of underground water fed by a river. The basic equations governing the problem studied are those of Navier-Stokes equations of conservation of momentum (flows between pores), coupled by the Darcy-Forchheimer equations (flows within these pores). To understand the phenomena involved, we first study the impact of flow rate on the pressure and the filtration velocity in the underground medium, the second part is devoted to the calculation of the elevation effect of the river water on the flow behaviour in the saturated and unsaturated zone of the aquifer.

  5. Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier-Stokes System with Vacuum and Large Oscillations

    Science.gov (United States)

    Huang, Xiangdi; Li, Jing

    2018-03-01

    For the three-dimensional full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid, we establish the global existence and uniqueness of classical solutions with smooth initial data which are of small energy but possibly large oscillations where the initial density is allowed to vanish. Moreover, for the initial data, which may be discontinuous and contain vacuum states, we also obtain the global existence of weak solutions. These results generalize previous ones on classical and weak solutions for initial density being strictly away from a vacuum, and are the first for global classical and weak solutions which may have large oscillations and can contain vacuum states.

  6. Incompressible Navier-Stokes and parabolized Navier-Stokes solution procedures and computational techniques

    Science.gov (United States)

    Rubin, S. G.

    1982-01-01

    Recent developments with finite-difference techniques are emphasized. The quotation marks reflect the fact that any finite discretization procedure can be included in this category. Many so-called finite element collocation and galerkin methods can be reproduced by appropriate forms of the differential equations and discretization formulas. Many of the difficulties encountered in early Navier-Stokes calculations were inherent not only in the choice of the different equations (accuracy), but also in the method of solution or choice of algorithm (convergence and stability, in the manner in which the dependent variables or discretized equations are related (coupling), in the manner that boundary conditions are applied, in the manner that the coordinate mesh is specified (grid generation), and finally, in recognizing that for many high Reynolds number flows not all contributions to the Navier-Stokes equations are necessarily of equal importance (parabolization, preferred direction, pressure interaction, asymptotic and mathematical character). It is these elements that are reviewed. Several Navier-Stokes and parabolized Navier-Stokes formulations are also presented.

  7. a Time-Dependent Three-Dimensional Numerical Study of Supersonic Rectangular Jet Flow and Noise Using the Full Navier-Stokes Equations.

    Science.gov (United States)

    Chyczewski, Thomas Stanley, Jr.

    A national interest in High Speed Civil Transports (HSCT) coupled with strict airport noise regulations has prompted the scientific community to investigate new and improved noise prediction strategies. Meeting these airport regulations is considered to be a major design challenge for the HSCT. In light of this effort, a direct simulation strategy for predicting supersonic jet noise is developed in this thesis. Direct simulations are quickly becoming the method of choice due to their generality and ever decreasing expense associated with the development of parallel processors. Supersonic jet noise is known to be dominated by the growth and decay of large scale turbulent structures. The direct simulation approach used here consists of solving the full Navier Stokes equations using high order finite difference techniques to simulate the evolution of these structures and the noise they radiate to the acoustic near field. This near field solution is then extrapolated to the far field using a Kirchhoff method. The numerical algorithm uses a fourth order Runge -Kutta method for the time integration. The spatial derivatives are approximated by a sixth order central scheme. A sixth order filter is used at each interior mesh point to damp frequencies that cannot be resolved by the spatial scheme. Second order filtering is provided only where required for stability. It is found to be confined to specific locations in the jet core and should have no effect on the acoustic solution. Characteristic based nonreflecting conditions are used to minimize reflections at the far field boundaries and have proven to be effective. Additional boundary conditions are required in the form of it model for the nozzle exit flow. The characteristics of the nozzle exit flow can have a significant impact on the noise radiation. This dependence is unfortunate since comprehensive experimental data is not available in this region of the jet. A model is developed here that addresses a variety of

  8. Evidence of weak land-atmosphere coupling under varying bare soil conditions: Are fully coupled Darcy/Navier-Stokes models necessary for simulating soil moisture dynamics?

    Science.gov (United States)

    Illangasekare, T. H.; Trautz, A. C.; Howington, S. E.; Cihan, A.

    2017-12-01

    It is a well-established fact that the land and atmosphere form a continuum in which the individual domains are coupled by heat and mass transfer processes such as bare-soil evaporation. Soil moisture dynamics can be simulated at the representative elementary volume (REV) scale using decoupled and fully coupled Darcy/Navier-Stokes models. Decoupled modeling is an asynchronous approach in which flow and transport in the soil and atmosphere is simulated independently; the two domains are coupled out of time-step via prescribed flux parameterizations. Fully coupled modeling in contrast, solves the governing equations for flow and transport in both domains simultaneously with the use of coupling interface boundary conditions. This latter approach, while being able to provide real-time two-dimensional feedbacks, is considerably more complex and computationally intensive. In this study, we investigate whether fully coupled models are necessary, or if the simpler decoupled models can sufficiently capture soil moisture dynamics under varying land preparations. A series of intermediate-scale physical and numerical experiments were conducted in which soil moisture distributions and evaporation estimates were monitored at high spatiotemporal resolutions for different heterogeneous packing and soil roughness scenarios. All experimentation was conducted at the newly developed Center for Experimental Study of Subsurface Environmental Processes (CESEP) wind tunnel-porous media user test-facility at the Colorado School of. Near-surface atmospheric measurements made during the experiments demonstrate that the land-atmosphere coupling was relatively weak and insensitive to the applied edaphic and surface conditions. Simulations with a decoupled multiphase heat and mass transfer model similarly show little sensitivity to local variations in atmospheric forcing; a single, simple flux parameterization can sufficiently capture the soil moisture dynamics (evaporation and redistribution

  9. Discretizations in isogeometric analysis of Navier-Stokes flow

    DEFF Research Database (Denmark)

    Nielsen, Peter Nørtoft; Gersborg, Allan Roulund; Gravesen, Jens

    2011-01-01

    This paper deals with isogeometric analysis of 2-dimensional, steady state, incompressible Navier-Stokes flow subjected to Dirichlet boundary conditions. We present a detailed description of the numerical method used to solve the boundary value problem. Numerical inf-sup stability tests for the s......This paper deals with isogeometric analysis of 2-dimensional, steady state, incompressible Navier-Stokes flow subjected to Dirichlet boundary conditions. We present a detailed description of the numerical method used to solve the boundary value problem. Numerical inf-sup stability tests...... for the simplified Stokes problem confirm the existence of many stable discretizations of the velocity and pressure spaces, and in particular show that stability may be achieved by means of knot refinement of the velocity space. Error convergence studies for the full Navier-Stokes problem show optimal convergence...

  10. Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations

    KAUST Repository

    Tamellini, L.

    2014-01-01

    In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.

  11. Reproductive solutions for the g-Navier-Stokes and g-Kelvin-Voight equations

    Directory of Open Access Journals (Sweden)

    Luis Friz

    2016-01-01

    Full Text Available This article presents the existence of reproductive solutions of g-Navier-Stokes and g-Kelvin-Voight equations. In this way, for weak solutions, we reach basically the same result as for classic Navier-Stokes equations.

  12. Unsteady coupling of Navier-Stokes and radiative heat transfer solvers applied to an anisothermal multicomponent turbulent channel flow

    International Nuclear Information System (INIS)

    Amaya, J.; Cabrit, O.; Poitou, D.; Cuenot, B.; El Hafi, M.

    2010-01-01

    Direct numerical simulations (DNS) of an anisothermal reacting turbulent channel flow with and without radiative source terms have been performed to study the influence of the radiative heat transfer on the optically non-homogeneous boundary layer structure. A methodology for the study of the emitting/absorbing turbulent boundary layer (TBL) is presented. Details on the coupling strategy and the parallelization techniques are exposed. An analysis of the first order statistics is then carried out. It is shown that, in the studied configuration, the global structure of the thermal boundary layer is not significantly modified by radiation. However, the radiative transfer mechanism is not negligible and contributes to the heat losses at the walls. The classical law-of-the-wall for temperature can thus be improved for RANS/LES simulations taking into account the radiative contribution.

  13. Generalized extended Navier-Stokes theory

    DEFF Research Database (Denmark)

    Hansen, J. S.; Daivis, Peter J.; Dyre, Jeppe C.

    2013-01-01

    The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present...... in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime...... and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies...

  14. ANALYSIS OF SOME ASSUMPTIONS OF NAVIER-STOKES EQUATION

    Directory of Open Access Journals (Sweden)

    Budarin V.

    2010-08-01

    Full Text Available Several stages of the derivation of Navier-Stokes equations in coordinate form are analyzed. The purpose of the analysis is the determination of long-term problems of system closure, of reasons for differences of exact solutions for low Reynolds numbers and the appearance of unstable solutions using computer programs.

  15. Stochastic 2-D Navier-Stokes Equation

    International Nuclear Information System (INIS)

    Menaldi, J.L.; Sritharan, S.S.

    2002-01-01

    In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution

  16. Solutions of Navier-Stokes Equation with Coriolis Force

    Directory of Open Access Journals (Sweden)

    Sunggeun Lee

    2017-01-01

    Full Text Available We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimensional flow, the vorticity vector ω gets shifted by the amount of -2Ω. Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow v→=∇→ϕ, the equation satisfied by ϕ is independent of Ω. The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration c and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of c.

  17. Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions

    Science.gov (United States)

    Tidriri, M. D.

    1995-01-01

    One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.

  18. HJB-POD feedback control for Navier-Stokes equations

    OpenAIRE

    Alla, Alessandro; Hinze, Michael

    2014-01-01

    In this report we present the approximation of an infinite horizon optimal control problem for the evolutive Navier-Stokes system. The method is based on a model reduction technique, using a POD approximation, coupled with a Hamilton-Jacobi equation which characterizes the value function of the corresponding control problem for the reduced system. Although the approximation schemes available for the HJB are shown to be convergent for any dimension, in practice we need to restrict the dimensio...

  19. About local fractional three-dimensional compressible Navier-Stokes equations in Cantor-type cylindrical co-ordinate system

    Directory of Open Access Journals (Sweden)

    Gao Guo-Ping

    2016-01-01

    Full Text Available In this article, we investigate the local fractional 3-D compressible Navier-Stokes equation via local fractional derivative. We use the Cantor-type cylindrical co-ordinate method to transfer 3-D compressible Navier-Stokes equation from the Cantorian co-ordinate system to the Cantor-type cylindrical co-ordinate system.

  20. Tip loss correction for actuator / Navier Stokes computations

    DEFF Research Database (Denmark)

    Shen, Wen Zhong; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming

    2004-01-01

    The new tip loss correction, initially developed for ID BEM computations [1], is now extended to 2D Actuator Disc / Navier-Stokes (AD/NS) computations and 3D Actuator Line / Navier-Stokes (AL/NS) computations. As shown in the paper, the tip loss correction is an important and necessary step...... for actuator / Navier-Stokes models. Comparisons of the present results with those obtained from a EM code with new tip correction and experimental data show that the tip loss correction is correctly implemented in the actuator / Navier-Stokes models. The results demonstrate also that difference between......, Actuator Line, Navier-Stokes equations, Tip loss correction....

  1. Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation.

    Science.gov (United States)

    Pesavento, Umberto; Wang, Z Jane

    2004-10-01

    We investigate the problem of falling paper by solving the two dimensional Navier-Stokes equations subject to the motion of a free-falling body at Reynolds numbers around 10(3). The aerodynamic lift on a tumbling plate is found to be dominated by the product of linear and angular velocities rather than velocity squared, as appropriate for an airfoil. This coupling between translation and rotation provides a mechanism for a brief elevation of center of mass near the cusplike turning points. The Navier-Stokes solutions further provide the missing quantity in the classical theory of lift, the instantaneous circulation, and suggest a revised model for the fluid forces.

  2. The Actuator Surface Model: A New Navier-Stokes Based Model for Rotor Computations

    DEFF Research Database (Denmark)

    Shen, Wen Zhong; Zhang, J.H.; Sørensen, Jens Nørkær

    2009-01-01

    This paper presents a new numerical technique for simulating two-dimensional wind turbine flow. The method, denoted as the 2D actuator surface technique, consists of a two-dimensional Navier-Stokes solver in which the pressure distribution is represented by body forces that are distributed along...... the chord of the airfoils. The distribution of body force is determined from a set of predefined functions that depend on angle of attack and airfoil shape. The predefined functions are curve fitted using pressure distributions obtained either from viscous-inviscid interactive codes or from full Navier-Stokes...... simulations. The actuator surface technique is evaluated by computing the two-dimensional flow past a NACA 0015 airfoil at a Reynolds number of 10(6) and an angle of attack of 10 deg and by comparing the computed streamlines with the results from a traditional Reynolds-averaged Navier-Stokes computation...

  3. Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations.

    Science.gov (United States)

    Vorobev, Anatoliy

    2010-11-01

    We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

  4. Solutions to three-dimensional Navier-Stokes equations for incompressible fluids

    Directory of Open Access Journals (Sweden)

    Jorma Jormakka

    2010-07-01

    Full Text Available This article gives explicit solutions to the space-periodic Navier-Stokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions, but the solution cannot be continued to the whole space.

  5. Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations

    Directory of Open Access Journals (Sweden)

    Junbai Ren

    2014-01-01

    Full Text Available This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with Lp-Lq estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C1(1+t-3/4≤uL2≤C2(1+t-3/4,  t>1. The decay rate is optimal since it coincides with that of heat equation.

  6. On three-dimensional incompressible Navier-Stokes fluid on cantor sets in spherical Cantor type co-ordinate system

    Directory of Open Access Journals (Sweden)

    Meng Zhi-Jun

    2016-01-01

    Full Text Available This paper addresses the systems of the incompressible Navier-Stokes equations on Cantor sets without the external force involving the fractal heat-conduction problem vial local fractional derivative. The spherical Cantor type co-ordinate method is used to transfer the incompressible Navier-Stokes equation from the Cantorian co-ordinate system into the spherical Cantor type co-ordinate system.

  7. Analyticity estimates for the Navier-Stokes equations

    DEFF Research Database (Denmark)

    Herbst, I.; Skibsted, Erik

    We study spatial analyticity properties of solutions of the Navier-Stokes equation and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes equation with data in and prove a stability result...

  8. Implications of Navier-Stokes turbulence theory for plasma turbulence

    International Nuclear Information System (INIS)

    Montgomery, David

    1977-01-01

    A brief discussion of Navier-Stokes turbulence theory is given with particular reference to the two dimensional case. The MHD turbulence is introduced with possible applications of techniques developed in Navier-Stokes theory. Turbulence in Vlasov plasma is also discussed from the point of view of the ''direct interaction approximation'' (DIA). (A.K.)

  9. A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

    Energy Technology Data Exchange (ETDEWEB)

    Hong Luo; Luqing Luo; Robert Nourgaliev; Vincent A. Mousseau

    2010-01-01

    A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.

  10. Application of homotopy perturbation method to the Navier-Stokes equations in cylindrical coordinates

    Directory of Open Access Journals (Sweden)

    H. A. Wahab

    2015-06-01

    Full Text Available This paper deals with the approximate analytical solution of the Navier-Stokes equations in cylindrical coordinates. The homotopy perturbation method is used to get the analytical approximation. Depending upon different available choices for the linear operator, we also have the advantage to choose different initial approximations to start our analysis. The analysis is done without calculating the Adomian's polynomials.

  11. Existence of global solutions to free boundary value problems for bipolar Navier-Stokes-Possion systems

    Directory of Open Access Journals (Sweden)

    Jian Liu

    2013-09-01

    Full Text Available In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.

  12. Flow split characterization of two immiscible phases with different wettability scenarios: a numerical investigation using a coupled Cahn-Hilliard and Navier-Stokes system

    KAUST Repository

    Bao, Kai

    2017-12-23

    Numerical investigation of flow branching of two-phase immiscible fluids in a Y-shaped, planner channel is conducted by solving the coupled Cahn-Hilliard and Naiver-Stokes system with finite element method. In this system a horizontal channel is branched into two identical and symmetric branches with the walls of the channels assigned several different wettability values. The studied scenarios consider a blob of one phase initially encompassed by the other phase. When an applied pressure difference induces flow, it is found that the motion of the blob in the two branches is significantly influenced by the wettability conditions at the channel walls. For the scenarios in which symmetric wettability configurations are applied, the blob divides equally among the two branches. For all the other scenarios in which the wettability configurations are asymmetric, the blob splits unequally. Comparisons between the different scenarios are performed in terms of the volume of the blob in each branch to investigate the percentage of the blob volume moving in each branch. In addition, we also considered the effect of the flow rate on the branching scenarios. In this work it is demonstrated that even though the pressure gradient is the same among the two symmetric branches, the phases partition differently when asymmetric wettability conditions are applied. The significance of this work may be that it provides evidences that relative permeability (a concept that has been introduced in the study of multiphase flow in porous media) may be more complex than just a mere scalar quantity function of saturation. It also highlights the importance of including the effects of wettability conditions in capillary pressure relationships

  13. Iterative methods for compressible Navier-Stokes and Euler equations

    Energy Technology Data Exchange (ETDEWEB)

    Tang, W.P.; Forsyth, P.A.

    1996-12-31

    This workshop will focus on methods for solution of compressible Navier-Stokes and Euler equations. In particular, attention will be focused on the interaction between the methods used to solve the non-linear algebraic equations (e.g. full Newton or first order Jacobian) and the resulting large sparse systems. Various types of block and incomplete LU factorization will be discussed, as well as stability issues, and the use of Newton-Krylov methods. These techniques will be demonstrated on a variety of model transonic and supersonic airfoil problems. Applications to industrial CFD problems will also be presented. Experience with the use of C++ for solution of large scale problems will also be discussed. The format for this workshop will be four fifteen minute talks, followed by a roundtable discussion.

  14. Hydrodynamic potentials for the micropolar Navier-Stokes problem

    International Nuclear Information System (INIS)

    Martynenko, M.D.; Dimian, M.

    1995-01-01

    An integral representation of linear and angular velocities and pressure for the description of linear stationary flows of micropolar viscous liquid media is obtained, and on its basis hydrodynamic potentials for the micropolar Navier-Stokes problem are introduced

  15. Regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations.

    Science.gov (United States)

    Gibbon, John D; Pal, Nairita; Gupta, Anupam; Pandit, Rahul

    2016-12-01

    We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter ϕ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J. T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984)CMPHAY0010-361610.1007/BF01212349]. By taking an L^{∞} norm of the energy of the full binary system, designated as E_{∞}, we have shown that ∫_{0}^{t}E_{∞}(τ)dτ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs) of the 3D CHNS equations for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with 128^{3} to 512^{3} collocation points and over the duration of our DNSs confirm that E_{∞} remains bounded as far as our computations allow.

  16. Relaxation Method for Navier-Stokes Equation

    Science.gov (United States)

    de Oliveira, P. M. C.

    2012-04-01

    The motivation for this work was a simple experiment [P. M. C. de Oliveira, S. Moss de Oliveira, F. A. Pereira and J. C. Sartorelli, preprint (2010), arXiv:1005.4086], where a little polystyrene ball is released falling in air. The interesting observation is a speed breaking. After an initial nearly linear time-dependence, the ball speed reaches a maximum value. After this, the speed finally decreases until its final, limit value. The provided explanation is related to the so-called von Kármán street of vortices successively formed behind the falling ball. After completely formed, the whole street extends for some hundred diameters. However, before a certain transient time needed to reach this steady-state, the street is shorter and the drag force is relatively reduced. Thus, at the beginning of the fall, a small and light ball may reach a speed superior to the sustainable steady-state value. Besides the real experiment, the numerical simulation of a related theoretical problem is also performed. A cylinder (instead of a 3D ball, thus reducing the effective dimension to 2) is positioned at rest inside a wind tunnel initially switched off. Suddenly, at t = 0 it is switched on with a constant and uniform wind velocity ěc{V} far from the cylinder and perpendicular to it. This is the first boundary condition. The second is the cylinder surface, where the wind velocity is null. In between these two boundaries, the velocity field is determined by solving the Navier-Stokes equation, as a function of time. For that, the initial condition is taken as the known Stokes laminar limit V → 0, since initially the tunnel is switched off. The numerical method adopted in this task is the object of the current text.

  17. Local strong solutions to the stochastic compressible Navier-Stokes system

    Czech Academy of Sciences Publication Activity Database

    Breit, D.; Feireisl, Eduard; Hofmanová, M.

    2018-01-01

    Roč. 43, č. 2 (2018), s. 313-345 ISSN 0360-5302 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible fluids * local strong solution s * Navier-Stokes system Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.608, year: 2016 https://www.tandfonline.com/doi/full/10.1080/03605302.2018.1442476

  18. Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations

    Directory of Open Access Journals (Sweden)

    Ning-Bo Tan

    2013-01-01

    Full Text Available An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.

  19. Local strong solutions to the stochastic compressible Navier-Stokes system

    Czech Academy of Sciences Publication Activity Database

    Breit, D.; Feireisl, Eduard; Hofmanová, M.

    2018-01-01

    Roč. 43, č. 2 (2018), s. 313-345 ISSN 0360-5302 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible fluids * local strong solutions * Navier-Stokes system Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.608, year: 2016 https://www.tandfonline.com/doi/full/10.1080/03605302.2018.1442476

  20. Incompressible limit of compressible Navier-Stokes equations

    International Nuclear Information System (INIS)

    Bessaih, H.

    1994-01-01

    In this paper we study the system which describes the motion of compressible viscous fluid in a bounded domain Ω of R 3 . When we introduce a parameter λ, that is the inverse of the Mach number, we prove, under small initial data and external force (for barotropic flows), that the solution of Navier-Stokes equations is the incompressible limit of the solution of compressible Navier-Stokes equations, as the Mach number becomes small. For this, we show the existence of a solution verifying estimates independent of λ. Compactness argument allow us to pass to the limit on λ in the nonlinear terms. (author). 17 refs

  1. Optimal control of compressible Navier-Stokes equations

    International Nuclear Information System (INIS)

    Ito, K.; Ravindran, S.S.

    1994-01-01

    Optimal control for the viscous incompressible flows, which are governed by incompressible Navier-Stokes equations, has been the subject of extensive study in recent years, see, e.g., [AT], [GHS], [IR], and [S]. In this paper we consider the optimal control of compressible isentropic Navier-Stokes equations. We develop the weak variational formulation and discuss the existence and necessary optimality condition characterizing the optimal control. A numerical method based on the mixed-finite element method is also discussed to compute the control and numerical results are presented

  2. Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term

    International Nuclear Information System (INIS)

    Johnston, Hans; Liu Jianguo

    2004-01-01

    We present numerical schemes for the incompressible Navier-Stokes equations based on a primitive variable formulation in which the incompressibility constraint has been replaced by a pressure Poisson equation. The pressure is treated explicitly in time, completely decoupling the computation of the momentum and kinematic equations. The result is a class of extremely efficient Navier-Stokes solvers. Full time accuracy is achieved for all flow variables. The key to the schemes is a Neumann boundary condition for the pressure Poisson equation which enforces the incompressibility condition for the velocity field. Irrespective of explicit or implicit time discretization of the viscous term in the momentum equation the explicit time discretization of the pressure term does not affect the time step constraint. Indeed, we prove unconditional stability of the new formulation for the Stokes equation with explicit treatment of the pressure term and first or second order implicit treatment of the viscous term. Systematic numerical experiments for the full Navier-Stokes equations indicate that a second order implicit time discretization of the viscous term, with the pressure and convective terms treated explicitly, is stable under the standard CFL condition. Additionally, various numerical examples are presented, including both implicit and explicit time discretizations, using spectral and finite difference spatial discretizations, demonstrating the accuracy, flexibility and efficiency of this class of schemes. In particular, a Galerkin formulation is presented requiring only C 0 elements to implement

  3. Multidimensional Stability of Large-Amplitude Navier-Stokes Shocks

    Science.gov (United States)

    Humpherys, Jeffrey; Lyng, Gregory; Zumbrun, Kevin

    2017-12-01

    Extending results of Humpherys-Lyng-Zumbrun in the one-dimensional case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the multidimensional stability of planar Navier-Stokes shocks across the full range of shock amplitudes, including the infinite-amplitude limit, for monatomic or diatomic ideal gas equations of state and viscosity and heat conduction coefficients {μ}, {μ +η}, and {ν=κ/c_v} constant and in the physical ratios predicted by statistical mechanics, and Mach number {M > 1.035}. Our results indicate unconditional stability within the parameter range considered; this agrees with the results of Erpenbeck and Majda for the corresponding inviscid case of Euler shocks. Notably, this study includes the first successful numerical computation of an Evans function associated with the multidimensional stability of a viscous shock wave. The methods introduced can be used in principle to decide stability for shocks in any polytropic gas, or indeed for shocks of other models, including in, particular, viscoelasticity, combustion, and magnetohydrodynamics (MHD).

  4. On analytical solution of the Navier-Stokes equations

    International Nuclear Information System (INIS)

    Scheffel, J.

    2001-04-01

    An analytical method for solving the dissipative, nonlinear and non-stationary Navier-Stokes equations is presented. Velocity and pressure is expanded in power series of cartesian coordinates and time. The method is applied to 2-D incompressible gravitational flow in a bounded, rectangular domain

  5. Navier-Stokes Calculations of Helicopter Fuselage Flowfield and Loads

    DEFF Research Database (Denmark)

    M, Costes; Filippone, Antonino; N, Kroll

    1999-01-01

    This paper describes the theoretically basedactivities conducted during the first year of theBrite/Euram Helifuse Porgramme. These activitiesmainly consisted of the numerical prediction ofhelicopter fuselage flowfields with existing Navier-Stokes solvers on a number of pre-selectedcases, taken out...

  6. Spatial Fourier modes controlling Navier-Stokes flow

    International Nuclear Information System (INIS)

    Treve, Y.M.

    1982-01-01

    As shown by Foias and Prodi in the limit of infinite times the solutions of the two-dimensional Navier-Stokes equations depend only on a finite number of modes, a number for which rigorous estimates can be obtained. A survey of these results is given together with further developments, notably in connection with the numerical approximation to the exact solutions. (Auth.)

  7. Symmetric approximations of the Navier-Stokes equations

    International Nuclear Information System (INIS)

    Kobel'kov, G M

    2002-01-01

    A new method for the symmetric approximation of the non-stationary Navier-Stokes equations by a Cauchy-Kovalevskaya-type system is proposed. Properties of the modified problem are studied. In particular, the convergence as ε→0 of the solutions of the modified problem to the solutions of the original problem on an infinite interval is established

  8. Analysis of regularized Navier-Stokes equations, 2

    Science.gov (United States)

    Ou, Yuh-Roung; Sritharan, S. S.

    1989-01-01

    A practically important regularization of the Navier-Stokes equations was analyzed. As a continuation of the previous work, the structure of the attractors characterizing the solutins was studied. Local as well as global invariant manifolds were found. Regularity properties of these manifolds are analyzed.

  9. The Navier-Stokes Equations Theory and Numerical Methods

    CERN Document Server

    Masuda, Kyûya; Rautmann, Reimund; Solonnikov, Vsevolod

    1990-01-01

    These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.

  10. A Regularity Criterion for Positive Part of Radial Component in the Case of Axially Symmetric Navier-Stokes Equations

    Directory of Open Access Journals (Sweden)

    Kubica Adam

    2015-03-01

    Full Text Available We examine the conditional regularity of the solutions of Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axially symmetric. We show that if positive part of the radial component of velocity satisfies a weighted Serrin type condition and in addition angular component satisfies some condition, then the solution is regular.

  11. Vanishing viscosity limit for the 3D nonhomogeneous incompressible Navier-Stokes equation with special slip boundary condition

    Directory of Open Access Journals (Sweden)

    Pengfei Chen

    2017-07-01

    Full Text Available In this article we consider the three-dimensional nonhomogeneous incompressible Navier-Stokes equation with special slip boundary conditions in a bounded domain. We discuss the problem of the vanishing viscosity limit and provide a rate of convergence estimates for the strong solution.

  12. Strong solutions for the Navier-Stokes equations on bounded and unbounded domains with a moving boundary

    Directory of Open Access Journals (Sweden)

    Juergen Saal

    2007-02-01

    Full Text Available It is proved under mild regularity assumptions on the data that the Navier-Stokes equations in bounded and unbounded noncylindrical regions admit a unique local-in-time strong solution. The result is based on maximal regularity estimates for the in spatial regions with a moving boundary obtained in [16] and the contraction mapping principle.

  13. Viscous-inviscid interaction using the parabolized Navier-Stokes equations

    DEFF Research Database (Denmark)

    Filippone, Antonino; Sørensen, Jens Nørkær

    1997-01-01

    adaptive grid is used.The interaction is achieved by iterative updatingof the boundary conditions, through the wall transpiration concept. The Navier-Stokes equationsare discretized on a semi-staggered grid.Space-marching integration is performed starting from the stagnation streamline ontwo independent......A numerical model for the calculation of incompressible viscous flows past airfoils andwings has been developed. The approach is based on a strong viscous-inviscid coupling of aboundary element method with the Navier-Stokesequations in vorticity-streamfunction formulation.A semi-adaptive or fully...

  14. A Navier-Stokes phase-field crystal model for colloidal suspensions.

    Science.gov (United States)

    Praetorius, Simon; Voigt, Axel

    2015-04-21

    We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier-Stokes Phase-Field Crystal model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and is used to analyze colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We further validate the model against other computational approaches for particulate flow systems for various colloidal sedimentation problems.

  15. Local lubrication model for spherical particles within incompressible Navier-Stokes flows

    Science.gov (United States)

    Lambert, B.; Weynans, L.; Bergmann, M.

    2018-03-01

    The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

  16. Partial Averaged Navier-Stokes approach for cavitating flow

    International Nuclear Information System (INIS)

    Zhang, L; Zhang, Y N

    2015-01-01

    Partial Averaged Navier Stokes (PANS) is a numerical approach developed for studying practical engineering problems (e.g. cavitating flow inside hydroturbines) with a resonance cost and accuracy. One of the advantages of PANS is that it is suitable for any filter width, leading a bridging method from traditional Reynolds Averaged Navier-Stokes (RANS) to direct numerical simulations by choosing appropriate parameters. Comparing with RANS, the PANS model will inherit many physical nature from parent RANS but further resolve more scales of motion in great details, leading to PANS superior to RANS. As an important step for PANS approach, one need to identify appropriate physical filter-width control parameters e.g. ratios of unresolved-to-total kinetic energy and dissipation. In present paper, recent studies of cavitating flow based on PANS approach are introduced with a focus on the influences of filter-width control parameters on the simulation results

  17. Euler and Navier-Stokes equations on the hyperbolic plane.

    Science.gov (United States)

    Khesin, Boris; Misiolek, Gerard

    2012-11-06

    We show that nonuniqueness of the Leray-Hopf solutions of the Navier-Stokes equation on the hyperbolic plane (2) observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on (n) whenever n ≥ 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.

  18. Navier-Stokes-like equations for traffic flow.

    Science.gov (United States)

    Velasco, R M; Marques, W

    2005-10-01

    The macroscopic traffic flow equations derived from the reduced Paveri-Fontana equation are closed starting with the maximization of the informational entropy. The homogeneous steady state taken as a reference is obtained for a specific model of the desired velocity and a kind of Chapman-Enskog method is developed to calculate the traffic pressure at the Navier-Stokes level. Numerical solution of the macroscopic traffic equations is obtained and its characteristics are analyzed.

  19. The Navier-Stokes equations on a bounded domain

    International Nuclear Information System (INIS)

    Scheffer, V.

    1980-01-01

    Suppose U is an open bounded subset of 3-space such that the boundary of U has Lebesgue measure zero. Then for any initial condition with finite kinetic energy we can find a global (i.e. for all time) weak solution u to the time dependent Navier-Stokes equations of incompressible fluid flow in U such that the curl of u is continuous outside a locally closed set whose 5/3 dimensional Hausdorff measure is finite. (orig.)

  20. Homogenization of the evolutionary Navier-Stokes system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Namlyeyeva, Yuliya; Nečasová, Šárka

    2016-01-01

    Roč. 149, č. 1 (2016), s. 251-274 ISSN 0025-2611 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes system Subject RIV: BA - General Mathematics Impact factor: 0.607, year: 2016 http://link.springer.com/article/10.1007%2Fs00229-015-0778-y

  1. Stability result for Navier-Stokes equations with entropy transport

    Czech Academy of Sciences Publication Activity Database

    Michálek, Martin

    2015-01-01

    Roč. 17, č. 2 (2015), s. 279-285 ISSN 1422-6928 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes system * entropy transport * effective viscous flux Subject RIV: BA - General Mathematics Impact factor: 1.023, year: 2015 http://link.springer.com/article/10.1007%2Fs00021-015-0205-x

  2. Homogenization of Stokes and Navier-Stokes equations

    International Nuclear Information System (INIS)

    Allaire, G.

    1990-04-01

    This thesis is devoted to homogenization of Stokes and Navier-Stokes equations with a Dirichlet boundary condition in a domain containing many tiny obstacles. Tipycally those obstacles are distributed at the modes of a periodic lattice with same small period in each axe's direction, and their size is always asymptotically smaller than the lattice's step. With the help of the energy method, and thanks to a suitable pressure's extension, we prove the convergence of the homogenization process when the lattice's step tends to zero (and thus the number of obstacles tends to infinity). For a so-called critical size of the obstacles, the homogenized problem turns out to be a Brinkman's law (i.e. Stokes or Navier-Stokes equation plus a linear zero-order term for the velocity in the momentum equation). For obstacles which have a size smaller than the critical one, the limit problem reduces to the initial Stokes or Navier-Stokes equations, while for larger sizes the homogenized problem a Darcy's law. Furthermore, those results have been extended to the case of obstacles included in a hyperplane, and we establish a simple model of fluid flows through grids, which is based on a special form of Brinkman's law [fr

  3. Self-similarity in incompressible Navier-Stokes equations.

    Science.gov (United States)

    Ercan, Ali; Kavvas, M Levent

    2015-12-01

    The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space.

  4. p-Euler equations and p-Navier-Stokes equations

    Science.gov (United States)

    Li, Lei; Liu, Jian-Guo

    2018-04-01

    We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

  5. Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations

    KAUST Repository

    Le Maitre, Olivier

    2014-01-06

    In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.

  6. Study of blade-tower interaction using a 2D Navier-Stokes solver

    Energy Technology Data Exchange (ETDEWEB)

    Bertagnolio, F. [Risoe National Lab., Wind Energy and Atmospheric Physics Dept., Roskilde (Denmark)

    1999-03-01

    The aim of this work is to model and study the dynamic interaction of the fluid flow with the structure which occurs when the blades of a wind turbine are passing in front of (or possibly behind) the tower. In order to capture the whole complexity of this phenomenon, the full unsteady Navier-Stokes equations for an incompressible fluid are used as a model. A new computational technique is described. For the sake of simplicity, we restrict ourselves to two-dimensional cases. The present methodology is illustrated by the computation of a wind turbine-like configuration in a periodic domain. (au)

  7. Direct and iterative algorithms for the parallel solution of the one-dimensional macroscopic Navier-Stokes equations

    International Nuclear Information System (INIS)

    Doster, J.M.; Sills, E.D.

    1986-01-01

    Current efforts are under way to develop and evaluate numerical algorithms for the parallel solution of the large sparse matrix equations associated with the finite difference representation of the macroscopic Navier-Stokes equations. Previous work has shown that these equations can be cast into smaller coupled matrix equations suitable for solution utilizing multiple computer processors operating in parallel. The individual processors themselves may exhibit parallelism through the use of vector pipelines. This wor, has concentrated on the one-dimensional drift flux form of the Navier-Stokes equations. Direct and iterative algorithms that may be suitable for implementation on parallel computer architectures are evaluated in terms of accuracy and overall execution speed. This work has application to engineering and training simulations, on-line process control systems, and engineering workstations where increased computational speeds are required

  8. Incompressible Navier-Stokes equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell theories

    International Nuclear Information System (INIS)

    Niu Chao; Tian Yu; Wu Xiaoning; Ling Yi

    2012-01-01

    The dual fluid description for a general cutoff surface at radius r=r c outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter ε, the coupled Einstein-Maxwell equations are solved up to O(ε 2 ). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density η/s is independent of both the cutoff r c and the black brane charge. Then, we extend our discussion to the Gauss-Bonnet-Maxwell case, where the incompressible Navier-Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio η/s is independent of the cutoff r c but dependent on the charge density of the black brane.

  9. Strong plasma shock structures based on the Navier--Stokes equations

    International Nuclear Information System (INIS)

    Abe, K.

    1975-01-01

    The structure of a plasma collisional shock wave is examined on the basis of the Navier--Stokes equations and simultaneously on the basis of the Fokker--Planck equation. The resultant structures are compared to check the validity of the Navier--Stokes equations applied to the structures of strong shock waves. The Navier--Stokes equations give quite correct structures for weak shock waves. For the strong shock waves, the detailed structures obtained from the Navier--Stokes equations differ from the results of the Fokker--Planck equation, but the shock thicknesses of the two shock waves are in relatively close agreement

  10. Towards an ideal preconditioner for linearized Navier-Stokes problems

    Energy Technology Data Exchange (ETDEWEB)

    Murphy, M.F. [Univ. of Bristol (United Kingdom)

    1996-12-31

    Discretizing certain linearizations of the steady-state Navier-Stokes equations gives rise to nonsymmetric linear systems with indefinite symmetric part. We show that for such systems there exists a block diagonal preconditioner which gives convergence in three GMRES steps, independent of the mesh size and viscosity parameter (Reynolds number). While this {open_quotes}ideal{close_quotes} preconditioner is too expensive to be used in practice, it provides a useful insight into the problem. We then consider various approximations to the ideal preconditioner, and describe the eigenvalues of the preconditioned systems. Finally, we compare these preconditioners numerically, and present our conclusions.

  11. Smooth solutions of the Navier-Stokes equations

    International Nuclear Information System (INIS)

    Pokhozhaev, S I

    2014-01-01

    We consider smooth solutions of the Cauchy problem for the Navier-Stokes equations on the scale of smooth functions which are periodic with respect to x∈R 3 . We obtain existence theorems for global (with respect to t>0) and local solutions of the Cauchy problem. The statements of these depend on the smoothness and the norm of the initial vector function. Upper bounds for the behaviour of solutions in both classes, which depend on t, are also obtained. Bibliography: 10 titles

  12. Boltzmann equation and hydrodynamics beyond Navier-Stokes.

    Science.gov (United States)

    Bobylev, A V

    2018-04-28

    We consider in this paper the problem of derivation and regularization of higher (in Knudsen number) equations of hydrodynamics. The author's approach based on successive changes of hydrodynamic variables is presented in more detail for the Burnett level. The complete theory is briefly discussed for the linearized Boltzmann equation. It is shown that the best results in this case can be obtained by using the 'diagonal' equations of hydrodynamics. Rigorous estimates of accuracy of the Navier-Stokes and Burnett approximations are also presented.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

  13. Capillary-gravity waves and the Navier-Stokes equation

    International Nuclear Information System (INIS)

    Behroozi, F.; Podolefsky, N.

    2001-01-01

    Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation. (author)

  14. Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations

    KAUST Repository

    Gomez, Hector

    2010-05-01

    This paper is devoted to the numerical simulation of the Navier-Stokes-Korteweg equations, a phase-field model for water/water-vapor two-phase flows. We develop a numerical formulation based on isogeometric analysis that permits straightforward treatment of the higher-order partial-differential operator that represents capillarity. We introduce a new refinement methodology that desensitizes the numerical solution to the computational mesh and achieves mesh invariant solutions. Finally, we present several numerical examples in two and three dimensions that illustrate the effectiveness and robustness of our approach. © 2010 Elsevier B.V.

  15. Implicit upwind methods for the compressible Navier-Stokes equations

    Science.gov (United States)

    Coakley, T. J.

    1983-01-01

    A class of implicit upwind-differencing methods for the compressible Navier-Stokes equations is described and applied. The methods are based on the use of local eigenvalues or wave speeds to control spatial differencing of inviscid terms and are aimed at increasing the level of accuracy and stability achievable in computation. Techniques for accelerating the rate of convergence to a steady-state solution are also used. Applications to inviscid and viscous transonic flows are discussed and compared with other methods and experimental measurements. It is shown that accurate and efficient transonic airfoil calculations can be made on the Cray-1 coomputer in less than 2 min.

  16. Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

    KAUST Repository

    Mohamed, Mamdouh S.

    2017-05-23

    A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

  17. Modeling Vortex Generators in a Navier-Stokes Code

    Science.gov (United States)

    Dudek, Julianne C.

    2011-01-01

    A source-term model that simulates the effects of vortex generators was implemented into the Wind-US Navier-Stokes code. The source term added to the Navier-Stokes equations simulates the lift force that would result from a vane-type vortex generator in the flowfield. The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, subsonic flow in an S-duct with 22 corotating vortex generators, and supersonic flow in a rectangular duct with a counter-rotating vortex-generator pair. The model was also used to successfully simulate microramps in supersonic flow by treating each microramp as a pair of vanes with opposite angles of incidence. The validation results indicate that the source-term vortex-generator model provides a useful tool for screening vortex-generator configurations and gives comparable results to solutions computed using gridded vanes.

  18. A stable penalty method for the compressible Navier-Stokes equations: I. Open boundary conditions

    DEFF Research Database (Denmark)

    Hesthaven, Jan; Gottlieb, D.

    1996-01-01

    The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization...

  19. A Sensitivity Study of the Navier-Stokes- α Model

    Science.gov (United States)

    Breckling, Sean; Neda, Monika

    2017-11-01

    We present a sensitivity study of the of the Navier Stokes- α model (NS α) with respect to perturbations of the differential filter length α. Parameter-sensitivity is evaluated using the sensitivity equations method. Once formulated, the sensitivity equations are discretized and computed alongside the NS α model using the same finite elements in space, and Crank-Nicolson in time. We provide a complete stability analysis of the scheme, along with the sensitivity results of several benchmark problems in both 2D and 3D. We further demonstrate a practical technique to determine the reliability of the NS α model in problem-specific settings. Lastly, we investigate the sensitivity and reliability of important functionals of the velocity and pressure solutions.

  20. Beyond the Navier-Stokes equations: Burnett hydrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Garcia-Colin, L.S. [Department of Physics, Universidad Autonoma Metropolitana - Iztapalapa, Mexico D. F. 09340 (Mexico); El Colegio Nacional, Centro Historico, Mexico, 06020 (Mexico)], E-mail: lgcs@xanum.uam.mx; Velasco, R.M. [Department of Physics, Universidad Autonoma Metropolitana - Iztapalapa, Mexico D. F. 09340 (Mexico)], E-mail: rmvb@xanum.uam.mx; Uribe, F.J. [Department of Physics, Universidad Autonoma Metropolitana - Iztapalapa, Mexico D. F. 09340 (Mexico)], E-mail: paco@xanum.uam.mx

    2008-08-15

    This work is mainly concerned with the extension of hydrodynamics beyond the Navier-Stokes equations, a regime known as Burnett hydrodynamics. The derivation of the Burnett equations is considered from several theoretical approaches. In particular we discuss the Chapman-Enskog, Grad's method, and Truesdell's approach for solving the Boltzmann equation. Also, their derivation using the macroscopic approach given by extended thermodynamics is mentioned. The problems and successes of these equations are discussed and some alternatives proposed to improve them are mentioned. Comparisons of the predictions coming from the Burnett equations with experiments and/or simulations are given in order to have the necessary elements to give a critical assessment of their validity and usefulness.

  1. Navier-Stokes Dynamics by a Discrete Boltzmann Model

    Science.gov (United States)

    Rubinstein, Robet

    2010-01-01

    This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

  2. An upwind algorithm for the parabolized Navier-Stokes equations

    Science.gov (United States)

    Lawrence, S. L.; Tannehill, J. C.; Chaussee, D. S.

    1986-01-01

    A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method does not require the addition of user specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming scheme in terms of accuracy, stability, computer time and storage, and programming effort. The new algorithm has been validated by applying it to three laminar test cases including flat plate boundary-layer flow, hypersonic flow past a 15 deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with the results obtained using the conventional Beam-Warming algorithm.

  3. Perturbation of eigenvalues of preconditioned Navier-Stokes operators

    Energy Technology Data Exchange (ETDEWEB)

    Elman, H.C. [Univ. of Maryland, College Park, MD (United States)

    1996-12-31

    We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steady-state Navier-Stokes equations. In particular, for several choices of preconditioners applied to the system of discrete equations, we derive upper bounds on perturbations of eigenvalues as functions of the viscosity and discretization mesh size. The bounds suggest that the sensitivity of the eigenvalues is at worst linear in the inverse of the viscosity and quadratic in the inverse of the mesh size, and that scaling can be used to decrease the sensitivity in some cases. Experimental results supplement these results and confirm the relatively mild dependence on viscosity. They also indicate a dependence on the mesh size of magnitude smaller than the analysis suggests.

  4. On Critical Spaces for the Navier-Stokes Equations

    Science.gov (United States)

    Prüss, Jan; Wilke, Mathias

    2017-10-01

    The abstract theory of critical spaces developed in Prüss and Wilke (J Evol Equ, 2017. doi: 10.1007/s00028-017-0382-6), Prüss et al. (Critical spaces for quasilinear parabolic evolution equations and applications, 2017) is applied to the Navier-Stokes equations in bounded domains with Navier boundary conditions as well as no-slip conditions. Our approach unifies, simplifies and extends existing work in the L_p -L_q setting, considerably. As an essential step, it is shown that the strong and weak Stokes operators with Navier conditions admit an H^∞-calculus with H^∞-angle 0, and the real and complex interpolation spaces of these operators are identified.

  5. Turbulence modeling methods for the compressible Navier-Stokes equations

    Science.gov (United States)

    Coakley, T. J.

    1983-01-01

    Turbulence modeling methods for the compressible Navier-Stokes equations, including several zero- and two-equation eddy-viscosity models, are described and applied. Advantages and disadvantages of the models are discussed with respect to mathematical simplicity, conformity with physical theory, and numerical compatibility with methods. A new two-equation model is introduced which shows advantages over other two-equation models with regard to numerical compatibility and the ability to predict low-Reynolds-number transitional phenomena. Calculations of various transonic airfoil flows are compared with experimental results. A new implicit upwind-differencing method is used which enhances numerical stability and accuracy, and leads to rapidly convergent steady-state solutions.

  6. Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

    Science.gov (United States)

    Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

    2015-01-01

    Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

  7. Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

    Science.gov (United States)

    Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

    2014-01-01

    Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

  8. Towards a Navier Stokes-Darcy Upscaling Based on Permeability Tensor Computation

    KAUST Repository

    Lieb, M.

    2012-06-02

    The micro scale simulation of CO2 sequestration involves complex, porous-like geometries. For the generation of such geometries, we present two approaches: In 2D, we construct a fractured domain by channel networks. In 3D, we approximate sand grain-like scenarios by dense sphere packings. The flow through these structures is simulated with the incompressible Navier-Stokes solver of the PDE framework Peano. Using an upscaling scheme, the results of the micro scale are used as input data for a Darcy solver on the coarse scales. The coupling concept and the scenario generators are presented together with first simulation results showing the validity of the approach.

  9. Investigation of the use of Prandtl/Navier--Stokes equation procedures for two-dimensional incompressible flows

    International Nuclear Information System (INIS)

    Anderson, C.R.; Reider, M.B.

    1994-01-01

    The technique of combining solutions of the Prandtl equations with solutions of the Navier--Stokes equations to compute incompressible flow around two-dimensional bodies is investigated herein. Computational evidence is presented which shows that if the ''obvious'' coupling is used to combine the solutions, then the resulting solution is not accurate. An alternate coupling procedure is described which greatly improves the accuracy of the solutions obtained with the combined equation approach. An alternate coupling that can be used to create a more accurate vortex sheet/vortex blob method is then shown

  10. Dimension reduction for the full Navier-Stokes-Fourier system

    Czech Academy of Sciences Publication Activity Database

    Březina, J.; Kreml, Ondřej; Mácha, Václav

    2017-01-01

    Roč. 19, č. 4 (2017), s. 659-683 ISSN 1422-6928 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier–Stokes–Fourier system * dimension reduction * relative entropy Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.106, year: 2016 https://link.springer.com/article/10.1007%2Fs00021-016-0301-6

  11. Dimension reduction for the full Navier-Stokes-Fourier system

    Czech Academy of Sciences Publication Activity Database

    Březina, J.; Kreml, Ondřej; Mácha, Václav

    2017-01-01

    Roč. 19, č. 4 (2017), s. 659-683 ISSN 1422-6928 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier–Stokes–Fourier system * dimension reduction * relative entropy Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.106, year: 2016 https://link. springer .com/article/10.1007%2Fs00021-016-0301-6

  12. Continuous Genetic Algorithm as a Novel Solver for Stokes and Nonlinear Navier Stokes Problems

    Directory of Open Access Journals (Sweden)

    Z. S. Abo-Hammour

    2014-01-01

    Full Text Available The one-dimensional continuous genetic algorithm (CGA previously developed by the principal author is extended and enhanced to deal with two-dimensional spaces in this paper. The enhanced CGA converts the partial differential equations into algebraic equations by replacing the derivatives appearing in the differential equation with their proper finite difference formula in 2D spaces. This optimization methodology is then applied for the solution of steady-state two-dimensional Stokes and nonlinear Navier Stokes problems. The main advantage of using CGA for the solution of partial differential equations is that the algorithm can be applied to linear and nonlinear equations without any modification in its structure. A comparison between the results obtained using the 2D CGA and the known Galerkin finite element method using COMSOL is presented in this paper. The results showed that CGA has an excellent accuracy as compared to other numerical solvers.

  13. Multigrid solution of the Navier-Stokes equations at low speeds with large temperature variations

    International Nuclear Information System (INIS)

    Sockol, Peter M.

    2003-01-01

    Multigrid methods for the Navier-Stokes equations at low speeds and large temperature variations are investigated. The compressible equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. Three implicit smoothers have been incorporated into a common multigrid procedure. Both full coarsening and semi-coarsening with directional fine-grid defect correction have been studied. The resulting methods have been tested on four 2D laminar problems over a range of Reynolds numbers on both uniform and highly stretched grids. Two of the three methods show efficient and robust performance over the entire range of conditions. In addition, none of the methods has any difficulty with the large temperature variations

  14. Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review

    Directory of Open Access Journals (Sweden)

    Bermejo Rodolfo

    2016-09-01

    Full Text Available We review in this paper the development of Lagrange-Galerkin (LG methods to integrate the incompressible Navier-Stokes equations (NSEs for engineering applications. These methods were introduced in the computational fluid dynamics community in the early eighties of the past century, and at that time they were considered good methods for both their theoretical stability properties and the way of dealing with the nonlinear terms of the equations; however, the numerical experience gained with the application of LG methods to different problems has identified drawbacks of them, such as the calculation of specific integrals that arise in their formulation and the calculation of the ow trajectories, which somehow have hampered the applicability of LG methods. In this paper, we focus on these issues and summarize the convergence results of LG methods; furthermore, we shall briefly introduce a new stabilized LG method suitable for high Reynolds numbers.

  15. Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation

    Directory of Open Access Journals (Sweden)

    Yuncheng You

    2008-12-01

    Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.

  16. Analysis of the Scramjet inlet flow field using two-dimensional Navier-Stokes equations

    Science.gov (United States)

    Kumar, A.; Tiwari, S. N.

    1982-01-01

    A computer code was developed to solve the full two dimensional Navier-Stokes equations in a scramjet inlet. The analysis uses a numerical coordinate transformation which generates a set of boundary-fitted curvilinear coordinates. The explicit finite difference algorithm of MacCormack is used to solve the governing equations. A two-layer eddy viscosity model is used for the turbulent flow. The code can analyze both inviscid and viscous flows with multiple struts in the flow field. Detailed results are presented for two model problems and two scramjet inlets with one and two struts. The application of the two dimensional analysis in the preliminary design of the actual scramjet inlet is briefly discussed.

  17. Boundedness, almost periodicity and stability of certain Navier-Stokes flows in unbounded domains

    Science.gov (United States)

    Nguyen, Thieu Huy; Trinh, Viet Duoc; Vu, Thi Ngoc Ha; Vu, Thi Mai

    2017-12-01

    We investigate the existence, uniqueness and stability of bounded and almost periodic mild solutions to several Navier-Stokes flow problems. In our strategy, we propose a general framework for studying the semi-linear evolution equations with certain smoothing properties of the linear part and with the local Lipschitz continuity of the nonlinear operator. Our method is based on interpolation functors combined with differential inequalities. Our abstract results are applied to Navier-Stokes-Oseen equations describing flows of incompressible viscous fluid passing a translating and rotating obstacle and to Navier-Stokes equations on aperture domains and/or in Besov spaces.

  18. Simulation of time-dependent free-surface Navier-Stokes flows

    International Nuclear Information System (INIS)

    Muldowney, G.P.

    1989-01-01

    Two numerical methods for simulation of time-dependent free-surface Navier-Stokes flows are developed. Both techniques are based on semi-implicit time advancement of the momentum equations, integral formulation of the spatial problem at each timestep, and spectral-element discretization to solve the resulting integral equation. Central to each algorithm is a boundary-specific solution step which permits the spatial treatment in two dimensions to be performed in O(N 3 ) operations per timestep despite the presence of deforming geometry. The first approach is a domain-integral formulation involving integrals over the entire flow domain of kernel functions which arise in time-differencing the Navier-Stokes equations. The second is a particular-solution formulation which replaces domain integration with an iterative scheme to generate particular velocity and pressure fields on individual elements, followed by a patching step to produce a particular solution continuous over the full domain. Two of the most difficult aspects of viscous free-surface flow simulations, namely time-dependent geometry and nontrivial boundary conditions, are well accommodated by these integral equation techniques. In addition the methods offer spectral accuracy in space and admit arbitrarily high-order discretization in time. For large-scale computations and/or long-term time advancement the domain-integral algorithm must be executed on a supercomputer to deliver results in reasonable processing time. A detailed simulation of gas liquid flow with full resolution of the free phase boundary requires approximately five CPU hours at 80 megaflops

  19. Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP

    Science.gov (United States)

    Vadyak, Joseph; Shrewsbury, George E.; Narramore, Jim C.; Montry, Gary; Holst, Terry; Kwak, Dochan (Technical Monitor)

    1995-01-01

    The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time

  20. Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization

    Science.gov (United States)

    Espejo, Elio; Winkler, Michael

    2018-04-01

    The interplay of chemotaxis, convection and reaction terms is studied in the particular framework of a refined model for coral broadcast spawning, consisting of three equations describing the population densities of unfertilized sperms and eggs and the concentration of a chemical released by the latter, coupled to the incompressible Navier-Stokes equations. Under mild assumptions on the initial data, global existence of classical solutions to an associated initial-boundary value problem in bounded planar domains is established. Moreover, all these solutions are shown to approach a spatially homogeneous equilibrium in the large time limit.

  1. Numerical study of a multigrid method with four smoothing methods for the incompressible Navier-Stokes equations in general coordinates

    Science.gov (United States)

    Zeng, S.; Wesseling, P.

    1993-01-01

    The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.

  2. Investigation of vortex breakdown on a delta wing using Euler and Navier-Stokes equations

    Science.gov (United States)

    Agrawal, S.; Barnett, R. M.; Robinson, B. A.

    1991-01-01

    A numerical investigation of leading edge vortex breakdown in a delta wing at high angles of attack is presented. The analysis was restricted to low speed flows on a flat plate wing with sharp leading edges. Both Euler and Navier-Stokes equations were used and the results were compared with experimental data. Predictions of vortex breakdown progression with angle of attack with both Euler and Navier-Stokes equations are shown to be consistent with the experimental data. However, the Navier-Stokes predictions show significant improvements in breakdown location at angles of attack where the vortex breakdown approaches the wing apex. The predicted trajectories of the primary vortex are in very good agreement with the test data, the laminar solutions providing the overall best comparison. The Euler shows a small displacement of the primary vortex, relative to experiment, due to the lack of secondary vortices. The turbulent Navier-Stokes, in general, fall between the Euler and laminar solutions.

  3. COMOC: a finite-element algorithm for the Navier-Stokes equations

    Science.gov (United States)

    Baker, A. J.; Bauer, A. M.; Manhardt, P. D.; Orzechowski, J. A.

    1976-01-01

    Finite-element algorithm devised to facilitate solution of two-dimensional Navier-Stokes equations governing kinematics and thermodynamics of variable-viscosity, compressible, multiple-species fluid. Algorithm has been implemented into existing computer program system.

  4. About Navier-Stokes Equation in the Theory of Convective Heat Transfer

    Science.gov (United States)

    Davidzon, M. Y.

    2017-10-01

    A system of differential equations (Navier-Stokes, continuity, heat conductivity) is used to solve convective heat transfer problems. While solving Navier-Stokes equation, it is usually assumed that tangent stress is proportional to the velocity gradient. This assumption is valid with a small velocity gradient, for example, near an axis of the channel, but velocity gradient can be very large near the channel wall. Our paper shows that if we accept power law instead of linear law for tangential stress, then the velocity profile for creeping, laminar, and turbulent flow in the channel can be calculated without using Navier-Stokes equation. Also, in this case Navier-Stokes equation itself changes: the coefficient of dynamic viscosity changes its value from normal (in case of the creeping flow) to tending to infinity (in case of the well-developed turbulent flow).

  5. Impact of the inherent separation of scales in the Navier-Stokes- alphabeta equations.

    Science.gov (United States)

    Kim, Tae-Yeon; Cassiani, Massimo; Albertson, John D; Dolbow, John E; Fried, Eliot; Gurtin, Morton E

    2009-04-01

    We study the effect of the length scales alpha and beta in the Navier-Stokes- alphabeta equations on the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor in three-dimensional homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier-Stokes- alpha and Navier-Stokes equations. A significant increase in the accuracy of the energy spectrum at large wave numbers arises for betaNavier-Stokes- alphabeta equations also improve as beta decreases away from alpha . However, optimal choices for alpha and beta depend not only on the problem of interest but also on the grid resolution.

  6. The incompressible non-relativistic Navier-Stokes equation from gravity

    International Nuclear Information System (INIS)

    Bhattacharyya, Sayantani; Minwalla, Shiraz; Wadia, Spenta R.

    2009-01-01

    We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.

  7. Decay Properties of Axially Symmetric D-Solutions to the Steady Navier-Stokes Equations

    Science.gov (United States)

    Weng, Shangkun

    2018-03-01

    We investigate the decay properties of smooth axially symmetric D-solutions to the steady Navier-Stokes equations. The achievements of this paper are two folds. One is improved decay rates of u_{θ } and \

  8. Moment realizability and the validity of the Navier - Stokes equations for rarefied gas dynamics

    International Nuclear Information System (INIS)

    Levermore, C.D.; Morokoff, W.J.; Nadiga, B.T.

    1998-01-01

    We present criteria for monitoring the validity of the Navier - Stokes approximation during the simulation of a rarefied gas. Our approach is based on an underlying kinetic formulation through which one can construct nondimensional non-negative definite matrices from moments of the molecular distribution. We then identify one such 3x3 matrix that can be evaluated intrinsically in the Navier - Stokes approximation. Our criteria are based on deviations of the eigenvalues of this matrix from their equilibrium value of unity. Not being tied to a particular benchmark problem, the resulting criteria are portable and may be applied to any Navier - Stokes simulation. We study its utility here by comparing stationary planar shock profiles computed using the Navier - Stokes equations with those computed using Monte Carlo simulations. copyright 1998 American Institute of Physics

  9. Random Attractors for the Stochastic Navier-Stokes Equations on the 2D Unit Sphere

    Science.gov (United States)

    Brzeźniak, Z.; Goldys, B.; Le Gia, Q. T.

    2018-03-01

    In this paper we prove the existence of random attractors for the Navier-Stokes equations on 2 dimensional sphere under random forcing irregular in space and time. We also deduce the existence of an invariant measure.

  10. Possible and impossible solutions of the Navier-Stokes equations

    International Nuclear Information System (INIS)

    Irmay, S.

    1998-01-01

    Flow of isochoric constant-viscosity fluids obeys continuity and the Navier-Stokes equations. They are difficult to solve being nonlinear with a nonslip boundary condition at solid walls. Berker presented many solutions, but some of them, e.g. irrotational velocity, contradict the repulsion condition. Radial flow, possible between two nonparallel planes, is shown to be impossible in a cone, though an approximate solution exists. Parallel (equidistant) streamlines are possible only if rectilinear, concentric or coaxial circles, or helices of equal inclination on coaxial cylinders. Two-way flows resemble ideal and Stokes flows. The author presents some spatial jets impacting on a fixed or parallelly moving boundary. A general unsteady spatial solution near a plane boundary is expressed as power series of z, distance from the wall, which shows most boundary layer solutions to be valid only up to z 2 terms. Uniform steady-state flow at a constant piezo metric gradient in the x-direction, between nonparallel planes, has a definite solution only up to second-order terms in (y,z), due to undefined boundary condition at ∞. Acceleration averaged over time gives insight into the properties of pseudoturbulent or chaotic (turbulent) flows. Turbulent shear is redefined and Reynolds (turbulent) stresses loose their meaning

  11. Hydrodynamics beyond Navier-Stokes: the slip flow model.

    Science.gov (United States)

    Yudistiawan, Wahyu P; Ansumali, Santosh; Karlin, Iliya V

    2008-07-01

    Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali, Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation-the nine-bit model in two dimensions--in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.

  12. Disentangling the triadic interactions in Navier-Stokes equations.

    Science.gov (United States)

    Sahoo, Ganapati; Biferale, Luca

    2015-10-01

    We study the role of helicity in the dynamics of energy transfer in a modified version of the Navier-Stokes equations with explicit breaking of the mirror symmetry. We select different set of triads participating in the dynamics on the basis of their helicity content. In particular, we remove the negative helically polarized Fourier modes at all wave numbers except for those falling on a localized shell of wave number, |k| ~ k(m). Changing k(m) to be above or below the forcing scale, k(f), we are able to assess the energy transfer of triads belonging to different interaction classes. We observe that when the negative helical modes are present only at a wave number smaller than the forced wave numbers, an inverse energy cascade develops with an accumulation of energy on a stationary helical condensate. Vice versa, when negative helical modes are present only at a wave number larger than the forced wave numbers, a transition from backward to forward energy transfer is observed in the regime when the minority modes become energetic enough.

  13. Hypersonic Navier Stokes Comparisons to Orbiter Flight Data

    Science.gov (United States)

    Campbell, Charles H.; Nompelis, Ioannis; Candler, Graham; Barnhart, Michael; Yoon, Seokkwan

    2009-01-01

    Hypersonic chemical nonequilibrium simulations of low earth orbit entry flow fields are becoming increasingly commonplace as software and computational capabilities become more capable. However, development of robust and accurate software to model these environments will always encounter a significant barrier in developing a suite of high quality calibration cases. The US3D hypersonic nonequilibrium Navier Stokes analysis capability has been favorably compared to a number of wind tunnel test cases. Extension of the calibration basis for this software to Orbiter flight conditions will provide an incremental increase in confidence. As part of the Orbiter Boundary Layer Transition Flight Experiment and the Hypersonic Thermodynamic Infrared Measurements project, NASA is performing entry flight testing on the Orbiter to provide valuable aerothermodynamic heating data. An increase in interest related to orbiter entry environments is resulting from this activity. With the advent of this new data, comparisons of the US3D software to the new flight testing data is warranted. This paper will provide information regarding the framework of analyses that will be applied with the US3D analysis tool. In addition, comparisons will be made to entry flight testing data provided by the Orbiter BLT Flight Experiment and HYTHIRM projects. If data from digital scans of the Orbiter windward surface become available, simulations will also be performed to characterize the difference in surface heating between the CAD reference OML and the digitized surface provided by the surface scans.

  14. Stochastic solutions of Navier-Stokes equations: an experimental evidence.

    Science.gov (United States)

    Djurek, Ivan; Djurek, Danijel; Petosić, Antonio

    2010-12-01

    An electrodynamic loudspeaker has been operated in anharmonic regime indicated by the nonlinear ordinary differential equation when spring constant γ in restoring term, as well as, viscoelasticity of the membrane material, increases with displacement. For driving currents in the range of 2.8-3.3 A, doubling of the vibration period appears, while for currents in the range of 3.3-3.6 A, multiple sequences of subharmonic vibrations begin with f/4 and 3f/4. An application of currents higher than 3.6 A results in a spectrum, characteristic for the chaotic state. The loudspeaker was then operated in a closed chamber, and subharmonic vibrations disappeared by an evacuation. Subsequent injection of air revoked them again at ∼ 120 mbar (Re(')=476) when air viscous forces dominate the Morse convection. At 430 mbar (Re=538) single vibration state was restored, and the phenomenon is in an agreement with prediction of the five mode truncation procedure applied to the Navier-Stokes equations describing a two-dimensional incompressible fluid. © 2010 American Institute of Physics.

  15. Upwind algorithm for the parabolized Navier-Stokes equations

    Science.gov (United States)

    Lawrence, Scott L.; Tannehill, John C.; Chausee, Denny S.

    1989-01-01

    A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes equations. This method does not require the addition of user-specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming (1978) scheme in terms of accuracy, stability, computer time and storage requirements, and programming effort. The new algorithm has been validated by applying it to three laminar test cases, including flat-plate boundary-layer flow, hypersonic flow past a 15-deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with results obtained using the conventional Beam-Warming algorithm.

  16. Isotropic Navier-Stokes turbulence. II. Statistical approximation methods

    International Nuclear Information System (INIS)

    Kraichnan, R.H.

    1990-01-01

    This chapter is concerned with the construction of systematic approximations to the statistics of Navier-Stokes (NS) turbulence. There are difficulties related both to nonlinearity and to the complexity of the dynamical system. The basic task in forming statistical approximations is to use partial information about a very large system in order to make valid predictions of desired averages. This can be a nontrivial undertaking even for linear systems whose exact solutions are completely understood. Guiding principles should include preservation of invariance and conservation properties in approximations and care not to violate realizability (positivity of probability density). The chapter surveys some kinds of statistical description and some approximation methods that have been applied to homogeneous, isotropic turbulence in an incompressible NS fluid. This is followed by an outline of one approach, centered about the construction of stochastic models, that has had some success. Finally, a little is said about new approaches. All of this discussion is tied back to the qualitative physics discussed in the preceding chapter. Equation numbering reflects the chapter number, the section number, and then the consecutive equation number. 32 refs

  17. Study of Tip-loss Using an Inverse 3D Navier-Stokes Method

    DEFF Research Database (Denmark)

    Mikkelsen, Robert; Sørensen, Jens Nørkær; Shen, Wen Zhong

    2003-01-01

    the 3D Navier-Stokes equations combined with the actuator line technique where blade loading is applied using an inverse method. The numerical simulations shows that the method captures the tip-correction when comparing with the theories of Prandtl and Goldstein, however, the accuracy of the obtained...... results reveal that further refinements still is needed. Keywords: Tip-loss; Actuator line; 3D Navier-Stokes methods....

  18. Time evolution of the eddy viscosity in two-dimensional navier-stokes flow

    Science.gov (United States)

    Chaves; Gama

    2000-02-01

    The time evolution of the eddy viscosity associated with an unforced two-dimensional incompressible Navier-Stokes flow is analyzed by direct numerical simulation. The initial condition is such that the eddy viscosity is isotropic and negative. It is shown by concrete examples that the Navier-Stokes dynamics stabilizes negative eddy viscosity effects. In other words, this dynamics moves monotonically the initial negative eddy viscosity to positive values before relaxation due to viscous term occurs.

  19. Numerical solution of Euler and Navier-Stokes equations for 2D transonic problems

    Science.gov (United States)

    Hulek, T.; Hunek, M.; Kozel, K.

    1992-12-01

    The present contribution is a numerical solution of Euler and Navier-Stokes equations for 2D transonic flow problems using several different numerical methods. The time marching cell centered and cell vertex finite volume methods were used for both flow models. Various explicit multistage Runge-Kutta methods (RK methods) were applied for inviscid flows and these methods were also used for numerical solution of incompressible and compressinble Navier-Stokes equations.

  20. Influence of the dispersive and dissipative scales alpha and beta on the energy spectrum of the Navier-Stokes alphabeta equations.

    Science.gov (United States)

    Chen, Xuemei; Fried, Eliot

    2008-10-01

    Lundgren's vortex model for the intermittent fine structure of high-Reynolds-number turbulence is applied to the Navier-Stokes alphabeta equations and specialized to the Navier-Stokes alpha equations. The Navier-Stokes alphabeta equations involve dispersive and dissipative length scales alpha and beta, respectively. Setting beta equal to alpha reduces the Navier-Stokes alphabeta equations to the Navier-Stokes alpha equations. For the Navier-Stokes alpha equations, the energy spectrum is found to obey Kolmogorov's -5/3 law in a range of wave numbers identical to that determined by Lundgren for the Navier-Stokes equations. For the Navier-Stokes alphabeta equations, Kolmogorov's -5/3 law is also recovered. However, granted that beta Navier-Stokes alphabeta equations may have the potential to resolve features smaller than those obtainable using the Navier-Stokes alpha equations.

  1. Parabolized Navier-Stokes Investigations of Hypersonic Intake Flows

    Science.gov (United States)

    Prince, S. A.; Williams, M. J.

    It is widely acknowledged that Parabolized Navier-Stokes (PNS) space marching is more efficient than time marching NS for the solution of supersonic and hypersonic viscous flow problems. The method, however, cannot deal with cases of strong upstream influence and subsequent streamwise flow separation without special treatment. This paper examines the applicabil- ity of the PNS equations to the prediction of flows associated with hypersonic propulsion and assesses the suitability of a multiple sweep algorithm to deal with the prediction of the flow in regions of strong streamwise adverse pressure gradient. Four experimental test cases of increasing complexity in terms of flow physics were chosen, each of which provided validation data for the type of flows which develop in the intakes of hypersonic propulsion systems such as the scramjet. A PNS solver has been shown to accurately predict these hypersonic flow fields including the complex shock-shock and shock-boundary layer interactions and associated flow separations and the resulting vortices which affect propulsion efficiency. A multiple sweep algorithm, applied to a manually defined region ahead of a compression ramp, has also been shown to deal with the accurate prediction of shock induced streamwise flow separation. The PNS space marching technique has been demonstrated to be significantly more efficient than a time marching solver, using the same computational grid, whilst providing results of comparable accuracy, even with the application of multiple sweeping. In addition the PNS solutions to these standard test cases have been shown to resolve small secondary flow features not seen in other studies such as corner vortices and embedded vortex shocks. This is because the PNS space marching approach, which stores only two or three 2-D grid planes at any one time, is able to employ computational grids of such a large size that memory requirements would be prohibitive for use with a 3D time marching code.

  2. An Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations with Fluid Structure Interaction

    Science.gov (United States)

    Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.

    2016-01-01

    An immersed boundary method for the compressible Navier-Stokes equation and the additional infrastructure that is needed to solve moving boundary problems and fully coupled fluid-structure interaction is described. All the methods described in this paper were implemented in NASA's LAVA solver framework. The underlying immersed boundary method is based on the locally stabilized immersed boundary method that was previously introduced by the authors. In the present paper this method is extended to account for all aspects that are involved for fluid structure interaction simulations, such as fast geometry queries and stencil computations, the treatment of freshly cleared cells, and the coupling of the computational fluid dynamics solver with a linear structural finite element method. The current approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems in 2D and 3D. As part of the validation procedure, results from the second AIAA aeroelastic prediction workshop are also presented. The current paper is regarded as a proof of concept study, while more advanced methods for fluid structure interaction are currently being investigated, such as geometric and material nonlinearities, and advanced coupling approaches.

  3. On convergence of trajectory attractors of the 3D Navier-Stokes-α model as α approaches 0

    International Nuclear Information System (INIS)

    Vishik, M I; Chepyzhov, V V; Titi, E S

    2007-01-01

    We study the relations between the long-time dynamics of the Navier-Stokes-α model and the exact 3D Navier-Stokes system. We prove that bounded sets of solutions of the Navier-Stokes-α model converge to the trajectory attractor A 0 of the 3D Navier-Stokes system as the time approaches infinity and α approaches zero. In particular, we show that the trajectory attractor A α of the Navier-Stokes-α model converges to the trajectory attractor A 0 of the 3D Navier-Stokes system as α→0+. We also construct the minimal limit A min (subset or equal A 0 ) of the trajectory attractor A α as α→0+ and prove that the set A min is connected and strictly invariant. Bibliography: 35 titles.

  4. Generalized extended Navier-Stokes theory: multiscale spin relaxation in molecular fluids.

    Science.gov (United States)

    Hansen, J S

    2013-09-01

    This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia per unit mass. In the regime of large moment of inertia the fast relaxation is wave-vector independent and dominated by the coupling between spin and the fluid streaming velocity, whereas for small inertia the relaxation is slow and spin diffusion plays a significant role. The fast wave-vector-independent relaxation is also observed for highly packed systems. The transverse and longitudinal spin modes have, to a good approximation, identical relaxation, indicating that the longitudinal and transverse spin viscosities have same value. The relaxation is also shown to be isomorphic invariant. Finally, the effect of the coupling in the zero frequency and wave-vector limit is quantified by a characteristic length scale; if the system dimension is comparable to this length the coupling must be included into the fluid dynamical description. It is found that the length scale is independent of moment of inertia but dependent on the state point.

  5. Infrasonic attenuation in the upper mesosphere-lower thermosphere: a comparison between Navier-Stokes and Burnett predictions.

    Science.gov (United States)

    Akintunde, Akinjide; Petculescu, Andi

    2014-10-01

    This paper presents the results of a pilot study comparing the use of continuum and non-continuum fluid dynamics to predict infrasound attenuation in the rarefied lower thermosphere. The continuum approach is embodied by the Navier-Stokes equations, while the non-continuum method is implemented via the Burnett equations [Proc. London Math. Soc. 39, 385-430 (1935); 40, 382-435 (1936)]. In the Burnett framework, the coupling between stress tensor and heat flux affects the dispersion equation, leading to an attenuation coefficient smaller than its Navier-Stokes counterpart by amounts of order 0.1 dB/km at 0.1 Hz, 10 dB/km at 1 Hz, and 100 dB/km at 10 Hz. It has been observed that many measured thermospheric arrivals are stronger than current predictions based on continuum mechanics. In this context, the consistently smaller Burnett-based absorption is cautiously encouraging.

  6. On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation

    International Nuclear Information System (INIS)

    Kawashima, S.; Matsumara, A.; Nishida, T.

    1979-01-01

    The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay rate tsup(-5/4)) as t → + infinitely to that of the compressible Navier-Stokes equation for the corresponding initial data. (orig.) 891 HJ/orig. 892 MKO

  7. Generalized extended Navier-Stokes theory: correlations in molecular fluids with intrinsic angular momentum.

    Science.gov (United States)

    Hansen, J S; Daivis, Peter J; Dyre, Jeppe C; Todd, B D; Bruus, Henrik

    2013-01-21

    The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies. To account for the correlations at these scales, we derive a phenomenological expression for the frequency dependent rotational viscosity and wavevector and frequency dependent longitudinal spin viscosity. From this we observe a significant coupling enhancement between the molecular angular velocity and translational velocity for large frequencies in the gas phase; this is not observed for the supercritical fluid and liquid state points.

  8. Exponential integrators for the incompressible Navier-Stokes equations.

    Energy Technology Data Exchange (ETDEWEB)

    Newman, Christopher K.

    2004-07-01

    We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is scalable in the sense that the computational costs grow linearly with problem size. Exponential integrators, used typically to solve systems of ODEs, utilize matrix vector products of the exponential of the Jacobian on a vector. For large systems, this product can be approximated efficiently by Krylov subspace methods. However, in contrast to explicit methods, KBEIs are not restricted by the time step. While implicit methods require a solution of a linear system with the Jacobian, KBEIs only require matrix vector products of the Jacobian. Furthermore, these methods are based on linearization, so there is no non-linear system solve at each time step. Differential-algebraic equations (DAEs) are ordinary differential equations (ODEs) subject to algebraic constraints. The discretized NSE constitute a system of DAEs, where the incompressibility condition is the algebraic constraint. Exponential integrators can be extended to DAEs with linear constraints imposed via a projection onto the constraint manifold. This results in a projected ODE that is integrated by a KBEI. In this approach, the Krylov subspace satisfies the constraint, hence the solution at the advanced time step automatically satisfies the constraint as well. For the NSE, the projection onto the constraint is typically achieved by a projection induced by the L{sup 2} inner product. We examine this L{sup 2} projection and an H{sup 1} projection induced by the H{sup 1} semi-inner product. The H

  9. Incompressible limit of the degenerate quantum compressible Navier-Stokes equations with general initial data

    Science.gov (United States)

    Kwon, Young-Sam; Li, Fucai

    2018-03-01

    In this paper we study the incompressible limit of the degenerate quantum compressible Navier-Stokes equations in a periodic domain T3 and the whole space R3 with general initial data. In the periodic case, by applying the refined relative entropy method and carrying out the detailed analysis on the oscillations of velocity, we prove rigorously that the gradient part of the weak solutions (velocity) of the degenerate quantum compressible Navier-Stokes equations converge to the strong solution of the incompressible Navier-Stokes equations. Our results improve considerably the ones obtained by Yang, Ju and Yang [25] where only the well-prepared initial data case is considered. While for the whole space case, thanks to the Strichartz's estimates of linear wave equations, we can obtain the convergence of the weak solutions of the degenerate quantum compressible Navier-Stokes equations to the strong solution of the incompressible Navier-Stokes/Euler equations with a linear damping term. Moreover, the convergence rates are also given.

  10. Evaluation study of a Navier-Stokes CFD aeroelastic model of wind turbine airfoils in classical flutter

    Energy Technology Data Exchange (ETDEWEB)

    Baxevanou, C.A.; Vlachos, N.S. [Department of Mechanical and Industrial Engineering, University of Thessaly, Athens Avenue, 38334 Volos (Greece); Chaviaropoulos, P.K. [Centre for Renewable Energy Sources, Pikermi Attikis (Greece); Voutsinas, S.G. [Department of Mechanical Engineering, National Technical University of Athens (Greece)

    2008-08-15

    This paper describes a new aeroelastic numerical model, which combines a Navier-Stokes CFD solver with an elastic model and two coupling schemes for the study of the aeroelastic behaviour of wind turbine blades undergoing classical flutter. The basic characteristics of the aerodynamic and elastic models are presented together with the coupling schemes. The present model is evaluated by comparing with previous numerical results and the corresponding linear analytical solutions. Consequently, a parametric study is carried out. Conclusions are drawn about the ability of the model to handle the aeroelastic behaviour of an airfoil and about the most appropriate coupling scheme in terms of predicting the modal damping and the flutter limiting point. The present study shows that the predictions are only slightly affected by the coupling or the space discretization scheme and mainly by the turbulence model used. (author)

  11. Fast pressure-correction method for incompressible Navier-Stokes equations in curvilinear coordinates

    Science.gov (United States)

    Aithal, Abhiram; Ferrante, Antonino

    2017-11-01

    In order to perform direct numerical simulations (DNS) of turbulent flows over curved surfaces and axisymmetric bodies, we have developed the numerical methodology to solve the incompressible Navier-Stokes (NS) equations in curvilinear coordinates for orthogonal meshes. The orthogonal meshes are generated by solving a coupled system of non-linear Poisson equations. The NS equations in orthogonal curvilinear coordinates are discretized in space on a staggered mesh using second-order central-difference scheme and are solved with an FFT-based pressure-correction method. The momentum equation is integrated in time using the second-order Adams-Bashforth scheme. The velocity field is advanced in time by applying the pressure correction to the approximate velocity such that it satisfies the divergence free condition. The novelty of the method stands in solving the variable coefficient Poisson equation for pressure using an FFT-based Poisson solver rather than the slower multigrid methods. We present the verification and validation results of the new numerical method and the DNS results of transitional flow over a curved axisymmetric body.

  12. Unstructed Navier-Stokes Analysis of Wind-Tunnel Aeroelastic Effects on TCA Model 2

    Science.gov (United States)

    Frink, Neal T.; Allison, Dennis O.; Parikh, Paresh C.

    1999-01-01

    The aim of this work is to demonstrate a simple technique which accounts for aeroelastic deformations experienced by HSR wind-tunnel models within CFD computations. With improved correlations, CFD can become a more effective tool for augmenting the post-test understanding of experimental data. The present technique involves the loose coupling of a low-level structural representation within the ELAPS code, to an unstructured Navier-Stokes flow solver, USM3Dns. The ELAPS model is initially calibrated against bending characteristics of the wind-tunnel model. The strength of this method is that, with a single point calibration of a simple structural representation, the static aeroelastic effects can be accounted for in CFD calculations across a range of test conditions. No prior knowledge of the model deformation during the wind-on test is required. This approach has been successfully applied to the high aspect-ratio planforms of subsonic transports. The current challenge is to adapt the procedure to low aspect-ratio planforms typical of HSR configurations.

  13. An analytical solution of the Navier-Stokes equation for internal flows

    International Nuclear Information System (INIS)

    Lyberg, Mats D; Tryggeson, Henrik

    2007-01-01

    This paper derives a solution to the Navier-Stokes equation by considering vorticity generated at system boundaries. The result is an explicit expression for the velocity. The Navier-Stokes equation is reformulated as a divergence and integrated, giving a tensor equation that splits into a symmetric and a skew-symmetric part. One equation gives an algebraic system of quadratic equations involving velocity components. A system of nonlinear partial differential equations is reduced to algebra. The velocity is then explicitly calculated and shown to depend on boundary conditions only. This removes the need to solve the Navier-Stokes equation by a 3D numerical computation, replacing it by computation of 2D surface integrals over the boundary. (fast track communication)

  14. Symmetry Reductions and Exact Solutions of the (2+1)-Dimensional Navier-Stokes Equations

    Science.gov (United States)

    Hua, Xiaorui; Dongb, Zhongzhou; Huangc, Fei; Chena, Yong

    2010-07-01

    By means of the classical symmetry method, we investigate the (2+1)-dimensional Navier-Stokes equations. The symmetry group of Navier-Stokes equations is studied and its corresponding group invariant solutions are constructed. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, using the associated vector fields of the obtained symmetry, we give out the reductions by one-dimensional and two-dimensional subalgebras, and some explicit solutions of Navier-Stokes equations are obtained. For three interesting solutions, the figures are given out to show their properties: the solution of stationary wave of fluid (real part) appears as a balance between fluid advection (nonlinear term) and friction parameterized as a horizontal harmonic diffusion of momentum.

  15. Estudio comparativo de flujo de fluido a través de una placa de orificio usando las ecuaciones de Stokes y de Navier-Stokes

    Directory of Open Access Journals (Sweden)

    Miryam Lucía Guerra-Mazo

    2016-05-01

    Full Text Available Presenta los resultados de la comparación entre las ecuaciones de Stokes y de Navier-Stokes para la simulación del flujo de agua líquida, a condiciones atmosféricas, a través de una placa orificio concéntrica. A partir de los datos experimentales que fueron tomados en el banco de fluidos, se evaluaron las simulaciones de ambas ecuaciones, usando el software libre Freefem++cs, que se basa en el método de los elementos finitos; las variables evaluadas son velocidad y presión en un intervalo de tiempo. Al analizar los resultados obtenidos con las simulaciones y comparar con los datos experimentales se encontró que las ecuaciones de Navier-Stokes representan mejor el sistema que la ecuación de Stokes.

  16. Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations

    Science.gov (United States)

    Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C.

    2015-07-01

    The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.

  17. Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis

    International Nuclear Information System (INIS)

    Bulicek, Miroslav; Haslinger, Jaroslav; Malek, Josef; Stebel, Jan

    2009-01-01

    We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by a generalized stationary Navier-Stokes system with nontrivial mixed boundary conditions. In this paper we prove the existence of solutions both to the generalized Navier-Stokes system and to the shape optimization problem

  18. Modeling shock waves in an ideal gas: Going beyond the Navier-Stokes level

    International Nuclear Information System (INIS)

    Holian, B.L.; Patterson, C.W.; Mareschal, M.; Salomons, E.

    1993-01-01

    We model a shock wave in an ideal gas by solving a modified version of the compressible Navier-Stokes equations of hydrodynamics, where, following an earlier conjecture by Holian [Phys. Rev. A 37, 2562 (1988)], we use the temperature in the direction of shock propagation T xx , rather than the average temperature T=(T xx +T yy +T zz )/3, in the evaluation of the linear transport coefficients. The results are found to agree much better with the molecular-dynamics simulations of Salomons and Mareschal [Phys. Rev. Lett. 69, 269 (1992)] than standard Navier-Stokes theory

  19. Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations.

    Science.gov (United States)

    Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C

    2015-07-01

    The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.

  20. Finite Volume Methods for Incompressible Navier-Stokes Equations on Collocated Grids with Nonconformal Interfaces

    DEFF Research Database (Denmark)

    Kolmogorov, Dmitry

    Direct numerical solutions of the Navier-Stokes equations using Computational Fluid Dynamics methods are recognized as some the most advanced and accurate methods for prediction of flows around wind turbines. The ability of these methods to capture the dynamics of the complex flow properties...... versions of the SIMPLE algorithm. The new technique is implemented in an existing conservative 2nd order finite-volume scheme flow solver (EllipSys), which is extended to cope with grids with nonconformal interfaces. The behavior of the discrete Navier-Stokes equations is discussed in detail...

  1. A nonperturbative approximation for the moderate Reynolds number Navier-Stokes equations.

    Science.gov (United States)

    Roper, Marcus; Brenner, Michael P

    2009-03-03

    The nonlinearity of the Navier-Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier-Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes.

  2. Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations

    International Nuclear Information System (INIS)

    Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C.; Michalowski, Nicholas

    2015-01-01

    The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation

  3. Incompressible Navier-Stokes inverse design method based on adaptive unstructured meshes

    International Nuclear Information System (INIS)

    Rahmati, M.T.; Charlesworth, D.; Zangeneh, M.

    2005-01-01

    An inverse method for blade design based on Navier-Stokes equations on adaptive unstructured meshes has been developed. In the method, unlike the method based on inviscid equations, the effect of viscosity is directly taken into account. In the method, the pressure (or pressure loading) is prescribed. The design method then computes the blade shape that would accomplish the target prescribed pressure distribution. The method is implemented using a cell-centered finite volume method, which solves the incompressible Navier-Stokes equations on unstructured meshes. An adaptive unstructured mesh method based on grid subdivision and local adaptive mesh method is utilized for increasing the accuracy. (author)

  4. Approximate controllability of the Navier-Stokes system in unbounded domains

    International Nuclear Information System (INIS)

    Shorygin, P O

    2003-01-01

    The question of the approximate controllability for the 2- and the 3-dimensional Navier-Stokes system defined in the exterior of a bounded domain ω or in the entire space is studied. It is shown that one can find boundary controls or locally distributed controls (having support in a prescribed bounded domain) defined on the right-hand side of the system such that in prescribed time the solution of the Navier-Stokes system becomes arbitrarily close to an arbitrary prescribed divergence-free vector field

  5. Higher-order time integration schemes for the unsteady Navier-Stokes equations on unstructured meshes

    International Nuclear Information System (INIS)

    Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.

    2003-01-01

    The efficiency gains obtained using higher-order implicit Runge-Kutta (RK) schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each time step are presented. The first algorithm (nonlinear multigrid, NMG) is a pseudo-time-stepping scheme which employs a nonlinear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the generalized minimal residual method. Results demonstrating the relative superiority of these Newton's method based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes such as fourth-order Runge-Kutta (RK64) with the more efficient inexact Newton's method based schemes (LMG)

  6. Exact integration of the unsteady incompressible Navier-Stokes equations, gauge criteria, and applications

    Science.gov (United States)

    Scholle, M.; Gaskell, P. H.; Marner, F.

    2018-04-01

    An exact first integral of the full, unsteady, incompressible Navier-Stokes equations is achieved in its most general form via the introduction of a tensor potential and parallels drawn with Maxwell's theory. Subsequent to this gauge freedoms are explored, showing that when used astutely they lead to a favourable reduction in the complexity of the associated equation set and number of unknowns, following which the inviscid limit case is discussed. Finally, it is shown how a change in gauge criteria enables a variational principle for steady viscous flow to be constructed having a self-adjoint form. Use of the new formulation is demonstrated, for different gauge variants of the first integral as the starting point, through the solution of a hierarchy of classical three-dimensional flow problems, two of which are tractable analytically, the third being solved numerically. In all cases the results obtained are found to be in excellent accord with corresponding solutions available in the open literature. Concurrently, the prescription of appropriate commonly occurring physical and necessary auxiliary boundary conditions, incorporating for completeness the derivation of a first integral of the dynamic boundary condition at a free surface, is established, together with how the general approach can be advantageously reformulated for application in solving unsteady flow problems with periodic boundaries.

  7. Development of Multigrid Methods for diffusion, Advection, and the incompressible Navier-Stokes Equations

    Energy Technology Data Exchange (ETDEWEB)

    Gjesdal, Thor

    1997-12-31

    This thesis discusses the development and application of efficient numerical methods for the simulation of fluid flows, in particular the flow of incompressible fluids. The emphasis is on practical aspects of algorithm development and on application of the methods either to linear scalar model equations or to the non-linear incompressible Navier-Stokes equations. The first part deals with cell centred multigrid methods and linear correction scheme and presents papers on (1) generalization of the method to arbitrary sized grids for diffusion problems, (2) low order method for advection-diffusion problems, (3) attempt to extend the basic method to advection-diffusion problems, (4) Fourier smoothing analysis of multicolour relaxation schemes, and (5) analysis of high-order discretizations for advection terms. The second part discusses a multigrid based on pressure correction methods, non-linear full approximation scheme, and papers on (1) systematic comparison of the performance of different pressure correction smoothers and some other algorithmic variants, low to moderate Reynolds numbers, and (2) systematic study of implementation strategies for high order advection schemes, high-Re flow. An appendix contains Fortran 90 data structures for multigrid development. 160 refs., 26 figs., 22 tabs.

  8. Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems

    Directory of Open Access Journals (Sweden)

    Neng Wan

    2014-01-01

    Full Text Available In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.

  9. Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

    Science.gov (United States)

    Bartels, Robert E.

    2005-01-01

    A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.

  10. One-way spatial integration of Navier-Stokes equations: stability of wall-bounded flows

    Science.gov (United States)

    Rigas, Georgios; Colonius, Tim; Towne, Aaron; Beyar, Michael

    2016-11-01

    For three-dimensional flows, questions of stability, receptivity, secondary flows, and coherent structures require the solution of large partial-derivative eigenvalue problems. Reduced-order approximations are thus required for engineering prediction since these problems are often computationally intractable or prohibitively expensive. For spatially slowly evolving flows, such as jets and boundary layers, a regularization of the equations of motion sometimes permits a fast spatial marching procedure that results in a huge reduction in computational cost. Recently, a novel one-way spatial marching algorithm has been developed by Towne & Colonius. The new method overcomes the principle flaw observed in Parabolized Stability Equations (PSE), namely the ad hoc regularization that removes upstream propagating modes. The one-way method correctly parabolizes the flow equations based on estimating, in a computationally efficient way, the local spectrum in each cross-stream plane and an efficient spectral filter eliminates modes with upstream group velocity. Results from the application of the method to wall-bounded flows will be presented and compared with predictions from the full linearized compressible Navier-Stokes equations and PSE.

  11. Regularity for 3D Navier-Stokes equations in terms of two components of the vorticity

    Directory of Open Access Journals (Sweden)

    Sadek Gala

    2010-10-01

    Full Text Available We establish regularity conditions for the 3D Navier-Stokes equation via two components of the vorticity vector. It is known that if a Leray-Hopf weak solution $u$ satisfies $$ ilde{omega}in L^{2/(2-r}(0,T;L^{3/r}(mathbb{R}^3quad hbox{with }0

  12. Stability Properties of the Regular Set for the Navier-Stokes Equation

    Science.gov (United States)

    D'Ancona, Piero; Lucà, Renato

    2017-11-01

    We investigate the size of the regular set for small perturbations of some classes of strong large solutions to the Navier-Stokes equation. We consider perturbations of the data that are small in suitable weighted L2 spaces but can be arbitrarily large in any translation invariant Banach space. We give similar results in the small data setting.

  13. Lower Bounds for Possible Singular Solutions for the Navier-Stokes and Euler Equations Revisited

    Science.gov (United States)

    Cortissoz, Jean C.; Montero, Julio A.

    2018-03-01

    In this paper we give optimal lower bounds for the blow-up rate of the \\dot{H}s( T^3) -norm, 1/2Navier-Stokes equations, and we also present an elementary proof for a lower bound on blow-up rate of the Sobolev norms of possible singular solutions to the Euler equations when s>5/2.

  14. Status for the two-dimensional Navier-Stokes solver EllipSys2D

    DEFF Research Database (Denmark)

    Bertagnolio, F.; Sørensen, Niels N.; Johansen, J.

    2001-01-01

    This report sets up an evaluation of the two-dimensional Navier-Stokes solver EllipSys2D in its present state. This code is used for blade aerodynamics simulations in the Aeroelastic Design group at Risø. Two airfoils are investigated by computing theflow at several angles of attack ranging from...

  15. Global solubility of the three-dimensional Navier-Stokes equations with uniformly large initial vorticity

    International Nuclear Information System (INIS)

    Makhalov, A S; Nikolaenko, V P

    2003-01-01

    This paper is a survey of results concerning the three-dimensional Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity. The existence of regular solutions of the three-dimensional Navier-Stokes equations on an unbounded time interval is proved for large initial data both in R 3 and in bounded cylindrical domains. Moreover, the existence of smooth solutions on large finite time intervals is established for the three-dimensional Euler equations. These results are obtained without additional assumptions on the behaviour of solutions for t>0. Any smooth solution is not close to any two-dimensional manifold. Our approach is based on the computation of singular limits of rapidly oscillating operators, non-linear averaging, and a consideration of the mutual absorption of non-linear oscillations of the vorticity field. The use of resonance conditions, methods from the theory of small divisors, and non-linear averaging of almost periodic functions leads to the limit resonant Navier-Stokes equations. Global solubility of these equations is proved without any conditions on the three-dimensional initial data. The global regularity of weak solutions of three-dimensional Navier-Stokes equations with uniformly large vorticity at t=0 is proved by using the regularity of weak solutions and the strong convergence

  16. On a model for the Navier-Stokes equations using magnetization variables

    Science.gov (United States)

    Pooley, Benjamin C.

    2018-04-01

    It is known that in a classical setting, the Navier-Stokes equations can be reformulated in terms of so-called magnetization variables w that satisfy Our main focus is the proof of global well-posedness in H 1 / 2 for a new variant of (1), where Pw is replaced by w in the second nonlinear term:

  17. Etude de l'equation de Navier-Stokes stochastique non homogene

    African Journals Online (AJOL)

    Resume. Le travail de cet article consiste a etudier !'existence et l'unicite de la solution des equations de Navier-Stokes stochastiques et non homogenes selon une methode directe due a Faedo-Galerkin [1]. Cette methode consiste a approcher les solutions de ces equations dans un espace de dimension finie. Dans ce ...

  18. Formal solution of the Navier-Stokes initial- and boundary-value problem for incompressible fluids

    International Nuclear Information System (INIS)

    Alankus, T.

    1984-01-01

    A general formal solution of the integral equivalent of Navier-Stokes equation for incompressible viscous fluids is presented through a linear operator acting on the functionals of solenoidal vector fields. This solution operator is completely determined by the Green functions of Laplace and diffusion equations corresponding to the flow region

  19. A rigorous derivation of the stationary compressible Reynolds equation via the Navier-Stokes equations

    Czech Academy of Sciences Publication Activity Database

    Ciuperca, I. S.; Feireisl, Eduard; Jai, M.; Petrov, A.

    2018-01-01

    Roč. 28, č. 4 (2018), s. 697-732 ISSN 0218-2025 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible fluids * stationary Navier - Stokes equations * thin films Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.860, year: 2016 https://www.worldscientific.com/doi/abs/10.1142/S0218202518500185

  20. A rigorous justification of the Euler and Navier-Stokes equations with geometric effects

    Czech Academy of Sciences Publication Activity Database

    Bella, P.; Feireisl, Eduard; Lewicka, M.; Novotný, A.

    2016-01-01

    Roč. 48, č. 6 (2016), s. 3907-3930 ISSN 0036-1410 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : isentropic Navier - Stokes system * isentropic Euler system * inviscid limit Subject RIV: BA - General Mathematics Impact factor: 1.648, year: 2016 http://epubs.siam.org/doi/10.1137/15M1048963

  1. Actuator Line/Navier-Stokes Computations for Flows past the Yawed MEXICO Rotor

    DEFF Research Database (Denmark)

    Shen, Wen Zhong; Sørensen, Jens Nørkær; Yang, H.

    2011-01-01

    In the paper the Actuator Line/Navier-Stokes model has been used to simulate flows past the yawed MEXICO rotor. The computed loads as well as the velocity field behind the yawed rotor are compared to detailed pressure and PIV measurements which were carried out in the EU funded MEXICO project...

  2. Validation of the actuator line/Navier Stokes technique using mexico measurements

    DEFF Research Database (Denmark)

    Shen, Wen Zhong; Zhu, Wei Jun; Sørensen, Jens Nørkær

    2010-01-01

    in Controlled Conditions). The Actuator Line/Navier Stokes (AL/NS) technique developed at DTU is validated against the detailed MEXICO measurements. The AL/NS computations without the DNW wind tunnel with speeds of 10m/s, 15m/s and 24m/s. Comparisons of blade loading between computations and measurements show...

  3. Exponential decay rate of the power spectrum for solutions of the Navier--Stokes equations

    International Nuclear Information System (INIS)

    Doering, C.R.; Titi, E.S.

    1995-01-01

    Using a method developed by Foias and Temam [J. Funct. Anal. 87, 359 (1989)], exponential decay of the spatial Fourier power spectrum for solutions of the incompressible Navier--Stokes equations is established and explicit rigorous lower bounds on a small length scale defined by the exponential decay rate are obtained

  4. Large Deviations for Stochastic Tamed 3D Navier-Stokes Equations

    International Nuclear Information System (INIS)

    Roeckner, Michael; Zhang, Tusheng; Zhang Xicheng

    2010-01-01

    In this paper, using weak convergence method, we prove a large deviation principle of Freidlin-Wentzell type for the stochastic tamed 3D Navier-Stokes equations driven by multiplicative noise, which was investigated in (Roeckner and Zhang in Probab. Theory Relat. Fields 145(1-2), 211-267, 2009).

  5. Length scales for the Navier-Stokes equations on a rotating sphere

    International Nuclear Information System (INIS)

    Kyrychko, Yuliya N.; Bartuccelli, Michele V.

    2004-01-01

    In this Letter we obtain the dissipative length scale for the Navier-Stokes equations on a two-dimensional rotating sphere S 2 . This system is a fundamental model of the large scale atmospheric dynamics. Using the equations of motion in their vorticity form, we construct the ladder inequalities from which a set of time-averaged length scales is obtained

  6. Continuum Navier-Stokes modelling of water flow past fullerene molecules

    DEFF Research Database (Denmark)

    Walther, J. H.; Popadic, A.; Koumoutsakos, P.

    We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest...

  7. Generalized extended Navier-Stokes theory: Multiscale spin relaxation in molecular fluids

    DEFF Research Database (Denmark)

    Hansen, Jesper Schmidt

    2013-01-01

    This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia...

  8. Aeroacoustic Calculations of Wind Turbine Noise with the Actuator Line/ Navier-Stokes Technique

    DEFF Research Database (Denmark)

    Debertshäuser, Harald; Shen, Wen Zhong; Zhu, Wei Jun

    2016-01-01

    technique where the wind turbine flow is calculated by using the in-house actuator line/LES/Navier-Stokes technique and the acoustics is obtained by solving the acoustic perturbation equations. In the flow solver, the wind turbine blades are modelled by rotating lines with body forces determined according...

  9. Identification of severe wind conditions using a Reynolds averaged Navier-Stokes solver

    DEFF Research Database (Denmark)

    Sørensen, Niels N.; Bechmann, Andreas; Johansen, Jeppe

    2007-01-01

    The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting...

  10. Regularity of the 3D Navier-Stokes equations with viewpoint of 2D flow

    Science.gov (United States)

    Bae, Hyeong-Ohk

    2018-04-01

    The regularity of 2D Navier-Stokes flow is well known. In this article we study the relationship of 3D and 2D flow, and the regularity of the 3D Naiver-Stokes equations with viewpoint of 2D equations. We consider the problem in the Cartesian and in the cylindrical coordinates.

  11. A study of plunging breaker mechanics by PIV measurements and a Navier-Stokes solver

    DEFF Research Database (Denmark)

    Emarat, Narumon; Forehand, David I. M.; Christensen, Erik Damgaard

    2000-01-01

    The mechanics of a surf-zone plunging breaker are studied from Particle Image Velocimetry (PIV) measurements and a numerical model based on the Navier-Stokes equations, using a Volume of Fluid (VOF) method. An additional numerical model using a Boundary-Integral Method (BIM) is also used in order...

  12. Continuum Navier-Stokes modelling of water ow past fullerene molecules

    DEFF Research Database (Denmark)

    Walther, J. H.; Popadic, A.; Koumoutsakos, P.

    We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest...

  13. Turbomachinery Heat Transfer and Loss Modeling for 3D Navier-Stokes Codes

    Science.gov (United States)

    DeWitt, Kenneth; Ameri, Ali

    2005-01-01

    This report's contents focus on making use of NASA Glenn on-site computational facilities,to develop, validate, and apply models for use in advanced 3D Navier-Stokes Computational Fluid Dynamics (CFD) codes to enhance the capability to compute heat transfer and losses in turbomachiney.

  14. On the equivalence between particular types of Navier-Stokes and non-linear Schroedinger equations

    International Nuclear Information System (INIS)

    Dietrich, K.; Vautherin, D.

    1985-01-01

    We derive a Schroedinger equation equivalent to the Navier-Stokes equation in the special case of constant kinematic viscosities. This equation contains a non-linear term similar to that proposed by Kostin for a quantum description of friction [fr

  15. A rigorous justification of the Euler and Navier-Stokes equations with geometric effects

    Czech Academy of Sciences Publication Activity Database

    Bella, P.; Feireisl, Eduard; Lewicka, M.; Novotný, A.

    2016-01-01

    Roč. 48, č. 6 (2016), s. 3907-3930 ISSN 0036-1410 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : isentropic Navier-Stokes system * isentropic Euler system * inviscid limit Subject RIV: BA - General Mathematics Impact factor: 1.648, year: 2016 http://epubs.siam.org/doi/10.1137/15M1048963

  16. Reynolds-averaged Navier-Stokes and Large-Eddy Simulation Over and Inside Inhomogeneous Forests

    DEFF Research Database (Denmark)

    Boudreault, Louis-Etienne

    ) and tree height is performed. The method is optimized both in terms of plant area index magnitude and spatial variability. A forest grid is generated from the LiDAR method using airplane scans of a 5×5 km2 forested site in Sweden. The grid serves as the basis for Reynolds-averaged Navier-Stokes (RANS...

  17. A convergent numerical method for the Navier-Stokes-Fourier system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Karper, T.; Novotný, A.

    2016-01-01

    Roč. 36, č. 4 (2016), s. 1477-1535 ISSN 0272-4979 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes- Fourier system * Crouzeix-Raviart finite element method * finite volume method Subject RIV: BA - General Mathematics Impact factor: 1.703, year: 2016 http://imajna.oxfordjournals.org/content/36/4/1477

  18. Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

    Czech Academy of Sciences Publication Activity Database

    Šístek, Jakub; Cirak, F.

    2015-01-01

    Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045793015003023

  19. Symbolic-numeric stability investigations of Jameson's scheme for this-layer Navier-Stokes equations

    NARCIS (Netherlands)

    Ganzha, V.G.; Vorozhtsov, E.V.; Boers, J.; van Hulzen, J.A.; van Hulzen, J.A.

    1994-01-01

    The Navier-Stokes equations governing the three-dimensional flows of viscous, compressible, heat-conducting gas and augmented by turbulence modeling present the most realistic model for gas flows around the elements of aircraft configurations. We study the stability of one of the Jameson's schemes

  20. A convergent numerical method for the Navier-Stokes-Fourier system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Karper, T.; Novotný, A.

    2016-01-01

    Roč. 36, č. 4 (2016), s. 1477-1535 ISSN 0272-4979 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * Crouzeix-Raviart finite element method * finite volume method Subject RIV: BA - General Mathematics Impact factor: 1.703, year: 2016 http://imajna.oxfordjournals.org/content/36/4/1477

  1. Existence of weak solutions for compressible Navier-Stokes equations with entropy transport

    Czech Academy of Sciences Publication Activity Database

    Maltese, D.; Michálek, Martin; Mucha, P.; Novotný, A.; Pokorný, M.; Zatorska, E.

    2016-01-01

    Roč. 261, č. 8 (2016), s. 4448-4485 ISSN 0022-0396 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022039616301656

  2. On time-periodic Navier-Stokes flows with fast spatial decay in the whole space

    Czech Academy of Sciences Publication Activity Database

    Nakatsuka, Tomoyuki

    2018-01-01

    Roč. 4, č. 1 (2018), s. 51-67 ISSN 2296-9020 Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * time-periodic solution * asymptotic property Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics https://link.springer.com/article/10. 1007 %2Fs41808-018-0011-8

  3. Mathematical geophysics an introduction to rotating fluids and the Navier-Stokes equations

    CERN Document Server

    Chemin, Jean-Yves; Gallagher, Isabelle; Grenier, Emmanuel

    2006-01-01

    Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.

  4. On time-periodic Navier-Stokes flows with fast spatial decay in the whole space

    Czech Academy of Sciences Publication Activity Database

    Nakatsuka, Tomoyuki

    2018-01-01

    Roč. 4, č. 1 (2018), s. 51-67 ISSN 2296-9020 Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * time -periodic solution * asymptotic property Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics https://link.springer.com/article/10.1007%2Fs41808-018-0011-8

  5. On solutions with infinite energy and enstrophy of the Navier-Stokes system

    Energy Technology Data Exchange (ETDEWEB)

    Bakhtin, Yu Yu [International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow (Russian Federation); Dinaburg, E I [Institute of Physics of the Earth, Russian Academy of Sciences, Moscow (Russian Federation); Sinai, Yakov G [Mathematics Department, Princeton University, Princeton, New Jersey (United States)

    2004-12-31

    The Cauchy problem is considered for the Navier-Stokes system. Local and global existence and uniqueness theorems are given for initial data whose Fourier transform decays at infinity as a power-law function with negative exponent and has a power-law singularity at zero. The paper contains a survey of known facts and some new results.

  6. Simulation of axisymmetric jets with a finite element Navier-Stokes solver and a multilevel VOF approach

    Science.gov (United States)

    Cervone, A.; Manservisi, S.; Scardovelli, R.

    2010-09-01

    A multilevel VOF approach has been coupled to an accurate finite element Navier-Stokes solver in axisymmetric geometry for the simulation of incompressible liquid jets with high density ratios. The representation of the color function over a fine grid has been introduced to reduce the discontinuity of the interface at the cell boundary. In the refined grid the automatic breakup and coalescence occur at a spatial scale much smaller than the coarse grid spacing. To reduce memory requirements, we have implemented on the fine grid a compact storage scheme which memorizes the color function data only in the mixed cells. The capillary force is computed by using the Laplace-Beltrami operator and a volumetric approach for the two principal curvatures. Several simulations of axisymmetric jets have been performed to show the accuracy and robustness of the proposed scheme.

  7. A study of infrasound propagation based on high-order finite difference solutions of the Navier-Stokes equations.

    Science.gov (United States)

    Marsden, O; Bogey, C; Bailly, C

    2014-03-01

    The feasibility of using numerical simulation of fluid dynamics equations for the detailed description of long-range infrasound propagation in the atmosphere is investigated. The two dimensional (2D) Navier Stokes equations are solved via high fidelity spatial finite differences and Runge-Kutta time integration, coupled with a shock-capturing filter procedure allowing large amplitudes to be studied. The accuracy of acoustic prediction over long distances with this approach is first assessed in the linear regime thanks to two test cases featuring an acoustic source placed above a reflective ground in a homogeneous and weakly inhomogeneous medium, solved for a range of grid resolutions. An atmospheric model which can account for realistic features affecting acoustic propagation is then described. A 2D study of the effect of source amplitude on signals recorded at ground level at varying distances from the source is carried out. Modifications both in terms of waveforms and arrival times are described.

  8. Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations.

    Science.gov (United States)

    Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre

    2014-12-14

    We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formation of the so-called "giant fluctuations" of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power -4 of the wavenumber-except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.

  9. A new forward-backward sweeping parabolized Navier-Stokes algorithm with application to magnetohydrodynamic flows

    Science.gov (United States)

    Kato, Hiromasa

    A new forward-backward sweeping parabolized Navier-Stokes algorithm has been developed to efficiently compute supersonic/hypersonic flowfields with embedded separated regions. The algorithm splits the streamwise flux vector using the Steger-Warming method and employs multiple forward/backward sweeps of the flowfield in order to duplicate the results that would be obtained with the complete Navier-Stokes equations. The forward/backward sweeping of the flowfield significantly reduces the number of iterations required over previous iterative parabolized Navier-Stokes algorithms. Once a separated flow region is computed, the algorithm returns to the usual forward-space-marching mode until the next separated flow region is encountered. The new algorithm has been applied to three separated flow test cases consisting of flow over a compression ramp and two flows over a hollow-cylinder-flare geometry. The present numerical results are in excellent agreement with complete Navier-Stokes computations and experimental data. In addition, the new algorithm has been extended to efficiently compute magnetohydrodynamic (NM) flows in the low magnetic Reynolds number regime. In this regime, the electrical conductivity is low and the induced magnetic field is negligible compared to the applied magnetic field. This allows the MHD effects to be modeled by introducing source terms into the governing equations. Turbulence has been included by modifying the Baldwin-Lomax turbulence model to account for MHD effects. The new algorithm with MHD effects included has been used to compute both laminar and turbulent, supersonic, MHD flows over flat plates, and 3-D supersonic viscous flows in an experimental MHD channel. The new algorithms have been successfully incorporated into NASA's parabolized Navier-Stokes (UPS) code.

  10. A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation.

    Science.gov (United States)

    Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

    2014-11-25

    A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.

  11. On the validity of the Navier-Stokes equations for nanoscale liquid flows: The role of channel size

    Directory of Open Access Journals (Sweden)

    Chong Liu

    2011-09-01

    Full Text Available In this work, we investigate the validity of the Navier-Stokes (NS equations for nanoscale liquid flows through molecular dynamics simulations. We focus on the role of channel size by considering the fluid-wall interaction. Liquid flows between two planar parallel walls driven by an external force with channel size ranging from 2 to 80 nm are studied. The volumetric flux is computed and the dependence of the volumetric flux on the channel size is explained both qualitatively and quantitatively. It is found that the flow is sensitive to the fluid-wall binding energy and the classical fluid mechanics falls apart in small nanochannels. However, the wall effects become insignificant and the NS equations are valid when the channel size is larger than about 150 molecular diameters (∼ 50 nm.

  12. A finite element solution algorithm for the Navier-Stokes equations

    Science.gov (United States)

    Baker, A. J.

    1974-01-01

    A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.

  13. Navier-Stokes-Voigt Equations with Memory in 3D Lacking Instantaneous Kinematic Viscosity

    Science.gov (United States)

    Di Plinio, Francesco; Giorgini, Andrea; Pata, Vittorino; Temam, Roger

    2017-11-01

    We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. Unlike the classical Navier-Stokes-Voigt system, the energy balance involves the spatial gradient of the past history of the velocity rather than providing an instantaneous control on the high modes. In spite of this difficulty, we show that our system is dissipative in the dynamical systems sense and even possesses regular global and exponential attractors of finite fractal dimension. Such features of asymptotic well-posedness in absence of instantaneous high modes dissipation appear to be unique within the realm of dynamical systems arising from fluid models.

  14. Pipe Flow and Wall Turbulence Using a Modified Navier-Stokes Equation

    International Nuclear Information System (INIS)

    Jirkovsky, L.; Muriel, A.

    2012-01-01

    We use a derived incompressible modified Navier-Stokes equation to model pipe flow and wall turbulence. We reproduce the observed flattened paraboloid velocity profiles of turbulence that cannot be obtained directly using standard incompressible Navier-Stokes equation. The solutions found are in harmony with multi-valued velocity fields as a definition of turbulence. Repeating the procedure for the flow of turbulent fluid between two parallel flat plates we find similar flattened velocity profiles. We extend the analysis to the turbulent flow along a single wall and compare the results with experimental data and the established controversial von Karman logarithmic law of the wall. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  15. Navier-Stokes-Voigt Equations with Memory in 3D Lacking Instantaneous Kinematic Viscosity

    Science.gov (United States)

    Di Plinio, Francesco; Giorgini, Andrea; Pata, Vittorino; Temam, Roger

    2018-04-01

    We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. Unlike the classical Navier-Stokes-Voigt system, the energy balance involves the spatial gradient of the past history of the velocity rather than providing an instantaneous control on the high modes. In spite of this difficulty, we show that our system is dissipative in the dynamical systems sense and even possesses regular global and exponential attractors of finite fractal dimension. Such features of asymptotic well-posedness in absence of instantaneous high modes dissipation appear to be unique within the realm of dynamical systems arising from fluid models.

  16. Simulations of transition and turbulence on the Navier-Stokes computer

    International Nuclear Information System (INIS)

    Krist, S.E.; Zang, T.A.

    1987-01-01

    The Navier-Stokes Computer (NSC) consists of multiple local memory parallel processors interconnected in a hypercube network. Efficient implementation of algorithms on the NSC thus requires the effective utilization of both the coarse and fine grain paralelism inherent in the architectural design. The basic approach to implementing an algorithm on the NSC is presented herein. The particular finite-difference algorithm considered was developed for performing transition and turbulence simulations by direct solution of the time-dependent incompressible Navier-Stokes equations. The suitability of this algorithm for performing simulations of the isotropic turbulence problem is verified from computations performed on a Cray 2. Projected timing results for the algorithm on the NSC itself are presented for both the isotropic turbulence and laminar turbulent transition problems. 7 references

  17. Three-Dimensional Navier-Stokes Calculations Using the Modified Space-Time CESE Method

    Science.gov (United States)

    Chang, Chau-lyan

    2007-01-01

    The space-time conservation element solution element (CESE) method is modified to address the robustness issues of high-aspect-ratio, viscous, near-wall meshes. In this new approach, the dependent variable gradients are evaluated using element edges and the corresponding neighboring solution elements while keeping the original flux integration procedure intact. As such, the excellent flux conservation property is retained and the new edge-based gradients evaluation significantly improves the robustness for high-aspect ratio meshes frequently encountered in three-dimensional, Navier-Stokes calculations. The order of accuracy of the proposed method is demonstrated for oblique acoustic wave propagation, shock-wave interaction, and hypersonic flows over a blunt body. The confirmed second-order convergence along with the enhanced robustness in handling hypersonic blunt body flow calculations makes the proposed approach a very competitive CFD framework for 3D Navier-Stokes simulations.

  18. Hydrodynamics at the smallest scales: a solvability criterion for Navier-Stokes equations in high dimensions.

    Science.gov (United States)

    Viswanathan, T M; Viswanathan, G M

    2011-01-28

    Strong global solvability is difficult to prove for high-dimensional hydrodynamic systems because of the complex interplay between nonlinearity and scale invariance. We define the Ladyzhenskaya-Lions exponent α(L)(n)=(2+n)/4 for Navier-Stokes equations with dissipation -(-Δ)(α) in R(n), for all n≥2. We review the proof of strong global solvability when α≥α(L)(n), given smooth initial data. If the corresponding Euler equations for n>2 were to allow uncontrolled growth of the enstrophy (1/2)∥∇u∥(L²)(2), then no globally controlled coercive quantity is currently known to exist that can regularize solutions of the Navier-Stokes equations for α<α(L)(n). The energy is critical under scale transformations only for α=α(L)(n).

  19. Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations

    Science.gov (United States)

    Lawrence, J. L.; Tannehill, J. C.; Chaussee, D. S.

    1984-01-01

    MacCormack's implicit finite-difference scheme was used to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method for solving the PNS equations does not require the inversion of block tridiagonal systems of algebraic equations and permits the original explicit MacCormack scheme to be employed in those regions where implicit treatment is not needed. The advantages and disadvantages of the present adaptation are discussed in relation to those of the conventional Beam-Warming scheme for a flat plate boundary layer test case. Comparisons are made for accuracy, stability, computer time, computer storage, and ease of implementation. The present method was also applied to a second test case of hypersonic laminar flow over a 15% compression corner. The computed results compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

  20. Parabolized Navier-Stokes solutions of separation and trailing-edge flows

    Science.gov (United States)

    Brown, J. L.

    1983-01-01

    A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.

  1. Validation of a tetrahedral spectral element code for solving the Navier Stokes equation

    International Nuclear Information System (INIS)

    Niewiadomski, C.; Paraschivoiu, M.

    2004-01-01

    The tetrahedral spectral element method is considered to solve the incompressible Navier-Stokes equations because it is capable to capture complex geometries and obtain highly accurate solutions. This method allows accuracy improvements both by decreasing the spatial discretization as well as increasing the expansion order. The method is presented here-in as a modification of an standard finite element code. Some recent improvement to the baseline spectral element method for the tetrahedron described in References 3 and 2 are presented. These improvements include: the continuity enforcement procedure avoiding the need to change the global assembly operation and the removal of the reference coordinate system from the elemental evaluations thus simplifying greatly the method. A study is performed on the Stokes and Navier-Stokes equations to validate the method and the resulting code. (author)

  2. An efficient numerical technique for solving navier-stokes equations for rotating flows

    International Nuclear Information System (INIS)

    Haroon, T.; Shah, T.M.

    2000-01-01

    This paper simulates an industrial problem by solving compressible Navier-Stokes equations. The time-consuming tri-angularization process of a large-banded matrix, performed by memory economical Frontal Technique. This scheme successfully reduces the time for I/O operations even for as large as (40, 000 x 40, 000) matrix. Previously, this industrial problem can solved by using modified Newton's method with Gaussian elimination technique for the large matrix. In the present paper, the proposed Frontal Technique is successfully used, together with Newton's method, to solve compressible Navier-Stokes equations for rotating cylinders. By using the Frontal Technique, the method gives the solution within reasonably acceptance computational time. Results are compared with the earlier works done, and found computationally very efficient. Some features of the solution are reported here for the rotating machines. (author)

  3. A Newton method for the resolution of steady stochastic Navier-Stokes equations

    International Nuclear Information System (INIS)

    Le Maitre, O.

    2009-01-01

    We present a Newton method to compute the stochastic solution of the steady incompressible Navier-Stokes equations with random data (boundary conditions, forcing term, fluid properties). The method assumes a spectral discretization at the stochastic level involving a orthogonal basis of random functionals (such as Polynomial Chaos or stochastic multi-wavelets bases). The Newton method uses the unsteady equations to derive a linear equation for the stochastic Newton increments. This linear equation is subsequently solved following a matrix-free strategy, where the iterations consist in performing integrations of the linearized unsteady Navier-Stokes equations, with an appropriate time scheme to allow for a decoupled integration of the stochastic modes. Various examples are provided to demonstrate the efficiency of the method in determining stochastic steady solution, even for regimes where it is likely unstable. (authors)

  4. A stable penalty method for the compressible Navier-Stokes equations: II: One-dimensional domain decomposition schemes

    DEFF Research Database (Denmark)

    Hesthaven, Jan

    1997-01-01

    This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a res......This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions...... and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers's equation and developed for the compressible Navier-Stokes equations in general curvilinear coordinates. The versatility of the proposed scheme for the compressible Navier-Stokes equations is illustrated...

  5. Gas-Kinetic Navier-Stokes Solver for Hypersonic Flows in Thermal and Chemical Non-Equilibrium, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — This SBIR project proposes to develop a gas-kinetic Navier-Stokes solver for simulation of hypersonic flows in thermal and chemical non-equilibrium. The...

  6. A steady Navier-Stokes model for compressible fluid with partially strong solutions

    Czech Academy of Sciences Publication Activity Database

    Muzereau, O.; Neustupa, Jiří; Penel, P.

    2010-01-01

    Roč. 348, 11-12 (2010), s. 619-624 ISSN 1631-073X R&D Projects: GA ČR GA201/08/0012 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes equations * Compressible fluids * Weak solution Subject RIV: BA - General Mathematics Impact factor: 0.399, year: 2010 http://www.sciencedirect.com/science/article/pii/S1631073X10001160

  7. Investigation of vortex breakdown on delta wings using Navier-Stokes equations

    Science.gov (United States)

    Hsu, C.-H.; Liu, C. H.

    1992-01-01

    An efficient finite-difference scheme solving for the three-dimensional incompressible Navier-Stokes equations is described. Numerical simulations of vortex breakdown are then carried out for a sharp-edged delta wing and a round-edged double-delta wing at high Reynolds numbers. Computed results show that several major features of vortex breakdown are qualitatively in agreement with observations made in experiments.

  8. The solutions of Navier-Stokes equations in squeezing flow between parallel plates

    Czech Academy of Sciences Publication Activity Database

    Petrov, A. G.; Kharlamova, Irina

    2014-01-01

    Roč. 48, November–December (2014), s. 40-48 ISSN 0997-7546 Grant - others:Russian Foundation for Basic Research(RU) 14-01- 00818; Russian Foundation for Basic Research(RU) 14-01-00892 Institutional support: RVO:67985874 Keywords : closed form solution * Navier-Stokes equations * squeezing flow between plates * counterflow Subject RIV: BK - Fluid Dynamics Impact factor: 1.656, year: 2014

  9. Convergence of a numerical method for the compressible Navier-Stokes system on general domains

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Karper, T.; Michálek, Martin

    2016-01-01

    Roč. 134, č. 4 (2016), s. 667-704 ISSN 0029-599X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : numerical methods * Navier-Stokes system Subject RIV: BA - General Mathematics Impact factor: 2.152, year: 2016 http://link.springer.com/article/10.1007%2Fs00211-015-0786-6

  10. The Navier-Stokes-Fourier system: From weak solutions to numerical analysis

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard

    2015-01-01

    Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300. xml

  11. Krylov Subspace and Multigrid Methods Applied to the Incompressible Navier-Stokes Equations

    Science.gov (United States)

    Vuik, C.; Wesseling, P.; Zeng, S.

    1996-01-01

    We consider numerical solution methods for the incompressible Navier-Stokes equations discretized by a finite volume method on staggered grids in general coordinates. We use Krylov subspace and multigrid methods as well as their combinations. Numerical experiments are carried out on a scalar and a vector computer. Robustness and efficiency of these methods are studied. It appears that good methods result from suitable combinations of GCR and multigrid methods.

  12. Homogenization and singular limits for the complete Navier-Stokes-Fourier system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Novotný, A.; Takahashi, T.

    2010-01-01

    Roč. 94, č. 1 (2010), s. 33-57 ISSN 0021-7824 R&D Projects: GA MŠk LC06052; GA ČR GA201/08/0315 Institutional research plan: CEZ:AV0Z10190503 Keywords : compressible Navier-Stokes-Fourier equation s * homogenization * porous medium equation Subject RIV: BA - General Mathematics Impact factor: 1.450, year: 2010 http://www.sciencedirect.com/science/article/pii/S0021782409001639

  13. A rigorous derivation of the stationary compressible Reynolds equation via the Navier-Stokes equations

    Czech Academy of Sciences Publication Activity Database

    Ciuperca, I. S.; Feireisl, Eduard; Jai, M.; Petrov, A.

    2018-01-01

    Roč. 28, č. 4 (2018), s. 697-732 ISSN 0218-2025 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible fluids * stationary Navier-Stokes equations * thin films Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.860, year: 2016 https://www.worldscientific.com/doi/abs/10.1142/S0218202518500185

  14. Comparison of generalized Reynolds and Navier Stokes equations for flow of a power law fluid

    Science.gov (United States)

    Mullen, R. L.; Prekwas, A.; Braun, M. J.; Hendricks, R. C.

    1987-01-01

    This paper compares a finite element solution of a modified Reynolds equation with a finite difference solution of the Navier-Stokes equation for a power law fluid. Both the finite element and finite difference formulation are reviewed. Solutions to spiral flow in parallel and conical geometries are compared. Comparison with experimental results are also given. The effects of the assumptions used in the Reynolds equation are discussed.

  15. Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

    Czech Academy of Sciences Publication Activity Database

    Šístek, Jakub; Cirak, F.

    2015-01-01

    Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace method s Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www. science direct.com/ science /article/pii/S0045793015003023

  16. On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Donatelli, D.; Feireisl, Eduard; Novotný, A.

    2010-01-01

    Roč. 13, č. 4 (2010), s. 783-798 ISSN 1531-3492 R&D Projects: GA MŠk LC06052; GA ČR GA201/08/0315 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes equations * singular limits * low Mach number * compressible fluids * unbounded domains Subject RIV: BA - General Mathematics Impact factor: 0.874, year: 2010 http://www.aimsciences.org/journals/displayArticles.jsp?paperID=4976

  17. Set of difference spitting schemes for solving the Navier-Stokes incompressible equations in natural variables

    International Nuclear Information System (INIS)

    Koleshko, S.B.

    1989-01-01

    A three-parametric set of difference schemes is suggested to solve Navier-Stokes equations with the use of the relaxation form of the continuity equation. The initial equations are stated for time increments. Use is made of splitting the operator into one-dimensional forms that reduce calculations to scalar factorizations. Calculated results for steady- and unsteady-state flows in a cavity are presented

  18. On lower bounds for possible blow-up solutions to the periodic Navier-Stokes equation

    International Nuclear Information System (INIS)

    Cortissoz, Jean C.; Montero, Julio A.; Pinilla, Carlos E.

    2014-01-01

    We show a new lower bound on the H .3/2 (T 3 ) norm of a possible blow-up solution to the Navier-Stokes equation, and also comment on the extension of this result to the whole space. This estimate can be seen as a natural limiting result for Leray's blow-up estimates in L p (R 3 ), 3 .5/2 (T 3 ), and give the corresponding extension to the case of the whole space

  19. Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.

    Science.gov (United States)

    Fouxon, Itzhak; Oz, Yaron

    2008-12-31

    We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.

  20. Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.

    Science.gov (United States)

    Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

    2013-01-01

    An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.

  1. Existence and Stability of Spatial Plane Waves for the Incompressible Navier-Stokes in R^3

    Science.gov (United States)

    Correia, Simão; Figueira, Mário

    2018-03-01

    We consider the three-dimensional incompressible Navier-Stokes equation on the whole space. We observe that this system admits a L^∞ family of global spatial plane wave solutions, which are connected with the two-dimensional equation. We then proceed to prove local well-posedness over a space which includes L^3(R^3) and these solutions. Finally, we prove L^3-stability of spatial plane waves, with no condition on their size.

  2. Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations

    International Nuclear Information System (INIS)

    Fouxon, Itzhak; Oz, Yaron

    2008-01-01

    We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them

  3. Time-Filtered Navier-Stokes Approach and Emulation of Turbulence-Chemistry Interaction

    Science.gov (United States)

    Liu, Nan-Suey; Wey, Thomas; Shih, Tsan-Hsing

    2013-01-01

    This paper describes the time-filtered Navier-Stokes approach capable of capturing unsteady flow structures important for turbulent mixing and an accompanying subgrid model directly accounting for the major processes in turbulence-chemistry interaction. They have been applied to the computation of two-phase turbulent combustion occurring in a single-element lean-direct-injection combustor. Some of the preliminary results from this computational effort are presented in this paper.

  4. Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

    Science.gov (United States)

    Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.

    2013-01-01

    Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

  5. New representation of Navier-Stokes equations governing self-similar homogeneous turbulence

    International Nuclear Information System (INIS)

    Foias, C.; Manley, O.P.; Temam, R.

    1983-01-01

    A new form of the Navier-Stokes equation resulting from a change of variables is presented. The new form has several advantages: It yields a new asymptotic behavior of the flow for long times and vanishingly small viscosity. In addition an interpretation of the new equation in terms of a simple random walk yields immediately not only the Kolmogorov (2/3)-power law but also an intermittency exponent well within the experimental uncertainty

  6. Convergence of a numerical method for the compressible Navier-Stokes system on general domains

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Karper, T.; Michálek, Martin

    2016-01-01

    Roč. 134, č. 4 (2016), s. 667-704 ISSN 0029-599X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : numerical methods * Navier - Stokes system Subject RIV: BA - General Mathematics Impact factor: 2.152, year: 2016 http://link.springer.com/article/10.1007%2Fs00211-015-0786-6

  7. Some Similarity Reduction Solutions to Two-Dimensional Incompressible Navier-Stokes Equation

    Science.gov (United States)

    Jiao, Xiao-Yu

    2009-09-01

    We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equation in conventional stream function form through Lie symmetry method and construct some similarity reduction solutions. Two special cases in [D.K. Ludlow, P.A. Clarkson, and A.P. Bassom, Stud. Appl. Math. 103 (1999) 183] and a theorem in [S.Y. Lou, M. Jia, X.Y. Tang, and F. Huang, Phys. Rev. E 75 (2007) 056318] are retrieved.

  8. Etude de l'équation de Navier-Stokes stochastique non homogène ...

    African Journals Online (AJOL)

    Le travail de cet article consiste à étudier l'existence et l'unicité de la solution des équations de Navier-Stokes Stochastiques et non homogènes selon une méthode directe due à Faedo-Galerkin [1]. Cette méthode consiste à approcher les solutions de ces équations dans un espace de dimension finie. Dans ce présent ...

  9. The Navier-Stokes-Fourier system: From weak solutions to numerical analysis

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard

    2015-01-01

    Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes- Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300.xml

  10. Ergodicity of stochastic 2D Navier-Stokes equation with Lévy noise

    Science.gov (United States)

    Dong, Zhao; Xie, Yingchao

    In this paper we deal with the 2D Navier-Stokes equation perturbed by a Lévy noise force whose white noise part is non-degenerate and that the intensity measure of Poisson measure is σ-finite. Existence and uniqueness of invariant measure for this equation is obtained, two main properties of the Markov semigroup associated with this equation are proved. In other words, strong Feller property and irreducibility hold in the same space.

  11. Robustness of strong solutions to the compressible Navier-Stokes system

    Czech Academy of Sciences Publication Activity Database

    Bella, P.; Feireisl, Eduard; Jin, B.J.; Novotný, A.

    2015-01-01

    Roč. 362, 1-2 (2015), s. 281-303 ISSN 0025-5831 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes system * smooth solution * stability Subject RIV: BA - General Mathematics Impact factor: 1.366, year: 2015 http://link.springer.com/article/10.1007%2Fs00208-014-1119-2

  12. Generalized Stokes eignefunctions: a new trial basis for the solution of incompressible Navier-Stokes equations

    International Nuclear Information System (INIS)

    Batcho, P.F.; Karniadakis, G.E.

    1994-01-01

    The present study focuses on the solution of the incompressible Navier-Stokes equations in general, non-separable domains, and employs a Galerkin projection of divergence-free vector functions as a trail basis. This basis is obtained from the solution of a generalized constrained Stokes eigen-problem in the domain of interest. Faster convergence can be achieved by constructing a singular Stokes eigen-problem in which the Stokes operator is modified to include a variable coefficient which vanishes at the domain boundaries. The convergence properties of such functions are advantageous in a least squares sense and are shown to produce significantly better approximations to the solution of the Navier-Stokes equations in post-critical states where unsteadiness characterizes the flowfield. Solutions for the eigen-systems are efficiently accomplished using a combined Lanczos-Uzawa algorithm and spectral element discretizations. Results are presented for different simulations using these global spectral trial basis on non-separable and multiply-connected domains. It is confirmed that faster convergence is obtained using the singular eigen-expansions in approximating stationary Navier-Stokes solutions in general domains. It is also shown that 100-mode expansions of time-dependent solutions based on the singular Stokes eigenfunctions are sufficient to accurately predict the dynamics of flows in such domains, including Hopf bifurcations, intermittency, and details of flow structures

  13. Convergence acceleration of Navier-Stokes equation using adaptive wavelet method

    International Nuclear Information System (INIS)

    Kang, Hyung Min; Ghafoor, Imran; Lee, Do Hyung

    2010-01-01

    An efficient adaptive wavelet method is proposed for the enhancement of computational efficiency of the Navier-Stokes equations. The method is based on sparse point representation (SPR), which uses the wavelet decomposition and thresholding to obtain a sparsely distributed dataset. The threshold mechanism is modified in order to maintain the spatial accuracy of a conventional Navier-Stokes solver by adapting the threshold value to the order of spatial truncation error. The computational grid can be dynamically adapted to a transient solution to reflect local changes in the solution. The flux evaluation is then carried out only at the points of the adapted dataset, which reduces the computational effort and memory requirements. A stabilization technique is also implemented to avoid the additional numerical errors introduced by the threshold procedure. The numerical results of the adaptive wavelet method are compared with a conventional solver to validate the enhancement in computational efficiency of Navier-Stokes equations without the degeneration of the numerical accuracy of a conventional solver

  14. Entropy Stable Staggered Grid Spectral Collocation for the Burgers' and Compressible Navier-Stokes Equations

    Science.gov (United States)

    Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.

    2015-01-01

    Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

  15. The direct Discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids

    Science.gov (United States)

    Yang, Xiaoquan; Cheng, Jian; Liu, Tiegang; Luo, Hong

    2015-11-01

    The direct discontinuous Galerkin (DDG) method based on a traditional discontinuous Galerkin (DG) formulation is extended and implemented for solving the compressible Navier-Stokes equations on arbitrary grids. Compared to the widely used second Bassi-Rebay (BR2) scheme for the discretization of diffusive fluxes, the DDG method has two attractive features: first, it is simple to implement as it is directly based on the weak form, and therefore there is no need for any local or global lifting operator; second, it can deliver comparable results, if not better than BR2 scheme, in a more efficient way with much less CPU time. Two approaches to perform the DDG flux for the Navier- Stokes equations are presented in this work, one is based on conservative variables, the other is based on primitive variables. In the implementation of the DDG method for arbitrary grid, the definition of mesh size plays a critical role as the formation of viscous flux explicitly depends on the geometry. A variety of test cases are presented to demonstrate the accuracy and efficiency of the DDG method for discretizing the viscous fluxes in the compressible Navier-Stokes equations on arbitrary grids.

  16. Capability of State-of-the-Art Navier-Stokes Solvers for the Prediction of Helicopter Fuselage Aerodynamics

    DEFF Research Database (Denmark)

    N., Kroll; P., Renzoni; M., Amato

    1998-01-01

    The purpose of this paper is to describe the influence of different Navier-Stokes solvers and grids on the prediction of the global coefficients for a simplified geometry of a helicopter fuselage.......The purpose of this paper is to describe the influence of different Navier-Stokes solvers and grids on the prediction of the global coefficients for a simplified geometry of a helicopter fuselage....

  17. Navier-Stokes wave models for investigations of breakwater characteristics

    CSIR Research Space (South Africa)

    Cannoo, BR

    2008-03-01

    Full Text Available The dynamics of full breakwater stability are of importance in coastal engineering, and numerical models are some of the tools that can be applied. Given the work that exists worldwide in numerical models of breakwaters and armour units, it appears that a... examines spectral wave diffraction and refraction, dolos contact dynamics, and experimental breakwater modelling. Wave interaction effects and turbulence effects on the stability of armour unit and rock beds have been investigated widely. Shallow...

  18. Eulerian derivations of non-inertial Navier-Stokes equations

    CSIR Research Space (South Africa)

    Combrinck, MA

    2014-09-01

    Full Text Available stream_source_info Dala3_2014_ABSTRACT ONLY.pdf.txt stream_content_type text/plain stream_size 655 Content-Encoding ISO-8859-1 stream_name Dala3_2014_ABSTRACT ONLY.pdf.txt Content-Type text/plain; charset=ISO-8859...

  19. On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations

    Science.gov (United States)

    Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

    2017-12-01

    The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space. For DG methods applied to the dual splitting projection method, instabilities have recently been reported that occur for small time step sizes. Since the critical time step size depends on the viscosity and the spatial resolution, these instabilities limit the robustness of the Navier-Stokes solver in case of complex engineering applications characterized by coarse spatial resolutions and small viscosities. By means of numerical investigation we give evidence that these instabilities are related to the discontinuous Galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure. Integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method. Since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity, a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high-order accuracy with respect to the temporal discretization. This new formulation is stable in the limit of small time steps for both equal-order and mixed-order polynomial approximations. Although the dual splitting scheme itself includes inf-sup stabilizing contributions, we demonstrate that spurious pressure oscillations appear for equal-order polynomials and small time steps highlighting the necessity to consider inf-sup stability explicitly.

  20. A deflation based parallel algorithm for spectral element solution of the incompressible Navier-Stokes equations

    Energy Technology Data Exchange (ETDEWEB)

    Fischer, P.F. [Brown Univ., Providence, RI (United States)

    1996-12-31

    Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.

  1. Finite volume methods for the incompressible Navier-Stokes equations on unstructured grids

    Energy Technology Data Exchange (ETDEWEB)

    Meese, Ernst Arne

    1998-07-01

    Most solution methods of computational fluid dynamics (CFD) use structured grids based on curvilinear coordinates for compliance with complex geometries. In a typical industry application, about 80% of the time used to produce the results is spent constructing computational grids. Recently the use of unstructured grids has been strongly advocated. For unstructured grids there are methods for generating them automatically on quite complex domains. This thesis focuses on the design of Navier-Stokes solvers that can cope with unstructured grids and ''low quality grids'', thus reducing the need for human intervention in the grid generation.

  2. A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations

    Science.gov (United States)

    Guruswamy, Guru P.; Lee, Henry

    2014-01-01

    The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no

  3. On a modified form of navier-stokes equations for three-dimensional flows.

    Science.gov (United States)

    Venetis, J

    2015-01-01

    A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

  4. Modeling digital pulse waveforms by solving one-dimensional Navier-stokes equations.

    Science.gov (United States)

    Fedotov, Aleksandr A; Akulova, Anna S; Akulov, Sergey A

    2016-08-01

    Mathematical modeling for composition distal arterial pulse wave in the blood vessels of the upper limbs was considered. Formation of distal arterial pulse wave is represented as a composition of forward and reflected pulse waves propagating along the arterial vessels. The formal analogy between pulse waves propagation along the human arterial system and the propagation of electrical oscillations in electrical transmission lines with distributed parameters was proposed. Dependencies of pulse wave propagation along the human arterial system were obtained by solving the one-dimensional Navier-Stokes equations for a few special cases.

  5. Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers

    Science.gov (United States)

    Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

    2014-01-01

    This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.

  6. 3-D Navier-Stokes Analysis of Blade Root Aerodynamics for a Tiltrotor Aircraft In Cruise

    Science.gov (United States)

    Romander, Ethan

    2006-01-01

    The blade root area of a tiltrotor aircraft's rotor is constrained by a great many factors, not the least of which is aerodynamic performance in cruise. For this study, Navier-Stokes CFD techniques are used to study the aerodynamic performance in cruise of a rotor design as a function of airfoil thickness along the blade and spinner shape. Reducing airfoil thickness along the entire blade will be shown to have the greatest effect followed by smaller but still significant improvements achieved by reducing the thickness of root airfoils only. Furthermore, altering the shape of the spinner will be illustrated as a tool to tune the aerodynamic performance very near the blade root.

  7. Dynamics of three-tori in a periodically forced navier-stokes flow

    Science.gov (United States)

    Lopez; Marques

    2000-07-31

    Three-tori solutions of the Navier-Stokes equations and their dynamics are elucidated by use of a global Poincare map. The flow is contained in a finite annular gap between two concentric cylinders, driven by the steady rotation and axial harmonic oscillations of the inner cylinder. The three-tori solutions undergo global bifurcations, including a new gluing bifurcation, associated with homoclinic and heteroclinic connections to unstable solutions (two-tori). These unstable two-tori act as organizing centers for the three-tori dynamics. A discrete space-time symmetry influences the dynamics.

  8. Large Scale Flutter Data for Design of Rotating Blades Using Navier-Stokes Equations

    Science.gov (United States)

    Guruswamy, Guru P.

    2012-01-01

    A procedure to compute flutter boundaries of rotating blades is presented; a) Navier-Stokes equations. b) Frequency domain method compatible with industry practice. Procedure is initially validated: a) Unsteady loads with flapping wing experiment. b) Flutter boundary with fixed wing experiment. Large scale flutter computation is demonstrated for rotating blade: a) Single job submission script. b) Flutter boundary in 24 hour wall clock time with 100 cores. c) Linearly scalable with number of cores. Tested with 1000 cores that produced data in 25 hrs for 10 flutter boundaries. Further wall-clock speed-up is possible by performing parallel computations within each case.

  9. Reynolds-Averaged Navier-Stokes Analysis of Zero Efflux Flow Control over a Hump Model

    Science.gov (United States)

    Rumsey, Christopher L.

    2006-01-01

    The unsteady flow over a hump model with zero efflux oscillatory flow control is modeled computationally using the unsteady Reynolds-averaged Navier-Stokes equations. Three different turbulence models produce similar results, and do a reasonably good job predicting the general character of the unsteady surface pressure coefficients during the forced cycle. However, the turbulent shear stresses are underpredicted in magnitude inside the separation bubble, and the computed results predict too large a (mean) separation bubble compared with experiment. These missed predictions are consistent with earlier steady-state results using no-flow-control and steady suction, from a 2004 CFD validation workshop for synthetic jets.

  10. Quasiconservation laws for compressible three-dimensional Navier-Stokes flow.

    Science.gov (United States)

    Gibbon, J D; Holm, D D

    2012-10-01

    We formulate the quasi-Lagrangian fluid transport dynamics of mass density ρ and the projection q=ω·∇ρ of the vorticity ω onto the density gradient, as determined by the three-dimensional compressible Navier-Stokes equations for an ideal gas, although the results apply for an arbitrary equation of state. It turns out that the quasi-Lagrangian transport of q cannot cross a level set of ρ. That is, in this formulation, level sets of ρ (isopycnals) are impermeable to the transport of the projection q.

  11. Nearly Interactive Parabolized Navier-Stokes Solver for High Speed Forebody and Inlet Flows

    Science.gov (United States)

    Benson, Thomas J.; Liou, May-Fun; Jones, William H.; Trefny, Charles J.

    2009-01-01

    A system of computer programs is being developed for the preliminary design of high speed inlets and forebodies. The system comprises four functions: geometry definition, flow grid generation, flow solver, and graphics post-processor. The system runs on a dedicated personal computer using the Windows operating system and is controlled by graphical user interfaces written in MATLAB (The Mathworks, Inc.). The flow solver uses the Parabolized Navier-Stokes equations to compute millions of mesh points in several minutes. Sample two-dimensional and three-dimensional calculations are demonstrated in the paper.

  12. An implicit three-dimensional Navier-Stokes solver for compressible flow

    International Nuclear Information System (INIS)

    Yoon, Seokkwan; Kwak, Dochan.

    1991-01-01

    A three-dimensional numerical method based on the lower-upper symmetric-Gauss-Seidel implicit scheme in conjunction with the flux-limited dissipation model is developed for solving the compressible Navier-Stokes equations. A new computer code which is based on this method requires only 9 microsec per grid-point per iteration on a single processor of a Cray YMP computer and executes at the sustained rate of 170 MFLOPS. A reduction of 4 orders of magnitude in the residual for a high Reynolds number flow using 230 K grid points is obtained in 24 minutes. The computational results compare well with available experimental data. 39 refs

  13. Compressible Navier-Stokes equations: A study of leading edge effects

    Science.gov (United States)

    Hariharan, S. I.; Karbhari, P. R.

    1987-01-01

    A computational method is developed that allows numerical calculations of the time dependent compressible Navier-Stokes equations.The current results concern a study of flow past a semi-infinite flat plate.Flow develops from given inflow conditions upstream and passes over the flat plate to leave the computational domain without reflecting at the downstream boundary. Leading edge effects are included in this paper. In addition, specification of a heated region which gets convected with the flow is considered. The time history of this convection is obtained, and it exhibits a wave phenomena.

  14. Discretely Self-Similar Solutions to the Navier-Stokes Equations with Besov Space Data

    Science.gov (United States)

    Bradshaw, Zachary; Tsai, Tai-Peng

    2017-12-01

    We construct self-similar solutions to the three dimensional Navier-Stokes equations for divergence free, self-similar initial data that can be large in the critical Besov space {\\dot{B}_{p,∞}^{3/p-1}} where 3 1. These results extend those of uc(Bradshaw) and uc(Tsai) (Ann Henri Poincaré 2016. https://doi.org/10.1007/s00023-016-0519-0) which dealt with initial data in L 3 w since {L^3_w\\subsetneq \\dot{B}_{p,∞}^{3/p-1}} for p > 3. We also provide several concrete examples of vector fields in the relevant function spaces.

  15. Solving the incompressible surface Navier-Stokes equation by surface finite elements

    Science.gov (United States)

    Reuther, Sebastian; Voigt, Axel

    2018-01-01

    We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g (S ) . The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding R3, penalization of the normal component, a Chorin projection method, and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincaré-Hopf theorem on n-tori.

  16. Stream function-vorticity finite elements and the resolution of the Navier-Stokes equations

    International Nuclear Information System (INIS)

    Almeida, R.C.C. de.

    1987-07-01

    A stream function-vorticity finite element formulation for the solution of the Navier-Stokes equations is proposed. The present work shows a procedure to solve the problem posed by the no-slip conditions on solid frontiers which can also be applied to flow problems in a multi-connected domain. Moreover, a methodology to solve the pressure is developed using the stream function-vorticity approximate solution. Numerical experiments were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) [pt

  17. An adaptive Petrov-Galerkin formulation for solving the compressible Euler and Navier-Stokes

    International Nuclear Information System (INIS)

    Almeida, Regina Celia Cerqueira de

    1993-01-01

    A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author)

  18. The solution of the Navier-Stokes equations using Gauss-Seidel line relaxation

    Science.gov (United States)

    Maccormack, Robert W.; Candler, Graham V.

    1989-01-01

    The Navier-Stokes equations in an implicit flux-split difference formulation are solved numerically using a Gauss-Seidel line-relaxation procedure. Particular attention is given to the selection of flux-vector splitting method and flux splitting in boundary layers. Results for sample problems involving (1) turbulent supersonic flow over a cone and (2) the viscous hypersonic flow of a chemically reacting gas in thermal nonequilibrium past a blunted cone are presented in extensive graphs and briefly characterized. The present flux-split procedures are shown to provide accurate shear-layer calculations.

  19. An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

    KAUST Repository

    Cockburn, Bernardo

    2008-12-20

    We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings. © 2008 Springer Science+Business Media, LLC.

  20. Large-Eddy / Reynolds-Averaged Navier-Stokes Simulations of a Dual-Mode Scramjet Combustor

    Science.gov (United States)

    Fulton, Jesse A.; Edwards, Jack R.; Hassan, Hassan A.; Rockwell, Robert; Goyne, Christopher; McDaniel, James; Smith, Chad; Cutler, Andrew; Johansen, Craig; Danehy, Paul M.; hide

    2012-01-01

    Numerical simulations of reacting and non-reacting flows within a scramjet combustor configuration experimentally mapped at the University of Virginia s Scramjet Combustion Facility (operating with Configuration A ) are described in this paper. Reynolds-Averaged Navier-Stokes (RANS) and hybrid Large Eddy Simulation / Reynolds-Averaged Navier-Stokes (LES / RANS) methods are utilized, with the intent of comparing essentially blind predictions with results from non-intrusive flow-field measurement methods including coherent anti-Stokes Raman spectroscopy (CARS), hydroxyl radical planar laser-induced fluorescence (OH-PLIF), stereoscopic particle image velocimetry (SPIV), wavelength modulation spectroscopy (WMS), and focusing Schlieren. NC State's REACTMB solver was used both for RANS and LES / RANS, along with a 9-species, 19- reaction H2-air kinetics mechanism by Jachimowski. Inviscid fluxes were evaluated using Edwards LDFSS flux-splitting scheme, and the Menter BSL turbulence model was utilized in both full-domain RANS simulations and as the unsteady RANS portion of the LES / RANS closure. Simulations were executed and compared with experiment at two equivalence ratios, PHI = 0.17 and PHI = 0.34. Results show that the PHI = 0.17 flame is hotter near the injector while the PHI = 0.34 flame is displaced further downstream in the combustor, though it is still anchored to the injector. Reactant mixing was predicted to be much better at the lower equivalence ratio. The LES / RANS model appears to predict lower overall heat release compared to RANS (at least for PHI = 0.17), and its capability to capture the direct effects of larger turbulent eddies leads to much better predictions of reactant mixing and combustion in the flame stabilization region downstream of the fuel injector. Numerical results from the LES/RANS model also show very good agreement with OH-PLIF and SPIV measurements. An un-damped long-wave oscillation of the pre-combustion shock train, which caused

  1. Drifting solutions with elliptic symmetry for the compressible Navier-Stokes equations with density-dependent viscosity

    International Nuclear Information System (INIS)

    An, Hongli; Yuen, Manwai

    2014-01-01

    In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for the Navier-Stokes model wherein the velocity components are governed by a generalized Emden dynamical system. In particular, when the viscosity variables are taken the same as Yuen [M. W. Yuen, “Analytical solutions to the Navier-Stokes equations,” J. Math. Phys. 49, 113102 (2008)], our solutions constitute a generalization of that obtained by Yuen. Interestingly, numerical simulations show that the analytical solutions can be used to explain the drifting phenomena of the propagation wave like Tsunamis in oceans

  2. Research on the optimal dynamical systems of three-dimensional Navier-Stokes equations based on weighted residual

    Science.gov (United States)

    Peng, NaiFu; Guan, Hui; Wu, ChuiJie

    2016-04-01

    In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.

  3. Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations

    Science.gov (United States)

    Hafez, Mohammed; Dacles, Jennifer

    1989-01-01

    The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.

  4. Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

    Science.gov (United States)

    Jiang, Bo-Nan; Loh, Ching Y.; Povinelli, Louis A.

    1994-01-01

    Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

  5. Dual Dynamically Orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions

    Science.gov (United States)

    Musharbash, Eleonora; Nobile, Fabio

    2018-02-01

    In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational principle can be set in the constrained manifold of all S rank random fields with a prescribed value on the boundary, expressed in low rank format, with rank smaller then S. We characterize the tangent space to the constrained manifold by means of a Dual Dynamically Orthogonal (Dual DO) formulation, in which the stochastic modes are kept orthonormal and the deterministic modes satisfy suitable boundary conditions, consistent with the original problem. The Dual DO formulation is also convenient to include the incompressibility constraint, when dealing with incompressible Navier Stokes equations. We show the performance of the proposed Dual DO approximation on two numerical test cases: the classical benchmark of a laminar flow around a cylinder with random inflow velocity, and a biomedical application for simulating blood flow in realistic carotid artery reconstructed from MRI data with random inflow conditions coming from Doppler measurements.

  6. Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations

    Science.gov (United States)

    Walters, R.A.; Carey, G.F.

    1983-01-01

    The origin and nature of spurious oscillation modes that appear in mixed finite element methods are examined. In particular, the shallow water equations are considered and a modal analysis for the one-dimensional problem is developed. From the resulting dispersion relations we find that the spurious modes in elevation are associated with zero frequency and large wave number (wavelengths of the order of the nodal spacing) and consequently are zero-velocity modes. The spurious modal behavior is the result of the finite spatial discretization. By means of an artificial compressibility and limiting argument we are able to resolve the similar problem for the Navier-Stokes equations. The relationship of this simpler analysis to alternative consistency arguments is explained. This modal approach provides an explanation of the phenomenon in question and permits us to deduce the cause of the very complex behavior of spurious modes observed in numerical experiments with the shallow water equations and Navier-Stokes equations. Furthermore, this analysis is not limited to finite element formulations, but is also applicable to finite difference formulations. ?? 1983.

  7. Source Term Model for Steady Micro Jets in a Navier-Stokes Computer Code

    Science.gov (United States)

    Waithe, Kenrick A.

    2005-01-01

    A source term model for steady micro jets was implemented into a non-proprietary Navier-Stokes computer code, OVERFLOW. The source term models the mass flow and momentum created by a steady blowing micro jet. The model is obtained by adding the momentum and mass flow created by the jet to the Navier-Stokes equations. The model was tested by comparing with data from numerical simulations of a single, steady micro jet on a flat plate in two and three dimensions. The source term model predicted the velocity distribution well compared to the two-dimensional plate using a steady mass flow boundary condition, which was used to simulate a steady micro jet. The model was also compared to two three-dimensional flat plate cases using a steady mass flow boundary condition to simulate a steady micro jet. The three-dimensional comparison included a case with a grid generated to capture the circular shape of the jet and a case without a grid generated for the micro jet. The case without the jet grid mimics the application of the source term. The source term model compared well with both of the three-dimensional cases. Comparisons of velocity distribution were made before and after the jet and Mach and vorticity contours were examined. The source term model allows a researcher to quickly investigate different locations of individual or several steady micro jets. The researcher is able to conduct a preliminary investigation with minimal grid generation and computational time.

  8. Navier-Stokes symmetry in the phenomenological transport theory for bacterial chemotaxis

    Science.gov (United States)

    Rosen, Gerald

    1984-05-01

    It is observed that the Navier-Stokes space-time dilatation invariance (x-->-->λx-->,t-->λ2t) implies that the random motility and chemotactic flux function take the forms observed experimentally for motile Escherichia coli attracted by low concentrations of oxygen; moreover, the rate function for E. coli consumption of dissolved oxygen is required to have the form (const) × (local oxygen concentration)2/3. It is also noteworthy that the Schrödinger-Bloch function for redistribution of chemotactic bacteria cells is invariant under the space-time dilatation transformations if and only if the chemotactic flux coefficient-random motility ratio equals 2, a value in the range 1.1 to 2.5 observed experimentally by Holz and Chen in the oxygen chemotaxis of motile E. coli. Suitably specialized governing equations for the phenomenological transport theory also admit a Galilean transformation invariance symmetry if and only if the chemotactic flux coefficient-critical substrate diffusivity ratio equals -2 and the consumption rate function is simply linear in the local oxygen concentration. Applicable to the regime of viscous incompressible flows with Reynolds numbers much less than unity, the Navier-Stokes superposition invariance may also give rise to a corresponding invariance symmetry in equivalent but linear phenomenological transport equations.

  9. Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations.

    Science.gov (United States)

    Ercan, Ali; Kavvas, M Levent

    2017-07-25

    Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions.

  10. Boundary Layers for the Navier-Stokes Equations Linearized Around a Stationary Euler Flow

    Science.gov (United States)

    Gie, Gung-Min; Kelliher, James P.; Mazzucato, Anna L.

    2018-03-01

    We study the viscous boundary layer that forms at small viscosity near a rigid wall for the solution to the Navier-Stokes equations linearized around a smooth and stationary Euler flow (LNSE for short) in a smooth bounded domain Ω \\subset R^3 under no-slip boundary conditions. LNSE is supplemented with smooth initial data and smooth external forcing, assumed ill-prepared, that is, not compatible with the no-slip boundary condition. We construct an approximate solution to LNSE on the time interval [0, T], 0Navier-Stokes solution and the proposed expansion vanishes as the viscosity tends to zero in L^2(Ω ) uniformly in time, and remains bounded independently of viscosity in the space L^2([0,T];H^1(Ω )) . We make this construction both for a 3D channel domain and a smooth domain with a curved boundary. The zero-viscosity limit for LNSE, that is, the convergence of the LNSE solution to the solution of the linearized Euler equations around the same profile when viscosity vanishes, then naturally follows from the validity of this asymptotic expansion. This article generalizes and improves earlier works, such as Temam and Wang (Indiana Univ Math J 45(3):863-916, 1996), Xin and Yanagisawa (Commun Pure Appl Math 52(4):479-541, 1999), and Gie (Commun Math Sci 12(2):383-400, 2014).

  11. A new nonlinear turbulence model based on Partially-Averaged Navier-Stokes Equations

    International Nuclear Information System (INIS)

    Liu, J T; Wu, Y L; Cai, C; Liu, S H; Wang, L Q

    2013-01-01

    Partially-averaged Navier-Stokes (PANS) Model was recognized as a Reynolds-averaged Navier-Stokes (RANS) to direct numerical simulation (DNS) bridging method. PANS model was purported for any filter width-from RANS to DNS. PANS method also shared some similarities with the currently popular URANS (unsteady RANS) method. In this paper, a new PANS model was proposed, which was based on RNG k-ε turbulence model. The Standard and RNG k-ε turbulence model were both isotropic models, as well as PANS models. The sheer stress in those PANS models was solved by linear equation. The linear hypothesis was not accurate in the simulation of complex flow, such as stall phenomenon. The sheer stress here was solved by nonlinear method proposed by Ehrhard. Then, the nonlinear PANS model was set up. The pressure coefficient of the suction side of the NACA0015 hydrofoil was predicted. The result of pressure coefficient agrees well with experimental result, which proves that the nonlinear PANS model can capture the high pressure gradient flow. A low specific centrifugal pump was used to verify the capacity of the nonlinear PANS model. The comparison between the simulation results of the centrifugal pump and Particle Image Velocimetry (PIV) results proves that the nonlinear PANS model can be used in the prediction of complex flow field

  12. Implementation and analysis of a Navier-Stokes algorithm on parallel computers

    Science.gov (United States)

    Fatoohi, Raad A.; Grosch, Chester E.

    1988-01-01

    The results of the implementation of a Navier-Stokes algorithm on three parallel/vector computers are presented. The object of this research is to determine how well, or poorly, a single numerical algorithm would map onto three different architectures. The algorithm is a compact difference scheme for the solution of the incompressible, two-dimensional, time-dependent Navier-Stokes equations. The computers were chosen so as to encompass a variety of architectures. They are the following: the MPP, an SIMD machine with 16K bit serial processors; Flex/32, an MIMD machine with 20 processors; and Cray/2. The implementation of the algorithm is discussed in relation to these architectures and measures of the performance on each machine are given. The basic comparison is among SIMD instruction parallelism on the MPP, MIMD process parallelism on the Flex/32, and vectorization of a serial code on the Cray/2. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Finally, conclusions are presented.

  13. Verification of Euler/Navier-Stokes codes using the method of manufactured solutions

    Science.gov (United States)

    Roy, C. J.; Nelson, C. C.; Smith, T. M.; Ober, C. C.

    2004-02-01

    The method of manufactured solutions is used to verify the order of accuracy of two finite-volume Euler and Navier-Stokes codes. The Premo code employs a node-centred approach using unstructured meshes, while the Wind code employs a similar scheme on structured meshes. Both codes use Roe's upwind method with MUSCL extrapolation for the convective terms and central differences for the diffusion terms, thus yielding a numerical scheme that is formally second-order accurate. The method of manufactured solutions is employed to generate exact solutions to the governing Euler and Navier-Stokes equations in two dimensions along with additional source terms. These exact solutions are then used to accurately evaluate the discretization error in the numerical solutions. Through global discretization error analyses, the spatial order of accuracy is observed to be second order for both codes, thus giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised. Examples of coding mistakes discovered using the method are also given.

  14. A Navier-Stokes Approximation of the 3D Euler Equation with the Zero Flux on the Boundary

    Czech Academy of Sciences Publication Activity Database

    Bellout, H.; Neustupa, Jiří

    2008-01-01

    Roč. 10, č. 4 (2008), s. 531-553 ISSN 1422-6928 R&D Projects: GA ČR GA201/05/0005 Institutional research plan: CEZ:AV0Z10190503 Keywords : Euler equations * Navier-Stokes equations Subject RIV: BA - General Mathematics Impact factor: 0.940, year: 2008

  15. Non-isothermal Smoluchowski-Poisson equation as a singular limit of the Navier-Stokes-Fourier-Poisson system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Laurençot, P.

    2007-01-01

    Roč. 88, - (2007), s. 325-349 ISSN 0021-7824 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes-Fourier- Poisson system * Smoluchowski- Poisson system * singular limit Subject RIV: BA - General Mathematics Impact factor: 1.118, year: 2007

  16. A note on local interior regularity of a suitable weak solution to the Navier--Stokes problem

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří

    2013-01-01

    Roč. 6, č. 5 (2013), s. 1391-1400 ISSN 1937-1632 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations * suitable weak solution * regularity Subject RIV: BA - General Mathematics http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=8344

  17. A regularity criterion for the Navier-Stokes equations based on the gradient of one velocity component

    Czech Academy of Sciences Publication Activity Database

    Skalák, Zdeněk

    2016-01-01

    Roč. 437, č. 1 (2016), s. 474-484 ISSN 0022-247X R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985874 Keywords : Navier - Stokes equations * regularity of solutions * regularity criteria Subject RIV: BK - Fluid Dynamics Impact factor: 1.064, year: 2016

  18. A superlinearly convergent finite volume method for the incompressible Navier-Stokes equations on staggered unstructured grids

    International Nuclear Information System (INIS)

    Vidovic, D.; Segal, A.; Wesseling, P.

    2004-01-01

    A method for linear reconstruction of staggered vector fields with special treatment of the divergence is presented. An upwind-biased finite volume scheme for solving the unsteady incompressible Navier-Stokes equations on staggered unstructured triangular grids that uses this reconstruction is described. The scheme is applied to three benchmark problems and is found to be superlinearly convergent in space

  19. Comparison of reynolds averaged navier stokes based simulation and large eddy simulation for one isothermal swirling flow

    DEFF Research Database (Denmark)

    Yang, Yang; Kær, Søren Knudsen

    2012-01-01

    The flow structure of one isothermal swirling case in the Sydney swirl flame database was studied using two numerical methods. Results from the Reynolds-averaged Navier-Stokes (RANS) approach and large eddy simulation (LES) were compared with experimental measurements. The simulations were applied...

  20. A unified approach to determining forms for the 2D Navier-Stokes equations -- the general interpolants case

    International Nuclear Information System (INIS)

    Foias, C; Jolly, M S; Kravchenko, R; Titi, E S

    2014-01-01

    It is shown that the long-time dynamics (the global attractor) of the 2D Navier-Stokes system is embedded in the long-time dynamics of an ordinary differential equation, called a determining form, in a space of trajectories which is isomorphic to C b 1 (R;R N ) for sufficiently large N depending on the physical parameters of the Navier-Stokes equations. A unified approach is presented, based on interpolant operators constructed from various determining parameters for the Navier-Stokes equations, namely, determining nodal values, Fourier modes, finite volume elements, finite elements, and so on. There are two immediate and interesting consequences of this unified approach. The first is that the constructed determining form has a Lyapunov function, and thus its solutions converge to the set of steady states of the determining form as the time goes to infinity. The second is that these steady states of the determining form can be uniquely identified with the trajectories in the global attractor of the Navier-Stokes system. It should be added that this unified approach is general enough that it applies, in an almost straightforward manner, to a whole class of dissipative dynamical systems. Bibliography: 23 titles

  1. On large-time energy concentration in solutions to the Navier-Stokes equations in the whole 3D space

    Czech Academy of Sciences Publication Activity Database

    Skalák, Zdeněk

    2012-01-01

    Roč. 92, č. 10 (2012), s. 801-815 ISSN 0044-2267 R&D Projects: GA AV ČR IAA200600801 Institutional research plan: CEZ:AV0Z20600510 Keywords : Navier-Stokes equations * large-time behavior of solutions * energy concentration Subject RIV: BA - General Mathematics Impact factor: 0.948, year: 2012

  2. Brezis-Gallouet-Wainger Type Inequalities and Blow-Up Criteria for Navier-Stokes Equations in Unbounded Domains

    Science.gov (United States)

    Nakao, Kohei; Taniuchi, Yasushi

    2017-12-01

    We shall find the weakest norm that satisfies the Brezis-Gallouet-Wainger type inequality, under some conditions. As an application of the Brezis-Gallouet-Wainger type inequality, we shall establish Beale-Kato-Majda type blow-up criteria of smooth solutions to the 3-D Navier-Stokes equations in unbounded domains.

  3. Convergence analysis of a class of massively parallel direction splitting algorithms for the Navier-Stokes equations in simple domains

    KAUST Repository

    Guermond, Jean-Luc

    2012-01-01

    We provide a convergence analysis for a new fractional timestepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization. © 2012 American Mathematical Society.

  4. Regularity of a weak solution to the Navier--Stokes equations via one component of a spectral projection of vorticity

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří; Penel, P.

    2014-01-01

    Roč. 46, č. 2 (2014), s. 1681-1700 ISSN 0036-1410 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equations * weak solution * regularity criteria Subject RIV: BA - General Mathematics Impact factor: 1.265, year: 2014 http://epubs.siam.org/doi/abs/10.1137/120874874

  5. On large-time energy concentration in solutions to the Navier-Stokes equations in general domains

    Czech Academy of Sciences Publication Activity Database

    Skalák, Zdeněk

    2011-01-01

    Roč. 91, č. 9 (2011), s. 724-732 ISSN 0044-2267 R&D Projects: GA AV ČR IAA100190905 Institutional research plan: CEZ:AV0Z20600510 Keywords : Navier-Stokes equations * large-time behavior * energy concentration Subject RIV: BA - General Mathematics Impact factor: 0.863, year: 2011

  6. Three-dimensional incompressible Navier-Stokes solver using lower-upper symmetric-Gauss-Seidel algorithm

    Science.gov (United States)

    Yoon, Seokkwan; Kwak, Dochan

    1991-01-01

    A numerical method based on the pseudocompressibility concept is developed for solving the three-dimensional incompressible Navier-Stokes equations using the lower-upper symmetric-Gauss-Seidel implicit scheme. Very high efficiency is achieved in a new flow solver, INS3D-LU code, by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.

  7. Identification of severe wind conditions using a Reynolds Averaged Navier-Stokes solver

    International Nuclear Information System (INIS)

    Soerensen, N N; Bechmann, A; Johansen, J; Myllerup, L; Botha, P; Vinther, S; Nielsen, B S

    2007-01-01

    The present paper describes the application of a Navier-Stokes solver to predict the presence of severe flow conditions in complex terrain, capturing conditions that may be critical to the siting of wind turbines in the terrain. First it is documented that the flow solver is capable of predicting the flow in the complex terrain by comparing with measurements from two meteorology masts. Next, it is illustrated how levels of turbulent kinetic energy can be used to easily identify areas with severe flow conditions, relying on a high correlation between high turbulence intensity and severe flow conditions, in the form of high wind shear and directional shear which may seriously lower the lifetime of a wind turbine

  8. Navier-Stokes prediction of a delta wing in roll with vortex breakdown

    Science.gov (United States)

    Chaderjian, Neal M.; Schiff, Lewis B.

    1993-01-01

    The three-dimensional, Reynolds-averaged, Navier-Stokes (RANS) equations are used to numerically simulate vortical flow about a 65 degree sweep delta wing. Subsonic turbulent flow computations are presented for this delta wing at 30 degrees angle of attack and static roll angles up to 42 degrees. This work is part of an on going effort to validate the RANS approach for predicting high-incidence vortical flows, with the eventual application to wing rock. The flow is unsteady and includes spiral-type vortex breakdown. The breakdown positions, mean surface pressures, rolling moments, normal forces, and streamwise center-of-pressure locations compare reasonably well with experiment. In some cases, the primary vortex suction peaks are significantly underpredicted due to grid coarseness. Nevertheless, the computations are able to predict the same nonlinear variation of rolling moment with roll angle that appeared in the experiment. This nonlinearity includes regions of local static roll instability, which is attributed to vortex breakdown.

  9. Implementation of compact finite-difference method to parabolized Navier-Stokes equations

    International Nuclear Information System (INIS)

    Esfahanian, V.; Hejranfar, K.; Darian, H.M.

    2005-01-01

    The numerical simulation of the Parabolized Navier-Stokes (PNS) equations for supersonic/hypersonic flow field is obtained by using the fourth-order compact finite-difference method. The PNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming. A shock fitting procedure is utilized to obtain the accurate solution in the vicinity of the shock. The computations are performed for hypersonic axisymmetric flow over a blunt cone. The present results for the flow field along with those of the second-order method are presented and accuracy analysis is performed to insure the fourth-order accuracy of the method. (author)

  10. A least-squares finite element method for 3D incompressible Navier-Stokes equations

    Science.gov (United States)

    Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.

    1993-01-01

    The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.

  11. An unsteady finite-difference scheme for 3-D incompressible Navier-Stokes equations

    Science.gov (United States)

    Shin, Byeong R.; Ikohagi, Toshiaki; Daiguji, Hisaaki

    An implicit finite-difference SMAC scheme is developed for solving unsteady 3D incompressible Navier-Stokes equations in general curvilinear coordinates. The time-dependent momentum equations of contravariant velocity components are solved by the approximate-factorization method and the Newton iterative method. Alternatively, an elliptic equation in pressure derived by decoupling the continuity equation from the momentum equations is solved by the Chebyshev SLOR method using a staggered mesh system. An unsteady 3D duct flow over a backward-facing step is computed and presented at a high Reynolds number. The present scheme is found to be robust on supercomputing for the unsteady flow simulation of long time runs.

  12. Simulating variable-density flows with time-consistent integration of Navier-Stokes equations

    Science.gov (United States)

    Lu, Xiaoyi; Pantano, Carlos

    2017-11-01

    In this talk, we present several features of a high-order semi-implicit variable-density low-Mach Navier-Stokes solver. A new formulation to solve pressure Poisson-like equation of variable-density flows is highlighted. With this formulation of the numerical method, we are able to solve all variables with a uniform order of accuracy in time (consistent with the time integrator being used). The solver is primarily designed to perform direct numerical simulations for turbulent premixed flames. Therefore, we also address other important elements, such as energy-stable boundary conditions, synthetic turbulence generation, and flame anchoring method. Numerical examples include classical non-reacting constant/variable-density flows, as well as turbulent premixed flames.

  13. Numerical solutions of Navier-Stokes equations for a Butler wing

    Science.gov (United States)

    Abolhassani, Jamshid S.; Tiwari, Surendra N.; Smith, Robert E.

    1987-01-01

    The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and Reynolds number of 2,000,000. The simulation is done by integrating the viscous Navier-Stokes equations. These equations govern the unsteady, viscous, compressible and heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. The O-type and H-type grids have been used for this study, and results are compared. The governing equations are solved by the MacCormack time-split method, and the results are compared with other theoretical and experimental results. The codes are written in FORTRAN, vectorized and currently run on the CDC Vector Processing System (VPS-32) computer.

  14. Conservative DEC Discretization of Incompressible Navier-Stokes Equations on Arbitrary Surface Simplicial Meshes

    Science.gov (United States)

    Mohamed, Mamdouh; Hirani, Anil; Samtaney, Ravi

    2017-11-01

    A conservative discretization of incompressible Navier-Stokes equations over surfaces is developed using discrete exterior calculus (DEC). The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of signed diagonal Hodge star operators, while using the circumcentric dual defined on arbitrary meshes, is shown to produce correct solutions even when many non-Delaunay triangles pairs exist. This allows the DEC discretization to admit arbitrary surface simplicial meshes, in contrast to the previously held notion that DEC was limited only to Delaunay meshes. The discretization scheme is presented along with several numerical test cases demonstrating its numerical convergence and conservation properties. Recent developments regarding the extension to conservative higher order methods are also presented. KAUST Baseline Research Funds of R. Samtaney.

  15. Globalization strategies for Newton Krylov methods for stabilized FEM discretization of Navier Stokes equations

    Science.gov (United States)

    Bellavia, Stefania; Berrone, Stefano

    2007-10-01

    In this work we study the numerical solution of nonlinear systems arising from stabilized FEM discretizations of Navier-Stokes equations. This is a very challenging problem and often inexact Newton solvers present severe difficulties to converge. Then, they must be wrapped into a globalization strategy. We consider the classical backtracking procedure, a subspace trust-region strategy and an hybrid approach. This latter strategy is proposed with the aim of improve the robustness of backtracking and it is obtained combining the backtracking procedure and the elliptical subspace trust-region strategy. Under standard assumptions, we prove global and fast convergence of the inexact Newton methods embedded in this new strategy as well as in the subspace trust-region procedure. Computational results on classical CFD benchmarks are performed. Comparisons among the classical backtracking strategy, the elliptical subspace trust-region approach and the hybrid procedure are presented. Our numerical experiments show the effectiveness of the proposed hybrid technique.

  16. Quantification of topological changes of vorticity contours in two-dimensional Navier-Stokes flow.

    Science.gov (United States)

    Ohkitani, Koji; Al Sulti, Fayeza

    2010-06-01

    A characterization of reconnection of vorticity contours is made by direct numerical simulations of the two-dimensional Navier-Stokes flow at a relatively low Reynolds number. We identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its Hessian matrix on the basis of critical-point theory. The numbers of hyperbolic (saddles) and elliptic (minima and maxima) points are confirmed to satisfy Euler's index theorem numerically. Time evolution of these indices is studied for a simple initial condition. Generally speaking, we have found that the indices are found to decrease in number with time. This result is discussed in connection with related works on streamline topology, in particular, the relationship between stagnation points and the dissipation. Associated elementary procedures in physical space, the merging of vortices, are studied in detail for a number of snapshots. A similar analysis is also done using the stream function.

  17. Entropic lattice Boltzmann representations required to recover Navier-Stokes flows.

    Science.gov (United States)

    Keating, Brian; Vahala, George; Yepez, Jeffrey; Soe, Min; Vahala, Linda

    2007-03-01

    There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in Tsallis-like forms. However, with the imposition of the pressure tensor moment constraint, as is fundamentally necessary for the recovery of the Navier-Stokes equations, it is proved that the entropy function must be of the discrete Boltzmann form. Three-dimensional simulations are performed which illustrate some of the differences between standard lattice Boltzmann and entropic lattice Boltzmann schemes, as well as the role played by the number of phase-space velocities used in the discretization.

  18. Lagrangian fractional step method for the incompressible Navier--Stokes equations on a periodic domain

    International Nuclear Information System (INIS)

    Boergers, C.; Peskin, C.S.

    1987-01-01

    In the Lagrangian fractional step method introduced in this paper, the fluid velocity and pressure are defined on a collection of N fluid markers. At each time step, these markers are used to generate a Voronoi diagram, and this diagram is used to construct finite-difference operators corresponding to the divergence, gradient, and Laplacian. The splitting of the Navier--Stokes equations leads to discrete Helmholtz and Poisson problems, which we solve using a two-grid method. The nonlinear convection terms are modeled simply by the displacement of the fluid markers. We have implemented this method on a periodic domain in the plane. We describe an efficient algorithm for the numerical construction of periodic Voronoi diagrams, and we report on numerical results which indicate the the fractional step method is convergent of first order. The overall work per time step is proportional to N log N. copyright 1987 Academic Press, Inc

  19. Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas.

    Science.gov (United States)

    Kolvin, Itamar; Livne, Eli; Meerson, Baruch

    2010-08-01

    We show that, in dimension higher than one, heat diffusion and viscosity cannot arrest thermal collapse in a freely evolving dilute granular gas, even in the absence of gravity. Thermal collapse involves a finite-time blowup of the gas density. It was predicted earlier in ideal, Euler hydrodynamics of dilute granular gases in the absence of gravity, and in nonideal, Navier-Stokes granular hydrodynamics in the presence of gravity. We determine, analytically and numerically, the dynamic scaling laws that characterize the gas flow close to collapse. We also investigate bifurcations of a freely evolving dilute granular gas in circular and wedge-shaped containers. Our results imply that, in general, thermal collapse can only be arrested when the gas density becomes comparable with the close-packing density of grains. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.

  20. Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.

    Science.gov (United States)

    Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

    2012-07-01

    We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

  1. A Navier-Stokes/Cahn-Hilliard model for the simulation of three phase immiscible incompressible flows

    International Nuclear Information System (INIS)

    Celine Lapuerta; Bruno Piar; Franck Boyer; Philippe Angot; Michel Quintard

    2005-01-01

    This paper presents a Navier-Stokes/Cahn-Hilliard model designed for incompressible flows of three immiscible phases, characterized by different surface tensions and without phase change. This physical context is relevant to study the late phase of a hypothetical severe accident in a nuclear pressurized water reactor. Thanks to a suitable choice of a free energy and a particular form of the Cahn-Hilliard equation, the evolution of the three phases is described by only two order parameters. Moreover, this model allows the simulation of purely two phase flows as a limiting case: no artificial apparition of the third phase occurs if this later is physically absent which contrasts with others models of the literature. We examine the spreading of a liquid lens at the interface between two stratified phases. We present results showing that the method gives correct contact angles and pressure jumps, at equilibrium. (authors)

  2. On the control of the chaotic attractors of the 2-d Navier-Stokes equations.

    Science.gov (United States)

    Smaoui, Nejib; Zribi, Mohamed

    2017-03-01

    The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, R e . Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

  3. An Empirical Model for Vane-Type Vortex Generators in a Navier-Stokes Code

    Science.gov (United States)

    Dudek, Julianne C.

    2005-01-01

    An empirical model which simulates the effects of vane-type vortex generators in ducts was incorporated into the Wind-US Navier-Stokes computational fluid dynamics code. The model enables the effects of the vortex generators to be simulated without defining the details of the geometry within the grid, and makes it practical for researchers to evaluate multiple combinations of vortex generator arrangements. The model determines the strength of each vortex based on the generator geometry and the local flow conditions. Validation results are presented for flow in a straight pipe with a counter-rotating vortex generator arrangement, and the results are compared with experimental data and computational simulations using a gridded vane generator. Results are also presented for vortex generator arrays in two S-duct diffusers, along with accompanying experimental data. The effects of grid resolution and turbulence model are also examined.

  4. Turbine Internal and Film Cooling Modeling For 3D Navier-Stokes Codes

    Science.gov (United States)

    DeWitt, Kenneth; Garg Vijay; Ameri, Ali

    2005-01-01

    The aim of this research project is to make use of NASA Glenn on-site computational facilities in order to develop, validate and apply aerodynamic, heat transfer, and turbine cooling models for use in advanced 3D Navier-Stokes Computational Fluid Dynamics (CFD) codes such as the Glenn-" code. Specific areas of effort include: Application of the Glenn-HT code to specific configurations made available under Turbine Based Combined Cycle (TBCC), and Ultra Efficient Engine Technology (UEET) projects. Validating the use of a multi-block code for the time accurate computation of the detailed flow and heat transfer of cooled turbine airfoils. The goal of the current research is to improve the predictive ability of the Glenn-HT code. This will enable one to design more efficient turbine components for both aviation and power generation. The models will be tested against specific configurations provided by NASA Glenn.

  5. Navier--Stokes relaxation to sinh--Poisson states at finite Reynolds numbers

    International Nuclear Information System (INIS)

    Montgomery, D.; Shan, X.; Matthaeus, W.H.

    1993-01-01

    A mathematical framework is proposed in which it seems possible to justify the computationally-observed relaxation of a two-dimensional Navier--Stokes fluid to a ''most probable,'' or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher-order ideal invariants such as enstrophy. A two-fluid formulation, involving interpenetrating positive and negative vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay problem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerically that, in two dimensions, passive scalars decay rapidly, relative to mean-square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two-fluid field variables

  6. Fluctuating Navier-Stokes equations for inelastic hard spheres or disks.

    Science.gov (United States)

    Brey, J Javier; Maynar, P; de Soria, M I García

    2011-04-01

    Starting from the fluctuating Boltzmann equation for smooth inelastic hard spheres or disks, closed equations for the fluctuating hydrodynamic fields to Navier-Stokes order are derived. This requires deriving constitutive relations for both the fluctuating fluxes and the correlations of the random forces. The former are identified as having the same form as the macroscopic average fluxes and involving the same transport coefficients. On the other hand, the random force terms exhibit two peculiarities as compared with their elastic limit for molecular systems. First, they are not white but have some finite relaxation time. Second, their amplitude is not determined by the macroscopic transport coefficients but involves new coefficients. ©2011 American Physical Society

  7. A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques

    Science.gov (United States)

    Kaul, U. K.; Chaussee, D. S.

    1985-01-01

    The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching-step sizes with the implicit shock fitting procedure. A correlation is found between the marching-step size, Reynolds number and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.

  8. Examination of wall functions for a Parabolized Navier-Stokes code for supersonic flow

    Energy Technology Data Exchange (ETDEWEB)

    Alsbrooks, T.H. [New Mexico Univ., Albuquerque, NM (United States). Dept. of Mechanical Engineering

    1993-04-01

    Solutions from a Parabolized Navier-Stokes (PNS) code with an algebraic turbulence model are compared with wall functions. The wall functions represent the turbulent flow profiles in the viscous sublayer, thus removing many grid points from the solution procedure. The wall functions are intended to replace the computed profiles between the body surface and a match point in the logarithmic region. A supersonic adiabatic flow case was examined first. This adiabatic case indicates close agreement between computed velocity profiles near the wall and the wall function for a limited range of suitable match points in the logarithmic region. In an attempt to improve marching stability, a laminar to turbulent transition routine was implemented at the start of the PNS code. Implementing the wall function with the transitional routine in the PNS code is expected to reduce computational time while maintaining good accuracy in computed skin friction.

  9. Examination of wall functions for a Parabolized Navier-Stokes code for supersonic flow

    Energy Technology Data Exchange (ETDEWEB)

    Alsbrooks, T.H. (New Mexico Univ., Albuquerque, NM (United States). Dept. of Mechanical Engineering)

    1993-01-01

    Solutions from a Parabolized Navier-Stokes (PNS) code with an algebraic turbulence model are compared with wall functions. The wall functions represent the turbulent flow profiles in the viscous sublayer, thus removing many grid points from the solution procedure. The wall functions are intended to replace the computed profiles between the body surface and a match point in the logarithmic region. A supersonic adiabatic flow case was examined first. This adiabatic case indicates close agreement between computed velocity profiles near the wall and the wall function for a limited range of suitable match points in the logarithmic region. In an attempt to improve marching stability, a laminar to turbulent transition routine was implemented at the start of the PNS code. Implementing the wall function with the transitional routine in the PNS code is expected to reduce computational time while maintaining good accuracy in computed skin friction.

  10. Three-Dimensional Navier-Stokes Simulation of Space Shuttle Main Propulsion 17-inch Disconnect Valves

    Science.gov (United States)

    Kandula, M.; Pearce, D. G.

    1991-01-01

    A steady incompressible three-dimensional viscous flow analysis has been conducted for the Space Shuttle external tank/orbiter propellant feed line disconnect flapper valves with upstream elbows. The Navier-Stokes code, INS3D, is modified to handle interior obstacles and a simple turbulence model. The flow solver is tested for stability and convergence in the presence of interior flappers. An under-relaxation scheme has been incorporated to improve the solution stability. Important flow characteristics such as secondary flows, recirculation, vortex and wake regions, and separated flows are observed. Computed values for forces, moments, and pressure drop are in satisfactory agreement with water flow test data covering a maximum tube Reynolds number of 3.5 million. The predicted hydrodynamical stability of the flappers correlates well with the measurements.

  11. Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries

    KAUST Repository

    Williams-Rioux, Bertrand

    2012-01-12

    Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.

  12. Isotropic Navier-Stokes turbulence. I. Qualitative features and basic equations

    International Nuclear Information System (INIS)

    Kraichnan, R.H.

    1990-01-01

    This set of two lectures is intended to give a taste of modern theoretical approaches to isotropic turbulence in an incompressible Navier-Stokes (NS) fluid. The first lecture is devoted to basic mathematical properties of the NS equation and qualitative physical features of turbulence. The second lecture surveys some theoretical approaches and then outlines the use of stochastic modeling to obtain self-consistent equations for low-order moments of the velocity field. Equation numbering reflects the lecture number, the section number, and then the consecutive equation number. Fully developed NS turbulence appears to exhibit an irreducibly large number of degrees of freedom (10 18 is not unusual in the atmosphere). It has not yielded to the techniques that have been powerful for small dynamical systems. Instead, it has pointed to the need for statistical approaches that can handle the strongly nonlinear interaction of huge numbers of modes that are far from absolute statistical equilibrium. 17 refs

  13. Effects of friction on forced two-dimensional Navier-Stokes turbulence.

    Science.gov (United States)

    Blackbourn, Luke A K; Tran, Chuong V

    2011-10-01

    Large-scale dissipation mechanisms have been routinely employed in numerical simulations of two-dimensional turbulence to absorb energy at large scales, presumably mimicking the quasisteady picture of Kraichnan in an unbounded fluid. Here, "side effects" of such a mechanism--mechanical friction--on the small-scale dynamics of forced two-dimensional Navier-Stokes turbulence are elaborated by both theoretical and numerical analysis. Given a positive friction coefficient α, viscous dissipation of enstrophy has been known to vanish in the inviscid limit ν→0. This effectively renders the scale-neutral friction the only mechanism responsible for enstrophy dissipation in that limit. The resulting dynamical picture is that the classical enstrophy inertial range becomes a dissipation range in which the dissipation of enstrophy by friction mainly occurs. For each α>0, there exists a critical viscosity ν(c), which depends on physical parameters, separating the regimes of predominant viscous and frictional dissipation of enstrophy. It is found that ν(c)=[η'(1/3)/(Ck(f)(2))]exp[-η'(1/3)/(Cα)], where η' is half the enstrophy injection rate, k(f) is the forcing wave number, and C is a nondimensional constant (the Kraichnan-Batchelor constant). The present results have important theoretical and practical implications. Apparently, mechanical friction is a poor choice in numerical attempts to address fundamental issues concerning the direct enstrophy transfer in two-dimensional Navier-Stokes turbulence. Furthermore, as relatively strong friction naturally occurs on the surfaces and at lateral boundaries of experimental fluids as well as at the interfaces of shallow layers in geophysical fluid models, the frictional effects discussed in this study are crucial in understanding the dynamics of these systems.

  14. Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces

    Science.gov (United States)

    Wang, Chi R.

    2005-01-01

    This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one

  15. Development of a general thermodynamically consistent projection method for the Navier-Stokes equations and its application to compressible natural convection of real fluids

    Science.gov (United States)

    Cook, Charles R.

    The development of a general method for the direct solution of the Navier-Stokes equations, where no assumptions or modeling are required, with any equation of state, while maintaining thermodynamic equilibrium is the subject. This is accomplished through generalization of the Characteristic Based Split (CBS) method by removing isentropic assumptions and fully coupling the equation of state with the pressure and energy fields. The Modified CBS (MCBS) method is developed in rigor from first principles with the Navier-Stokes equations, where the equation of state is not required to be known or an analytical expression. Thermodynamic equilibrium, or thermodynamic consistency, where the pressure field from the equation of state, p(rho,T), is the same as the dynamic pressure field, is recovered through the implicit treatment of the temperature field during the solution of conservation of energy. Implicit treatment of both the pressure and temperature fields further enhances the MCBS method by permitting the integration over acoustic time scales if desired, achieving acoustic filtering without modification to the underlying governing equations. The MCBS as implemented in a new Finite Element Method (FEM) code is applied to the study of compressible natural convection, where the entirety of Navier-Stokes equations is expressed, with several equations of state. Validation of the MCBS method for incompressible Boussinesq, incompressible thermodynamic Boussinesq, and compressible low-Mach natural convection in a cavity and near wall compressible thermal expansion waves is achieved with exceptional accuracy with the single MCBS implementation. Further, the solution of natural convection in a cavity using RefProp for the equation of state as well as all thermodynamic and transport properties was successfully achieved with the same implementation, providing real fluid results. The case of natural convection in a cavity is further pushed into higher Rayleigh numbers where the

  16. An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ.

    Science.gov (United States)

    Coirier, William John

    1994-01-01

    A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a

  17. Comparative Study between the Darcy-Brinkman Model and the Modified Navier-Stokes Equations in the Case of Natural Convection in a Porous Cavity

    Directory of Open Access Journals (Sweden)

    Razli MEHDAOUI

    2008-06-01

    Full Text Available The objective of this study is the comparison between the model of Darcy-Brinkman and the Navier-Stokes equations modified, in the case of the natural convection. The study is made in a porous vertical square cavity saturated by a Newtonian fluid. A cylindrical heat source maintained at a uniform heat flux is introduced into porous medium. The equations which describe the thermal transfer and the hydrodynamic flow of the two models are solved numerically by means of the software package Femlab 3.2 based on the finite element method. The results obtained are in the form of average kinetic energy per unit mass, the local and the average Nusselt numbers, the pressure and the viscous force per unit area.

  18. Automated Euler and Navier-Stokes Database Generation for a Glide-Back Booster

    Science.gov (United States)

    Chaderjian, Neal M.; Rogers, Stuart E.; Aftosmis, Mike J.; Pandya, Shishir A.; Ahmad, Jasim U.; Tejnil, Edward

    2004-01-01

    The past two decades have seen a sustained increase in the use of high fidelity Computational Fluid Dynamics (CFD) in basic research, aircraft design, and the analysis of post-design issues. As the fidelity of a CFD method increases, the number of cases that can be readily and affordably computed greatly diminishes. However, computer speeds now exceed 2 GHz, hundreds of processors are currently available and more affordable, and advances in parallel CFD algorithms scale more readily with large numbers of processors. All of these factors make it feasible to compute thousands of high fidelity cases. However, there still remains the overwhelming task of monitoring the solution process. This paper presents an approach to automate the CFD solution process. A new software tool, AeroDB, is used to compute thousands of Euler and Navier-Stokes solutions for a 2nd generation glide-back booster in one week. The solution process exploits a common job-submission grid environment, the NASA Information Power Grid (IPG), using 13 computers located at 4 different geographical sites. Process automation and web-based access to a MySql database greatly reduces the user workload, removing much of the tedium and tendency for user input errors. The AeroDB framework is shown. The user submits/deletes jobs, monitors AeroDB's progress, and retrieves data and plots via a web portal. Once a job is in the database, a job launcher uses an IPG resource broker to decide which computers are best suited to run the job. Job/code requirements, the number of CPUs free on a remote system, and queue lengths are some of the parameters the broker takes into account. The Globus software provides secure services for user authentication, remote shell execution, and secure file transfers over an open network. AeroDB automatically decides when a job is completed. Currently, the Cart3D unstructured flow solver is used for the Euler equations, and the Overflow structured overset flow solver is used for the

  19. A frequency domain linearized Navier-Stokes equations approach to acoustic propagation in flow ducts with sharp edges.

    Science.gov (United States)

    Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla

    2010-02-01

    Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.

  20. Regularity criteria for weak solutions to the Navier-Stokes equations based on spectral projections of vorticity

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří; Penel, P.

    2012-01-01

    Roč. 350, 11-12 (2012), s. 597-602 ISSN 1631-073X R&D Projects: GA ČR GA201/08/0012 Institutional support: RVO:67985840 Keywords : Navier-Stokes equations * weak solution * regularity Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2012 http://www.sciencedirect.com/science/article/pii/S1631073X12001926#

  1. The Role of the Pressure in the Partial Regularity Theory for Weak Solutions of the Navier-Stokes Equations

    Science.gov (United States)

    Chamorro, Diego; Lemarié-Rieusset, Pierre-Gilles; Mayoufi, Kawther

    2018-04-01

    We study the role of the pressure in the partial regularity theory for weak solutions of the Navier-Stokes equations. By introducing the notion of dissipative solutions, due to D uchon and R obert (Nonlinearity 13:249-255, 2000), we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach sheels new light on the role of the pressure in this theory in connection to Serrin's local regularity criterion.

  2. On the energy inequality for weak solutions to the Navier-Stokes equations of compressible fluids on unbounded domains

    Czech Academy of Sciences Publication Activity Database

    Dell'Oro, Filippo; Feireisl, Eduard

    2015-01-01

    Roč. 128, November (2015), s. 136-148 ISSN 0362-546X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : compressible Navier - Stokes equations * unbounded domain * weak solutions * energy inequality Subject RIV: BA - General Mathematics Impact factor: 1.125, year: 2015 http://www.sciencedirect.com/science/article/pii/S0362546X15002692

  3. Involving the Navier-Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method.

    Science.gov (United States)

    Verschaeve, Joris C G

    2011-06-13

    By means of the continuity equation of the incompressible Navier-Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

  4. On the energy inequality for weak solutions to the Navier-Stokes equations of compressible fluids on unbounded domains

    Czech Academy of Sciences Publication Activity Database

    Dell'Oro, Filippo; Feireisl, Eduard

    2015-01-01

    Roč. 128, November (2015), s. 136-148 ISSN 0362-546X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes equations * unbounded domain * weak solutions * energy inequality Subject RIV: BA - General Mathematics Impact factor: 1.125, year: 2015 http://www.sciencedirect.com/science/article/pii/S0362546X15002692

  5. Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Medviďová-Lukáčová, M.; Nečasová, Šárka; Novotný, A.; She, Bangwei

    2018-01-01

    Roč. 16, č. 1 (2018), s. 150-183 ISSN 1540-3459 R&D Projects: GA ČR GA16-03230S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method * asymptotic preserving schemes Subject RIV: BA - General Mathematics Impact factor: 1.865, year: 2016 http://epubs.siam.org/doi/10.1137/16M1094233

  6. A comparative study of accuracy and convergence properties of upwind schemes for the compressible Navier-Stokes equations

    Science.gov (United States)

    Fortin, F.; Degrez, G.

    An investigation of the accuracy and convergence properties of various upwind schemes for the compressible Navier-Stokes equations has been performed. Explicit operators included van Leer's FVS and Roe's FDS at first and second order. Implicit operators included first order van Leer FVS and first order Steger and Warming FVS using true or approximate jacobians. Finally, horizontal and vertical line Gauss-Seidel, and approximate factorization solution strategies were compared.

  7. Regularity criterion for solutions to the Navier Stokes equations in the whole 3D space based on two vorticity components

    Czech Academy of Sciences Publication Activity Database

    Guo, Z.; Kučera, P.; Skalák, Zdeněk

    2018-01-01

    Roč. 458, č. 1 (2018), s. 755-766 ISSN 0022-247X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985874 Keywords : Navier Stokes equations * conditional regularity * regularity criteria * vorticity * Besov spaces * bony decomposition Subject RIV: BA - General Mathematics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.064, year: 2016

  8. The fundamental solution of linearized nonstationary Navier-Stokes equations of motion around a rotating and translating body

    Czech Academy of Sciences Publication Activity Database

    Farwig, R.; Guenther, R.; Thomann, E.; Nečasová, Šárka

    2014-01-01

    Roč. 34, č. 2 (2014), s. 511-529 ISSN 1078-0947 R&D Projects: GA ČR(CZ) GAP201/11/1304; GA MŠk LC06052 Institutional support: RVO:67985840 Keywords : fundamental solution * linearized problem * Navier-Stokes problem Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2014 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=8831

  9. Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty

    Science.gov (United States)

    Ling, J.; Templeton, J.

    2015-08-01

    Reynolds Averaged Navier Stokes (RANS) models are widely used in industry to predict fluid flows, despite their acknowledged deficiencies. Not only do RANS models often produce inaccurate flow predictions, but there are very limited diagnostics available to assess RANS accuracy for a given flow configuration. If experimental or higher fidelity simulation results are not available for RANS validation, there is no reliable method to evaluate RANS accuracy. This paper explores the potential of utilizing machine learning algorithms to identify regions of high RANS uncertainty. Three different machine learning algorithms were evaluated: support vector machines, Adaboost decision trees, and random forests. The algorithms were trained on a database of canonical flow configurations for which validated direct numerical simulation or large eddy simulation results were available, and were used to classify RANS results on a point-by-point basis as having either high or low uncertainty, based on the breakdown of specific RANS modeling assumptions. Classifiers were developed for three different basic RANS eddy viscosity model assumptions: the isotropy of the eddy viscosity, the linearity of the Boussinesq hypothesis, and the non-negativity of the eddy viscosity. It is shown that these classifiers are able to generalize to flows substantially different from those on which they were trained. Feature selection techniques, model evaluation, and extrapolation detection are discussed in the context of turbulence modeling applications.

  10. On one-dimensional compressible Navier-Stokes equations for a reacting mixture in unbounded domains

    Science.gov (United States)

    Li, Siran

    2017-10-01

    In this paper we consider the one-dimensional Navier-Stokes system for a heat-conducting, compressible reacting mixture which describes the dynamic combustion of fluids of mixed kinds on unbounded domains. This model has been discussed on bounded domains by Chen (SIAM J Math Anal 23:609-634, 1992) and Chen-Hoff-Trivisa (Arch Ration Mech Anal 166:321-358, 2003), among others, in which the reaction rate function is a discontinuous function obeying the Arrhenius' law of thermodynamics. We prove the global existence of weak solutions to this model on one-dimensional unbounded domains with large initial data in H^1. Moreover, the large-time behaviour of the weak solution is identified. In particular, the uniform-in-time bounds for the temperature and specific volume have been established via energy estimates. For this purpose we utilise techniques developed by Kazhikhov-Shelukhin (cf. Kazhikhov in Siber Math J 23:44-49, 1982; Solonnikov and Kazhikhov in Annu Rev Fluid Mech 13:79-95, 1981) and refined by Jiang (Commun Math Phys 200:181-193, 1999, Proc R Soc Edinb Sect A 132:627-638, 2002), as well as a crucial estimate in the recent work by Li-Liang (Arch Ration Mech Anal 220:1195-1208, 2016). Several new estimates are also established, in order to treat the unbounded domain and the reacting terms.

  11. Finite-analytic numerical method for unsteady two-dimensional Navier-Stokes equations

    Science.gov (United States)

    Chen, C.-J.; Chen, H.-C.

    1984-01-01

    A finite analytic (FA) numerical solution is developed for unsteady two-dimensional Navier-Stokes equations. The FA method utilizes the analytic solution in a small local element to formulate the algebraic representation of partial differential equations. The combination of linear and exponential functions that satisfy the governing equation is adopted as the boundary function, thereby improving the accuracy of the finite analytic solution. Two flows, one a starting cavity flow and the other a vortex shedding flow behind a rectangular block, are solved by the FA method. The starting square cavity flow is solved for Reynolds number of 400, 1000, and 2000 to show the accuracy and stability of the FA solution. The FA solution for flow over a rectangular block (H x H/4) predicts the Strouhal number for Reynolds numbers of 100 and 500 to be 0.156 and 0.125. Details of the flow patterns are given. In addition to streamlines and vorticity distribution, rest-streamlines are given to illustrate the vortex motion downstream of the block.

  12. A meshless local radial basis function method for two-dimensional incompressible Navier-Stokes equations

    KAUST Repository

    Wang, Zhiheng

    2014-12-10

    A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.

  13. Solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

    International Nuclear Information System (INIS)

    Rosenfeld, M.; Kwak, D.; Vinokur, M.

    1988-01-01

    A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method. 23 references

  14. A spectral/B-spline method for the Navier-Stokes equations in unbounded domains

    International Nuclear Information System (INIS)

    Dufresne, L.; Dumas, G.

    2003-01-01

    The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the θ and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r→∞. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the local character of the B-splines allows for a great flexibility in node positioning while keeping narrow bandwidth matrices. Numerical tests show that the present method compares advantageously with other similar methodologies using purely global expansions

  15. Reynolds-Averaged Navier-Stokes Modeling of Turbulent Free Shear Layers

    Science.gov (United States)

    Schilling, Oleg

    2017-11-01

    Turbulent mixing of gases in free shear layers is simulated using a weighted essentially nonoscillatory implementation of ɛ- and L-based Reynolds-averaged Navier-Stokes models. Specifically, the air/air shear layer with velocity ratio 0.6 studied experimentally by Bell and Mehta (1990) is modeled. The detailed predictions of turbulent kinetic energy dissipation rate and lengthscale models are compared to one another, and to the experimental data. The role of analytical, self-similar solutions for model calibration and physical insights is also discussed. It is shown that turbulent lengthscale-based models are unable to predict both the growth parameter (spreading rate) and turbulent kinetic energy normalized by the square of the velocity difference of the streams. The terms in the K, ɛ, and L equation budgets are compared between the models, and it is shown that the production and destruction mechanisms are substantially different in the ɛ and L equations. Application of the turbulence models to the Brown and Roshko (1974) experiments with streams having various velocity and density ratios is also briefly discussed. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  16. Two-level method for unsteady Navier-Stokes equations based on a new projection

    International Nuclear Information System (INIS)

    Hou Yanren; Li Kaitai

    2004-12-01

    A two-level algorithm for the two dimensional unsteady Navier-Stokes equations based on a new projection is proposed and investigated. The approximate solution is solved as a sum of a large eddy component and a small eddy component, which are in the sense of the new projection, constructed in this paper. These two terms advance in time explicitly. Actually, the new algorithm proposed here can be regarded as a sort of postprocessing algorithm for the standard Galerkin method (SGM). The large eddy part is solved by SGM in the usual L 2 -based large eddy subspace while the small eddy part (the correction part) is obtained in its complement subspace in the sense of the new projection. The stability analysis indicates the improvement of the stability comparing with SGM of the same scale, and the L 2 -error estimate shows that the scheme can improve the accuracy of SGM approximation for half order. We also propose a numerical implementation based on Lagrange multiplier for this two-level algorithm. (author)

  17. Finite analytic numerical solution axisymmetric Navier-Stokes and energy equations

    International Nuclear Information System (INIS)

    Chen, C.; Yoon, Y.H.

    1983-01-01

    Convective heat transfer for steady-state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature, and heat transfer coefficients for flow with Reynolds numbers of 5, 100, 1000, and 2000, and Prandtl numbers of 0.1, 1.0, and 10.0 with uniform grid sizes, are reported for an axisymmetric pipe with a sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic is stable converges rapidly, and simulates the convection of fluid flow accurately, since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values, thereby minimizing the false numerical diffusion

  18. Drop separation by numerical solution of the Navier--Stokes equation

    Energy Technology Data Exchange (ETDEWEB)

    Fitzgibbons, D.A.

    1978-01-01

    A numerical model of separating drop behavior was constructed and tested by simulation, on a general-purpose digital computer, of a hypothetical two-immiscible-phase system. The model uses the Marker-and-Cell (MAC) method to solve the unsteady-state Navier--Stokes (momentum balance) equation with incompressible flow. Input to the model consists of fluid parameters (density, viscosity, interfacial tension), initial conditions( interface profile and velocities), and forcing functions. Simulation results consist of time-varying velocity and pressure fields, and all transformations of the interface profile. The simulation was seen to exhibit many of the features known to accompany separations observed in the laboratory, including characteristic profiles and flow patterns. The simulatio incorporates a one-parameter model of the interface, with the parameter being the equilibrium interfacial tension. Dynamic interfacial tension and interface viscosity are omitted. At each computational time frame the curvature of the interface is computed by numerically fitting a set of cubic splines to the coordinates of the particles which compose the interface. This curvature is used to compute the pressure drop across the phase boundary, and comprises the boundary condition for teh calculation of pressures within the drop. 62 references, 28 figures, 3 tables.

  19. Reynolds-Averaged Navier-Stokes Simulation of a 2D Circulation Control Wind Tunnel Experiment

    Science.gov (United States)

    Allan, Brian G.; Jones, Greg; Lin, John C.

    2011-01-01

    Numerical simulations are performed using a Reynolds-averaged Navier-Stokes (RANS) flow solver for a circulation control airfoil. 2D and 3D simulation results are compared to a circulation control wind tunnel test conducted at the NASA Langley Basic Aerodynamics Research Tunnel (BART). The RANS simulations are compared to a low blowing case with a jet momentum coefficient, C(sub u), of 0:047 and a higher blowing case of 0.115. Three dimensional simulations of the model and tunnel walls show wall effects on the lift and airfoil surface pressures. These wall effects include a 4% decrease of the midspan sectional lift for the C(sub u) 0.115 blowing condition. Simulations comparing the performance of the Spalart Allmaras (SA) and Shear Stress Transport (SST) turbulence models are also made, showing the SST model compares best to the experimental data. A Rotational/Curvature Correction (RCC) to the turbulence model is also evaluated demonstrating an improvement in the CFD predictions.

  20. Computational simulations of vocal fold vibration: Bernoulli versus Navier-Stokes.

    Science.gov (United States)

    Decker, Gifford Z; Thomson, Scott L

    2007-05-01

    The use of the mechanical energy (ME) equation for fluid flow, an extension of the Bernoulli equation, to predict the aerodynamic loading on a two-dimensional finite element vocal fold model is examined. Three steady, one-dimensional ME flow models, incorporating different methods of flow separation point prediction, were compared. For two models, determination of the flow separation point was based on fixed ratios of the glottal area at separation to the minimum glottal area; for the third model, the separation point determination was based on fluid mechanics boundary layer theory. Results of flow rate, separation point, and intraglottal pressure distribution were compared with those of an unsteady, two-dimensional, finite element Navier-Stokes model. Cases were considered with a rigid glottal profile as well as with a vibrating vocal fold. For small glottal widths, the three ME flow models yielded good predictions of flow rate and intraglottal pressure distribution, but poor predictions of separation location. For larger orifice widths, the ME models were poor predictors of flow rate and intraglottal pressure, but they satisfactorily predicted separation location. For the vibrating vocal fold case, all models resulted in similar predictions of mean intraglottal pressure, maximum orifice area, and vibration frequency, but vastly different predictions of separation location and maximum flow rate.

  1. A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics.

    Science.gov (United States)

    Hageman, Nathan S; Toga, Arthur W; Narr, Katherine L; Shattuck, David W

    2009-03-01

    We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.

  2. Cellular neural networks, the Navier-Stokes equation, and microarray image reconstruction.

    Science.gov (United States)

    Zineddin, Bachar; Wang, Zidong; Liu, Xiaohui

    2011-11-01

    Although the last decade has witnessed a great deal of improvements achieved for the microarray technology, many major developments in all the main stages of this technology, including image processing, are still needed. Some hardware implementations of microarray image processing have been proposed in the literature and proved to be promising alternatives to the currently available software systems. However, the main drawback of those proposed approaches is the unsuitable addressing of the quantification of the gene spot in a realistic way without any assumption about the image surface. Our aim in this paper is to present a new image-reconstruction algorithm using the cellular neural network that solves the Navier-Stokes equation. This algorithm offers a robust method for estimating the background signal within the gene-spot region. The MATCNN toolbox for Matlab is used to test the proposed method. Quantitative comparisons are carried out, i.e., in terms of objective criteria, between our approach and some other available methods. It is shown that the proposed algorithm gives highly accurate and realistic measurements in a fully automated manner within a remarkably efficient time.

  3. Reynolds-Averaged Navier-Stokes Solutions to Flat Plate Film Cooling Scenarios

    Science.gov (United States)

    Johnson, Perry L.; Shyam, Vikram; Hah, Chunill

    2011-01-01

    The predictions of several Reynolds-Averaged Navier-Stokes solutions for a baseline film cooling geometry are analyzed and compared with experimental data. The Fluent finite volume code was used to perform the computations with the realizable k-epsilon turbulence model. The film hole was angled at 35 to the crossflow with a Reynolds number of 17,400. Multiple length-to-diameter ratios (1.75 and 3.5) as well as momentum flux ratios (0.125 and 0.5) were simulated with various domains, boundary conditions, and grid refinements. The coolant to mainstream density ratio was maintained at 2.0 for all scenarios. Computational domain and boundary condition variations show the ability to reduce the computational cost as compared to previous studies. A number of grid refinement and coarsening variations are compared for further insights into the reduction of computational cost. Liberal refinement in the near hole region is valuable, especially for higher momentum jets that tend to lift-off and create a recirculating flow. A lack of proper refinement in the near hole region can severely diminish the accuracy of the solution, even in the far region. The effects of momentum ratio and hole length-to-diameter ratio are also discussed.

  4. Knudsen temperature jump and the Navier-Stokes hydrodynamics of granular gases driven by thermal walls.

    Science.gov (United States)

    Khain, Evgeniy; Meerson, Baruch; Sasorov, Pavel V

    2008-10-01

    Thermal wall is a convenient idealization of a rapidly vibrating plate used for vibrofluidization of granular materials. The objective of this work is to incorporate the Knudsen temperature jump at thermal wall in the Navier-Stokes hydrodynamic modeling of dilute granular gases of monodisperse particles that collide nearly elastically. The Knudsen temperature jump manifests itself as an additional term, proportional to the temperature gradient, in the boundary condition for the temperature. Up to a numerical prefactor O(1) , this term is known from kinetic theory of elastic gases. We determine the previously unknown numerical prefactor by measuring, in a series of molecular dynamics (MD) simulations, steady-state temperature profiles of a gas of elastically colliding hard disks, confined between two thermal walls kept at different temperatures, and comparing the results with the predictions of a hydrodynamic calculation employing the modified boundary condition. The modified boundary condition is then applied, without any adjustable parameters, to a hydrodynamic calculation of the temperature profile of a gas of inelastic hard disks driven by a thermal wall. We find the hydrodynamic prediction to be in very good agreement with MD simulations of the same system. The results of this work pave the way to a more accurate hydrodynamic modeling of driven granular gases.

  5. Divergent expansion, Borel summability and three-dimensional Navier-Stokes equation.

    Science.gov (United States)

    Costin, Ovidiu; Luo, Guo; Tanveer, Saleh

    2008-08-13

    We describe how the Borel summability of a divergent asymptotic expansion can be expanded and applied to nonlinear partial differential equations (PDEs). While Borel summation does not apply for non-analytic initial data, the present approach generates an integral equation (IE) applicable to much more general data. We apply these concepts to the three-dimensional Navier-Stokes (NS) system and show how the IE approach can give rise to local existence proofs. In this approach, the global existence problem in three-dimensional NS systems, for specific initial condition and viscosity, becomes a problem of asymptotics in the variable p (dual to 1/t or some positive power of 1/t). Furthermore, the errors in numerical computations in the associated IE can be controlled rigorously, which is very important for nonlinear PDEs such as NS when solutions are not known to exist globally.Moreover, computation of the solution of the IE over an interval [0,p0] provides sharper control of its p-->infinity behaviour. Preliminary numerical computations give encouraging results.

  6. Navier-Stokes Simulation of a Heavy Lift Slowed-Rotor Compound Helicopter Configuration

    Science.gov (United States)

    Allan, Brian G.; Jenkins, Luther N.; Yao, Chung-Sheng; Bartram, Scott M.; Hallissy, Jim B.; Harris, Jerome; Noonan, Kevin W.; Wong, Oliver D.; Jones, Henry E.; Malovrh, Brendon D.; hide

    2009-01-01

    Time accurate numerical simulations were performed using the Reynolds-averaged Navier-Stokes (RANS) flow solver OVERFLOW for a heavy lift, slowed-rotor, compound helicopter configuration, tested at the NASA Langley 14- by 22-Foot Subsonic Tunnel. The primary purpose of these simulations is to provide support for the development of a large field of view Particle Imaging Velocimetry (PIV) flow measurement technique supported by the Subsonic Rotary Wing (SRW) project under the NASA Fundamental Aeronautics program. These simulations provide a better understanding of the rotor and body wake flows and helped to define PIV measurement locations as well as requirements for validation of flow solver codes. The large field PIV system can measure the three-dimensional velocity flow field in a 0.914m by 1.83m plane. PIV measurements were performed upstream and downstream of the vertical tail section and are compared to simulation results. The simulations are also used to better understand the tunnel wall and body/rotor support effects by comparing simulations with and without tunnel floor/ceiling walls and supports. Comparisons are also made to the experimental force and moment data for the body and rotor.

  7. Planar incompressible Navier-Stokes and Euler equations: A geometric formulation

    Science.gov (United States)

    Dimitriou, Ioannis

    2017-11-01

    In this paper, a novel geometric approach for studying steady, two-dimensional, incompressible flows has been thoroughly developed. The continuity and momentum equations were expressed in the flow's intrinsic coordinate system in order to "accommodate" the geometric parameters characterizing it, namely, the local curvatures of the streamlines and their orthogonal trajectories. As a result, a new description of the governing equations was obtained, in which the concerned variables are the velocity magnitude v and a new quantity which was named geometric vorticity, Γ. The latter is defined by the curl of the global curvature vector KG and can be interpreted as the geometric signature of the known vorticity Ω. This approach leads to a new formulation of the Navier-Stokes and Euler equations, the so-called "velocity-curvature" formulation. In this framework, an expression for the flow velocity as a function of geometric parameters only was developed. This reveals that the physical information of a steady incompressible flow is imprinted in its geometry. It is this insight that makes the aforementioned formulation not only conceptually different to the existing classical descriptions, traditionally employed in both analytical and numerical applications, but also attractive, due to the advantages that it could provide at a theoretical and an experimental level. Finally, the derived results are briefly discussed, while emphasizing the implications that the identified geometry-physics interface might have in the future for planar flow analysis.

  8. Resolvent analysis of shear flows using One-Way Navier-Stokes equations

    Science.gov (United States)

    Rigas, Georgios; Schmidt, Oliver; Towne, Aaron; Colonius, Tim

    2017-11-01

    For three-dimensional flows, questions of stability, receptivity, secondary flows, and coherent structures require the solution of large partial-derivative eigenvalue problems. Reduced-order approximations are thus required for engineering prediction since these problems are often computationally intractable or prohibitively expensive. For spatially slowly evolving flows, such as jets and boundary layers, the One-Way Navier-Stokes (OWNS) equations permit a fast spatial marching procedure that results in a huge reduction in computational cost. Here, an adjoint-based optimization framework is proposed and demonstrated for calculating optimal boundary conditions and optimal volumetric forcing. The corresponding optimal response modes are validated against modes obtained in terms of global resolvent analysis. For laminar base flows, the optimal modes reveal modal and non-modal transition mechanisms. For turbulent base flows, they predict the evolution of coherent structures in a statistical sense. Results from the application of the method to three-dimensional laminar wall-bounded flows and turbulent jets will be presented. This research was supported by the Office of Naval Research (N00014-16-1-2445) and Boeing Company (CT-BA-GTA-1).

  9. Exact Jacobians for implicit Navier-Stokes simulations of equilibrium real gas flows

    Science.gov (United States)

    Rinaldi, Enrico; Pecnik, Rene; Colonna, Piero

    2014-08-01

    This paper documents the extension of several widespread flux schemes, used in finite-volume Navier-Stokes solvers, for the simulation of flows whose fluid properties must be estimated with complex thermophysical models. Exact Jacobian matrices for the convective fluxes are derived with no assumption on the fluid equations of state model for Liou's AUSM+, Toro et al.'s HLLC, and Kurganov and Tadmor's central scheme. The Jacobians of the diffusive fluxes are expressed using the formulation proposed by Pulliam and Steger, resulting in additional terms due to the viscosity and thermal conductivity variations. An efficient look-up table approach is thoroughly studied and proposed as an alternative to the direct solution of the equation of state model for the fluid thermophysical property evaluation. The newly introduced schemes are validated and tested in terms of accuracy and convergence rate on a series of one- and two-dimensional test cases. The results indicate that the Jacobian must be based on the same flux formulation as the one used on the right-hand side of the implicit equation to achieve numerically converged solutions.

  10. Solutions to the linearized Navier-Stokes equations for channel flow via the WKB approximation

    Science.gov (United States)

    Leonard, Anthony

    2017-11-01

    Progress on determining semi-analytical solutions to the linearized Navier-Stokes equations for incompressible channel flow, laminar and turbulent, is reported. Use of the WKB approximation yields, e.g., solutions to initial-value problem for the inviscid Orr-Sommerfeld equation in terms of the Bessel functions J+ 1 / 3 ,J- 1 / 3 ,J1 , and Y1 and their modified counterparts for any given wave speed c = ω /kx and k⊥ ,(k⊥2 =kx2 +kz2) . Of particular note to be discussed is a sequence i = 1 , 2 , . . . of homogeneous inviscid solutions with complex k⊥ i for each speed c, (0 < c <=Umax), in the downstream direction. These solutions for the velocity component normal to the wall v are localized in the plane parallel to the wall. In addition, for limited range of negative c, (- c * <= c <= 0) , we have found upstream-traveling homogeneous solutions with real k⊥(c) . In both cases the solutions for v serve as a source for corresponding solutions to the inviscid Squire equation for the vorticity component normal to the wall ωy.

  11. A spectral/B-spline method for the Navier-Stokes equations in unbounded domains

    CERN Document Server

    Dufresne, L

    2003-01-01

    The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the theta and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r-> infinity. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the lo...

  12. Multitasking a three-dimensional Navier-Stokes algorithm on the Cray-2

    Science.gov (United States)

    Swisshelm, Julie M.

    1989-01-01

    A three-dimensional computational aerodynamics algorithm has been multitasked for efficient parallel execution on the Cray-2. It provides a means for examining the multitasking performance of a complete CFD application code. An embedded zonal multigrid scheme is used to solve the Reynolds-averaged Navier-Stokes equations for an internal flow model problem. The explicit nature of each component of the method allows a spatial partitioning of the computational domain to achieve a well-balanced task load for MIMD computers with vector-processing capability. Experiments have been conducted with both two- and three-dimensional multitasked cases. The best speedup attained by an individual task group was 3.54 on four processors of the Cray-2, while the entire solver yielded a speedup of 2.67 on four processors for the three-dimensional case. The multiprocessing efficiency of various types of computational tasks is examined, performance on two Cray-2s with different memory access speeds is compared, and extrapolation to larger problems is discussed.

  13. Stabilizing the long-time behavior of the forced Navier-Stokes and damped Euler systems by large mean flow

    Science.gov (United States)

    Cyranka, Jacek; Mucha, Piotr B.; Titi, Edriss S.; Zgliczyński, Piotr

    2018-04-01

    The paper studies the issue of stability of solutions to the forced Navier-Stokes and damped Euler systems in periodic boxes. It is shown that for large, but fixed, Grashoff (Reynolds) number the turbulent behavior of all Leray-Hopf weak solutions of the three-dimensional Navier-Stokes equations, in periodic box, is suppressed, when viewed in the right frame of reference, by large enough average flow of the initial data; a phenomenon that is similar in spirit to the Landau damping. Specifically, we consider an initial data which have large enough spatial average, then by means of the Galilean transformation, and thanks to the periodic boundary conditions, the large time independent forcing term changes into a highly oscillatory force; which then allows us to employ some averaging principles to establish our result. Moreover, we also show that under the action of fast oscillatory-in-time external forces all two-dimensional regular solutions of the Navier-Stokes and the damped Euler equations converge to a unique time-periodic solution.

  14. Numerics made easy: solving the Navier-Stokes equation for arbitrary channel cross-sections using Microsoft Excel.

    Science.gov (United States)

    Richter, Christiane; Kotz, Frederik; Giselbrecht, Stefan; Helmer, Dorothea; Rapp, Bastian E

    2016-06-01

    The fluid mechanics of microfluidics is distinctively simpler than the fluid mechanics of macroscopic systems. In macroscopic systems effects such as non-laminar flow, convection, gravity etc. need to be accounted for all of which can usually be neglected in microfluidic systems. Still, there exists only a very limited selection of channel cross-sections for which the Navier-Stokes equation for pressure-driven Poiseuille flow can be solved analytically. From these equations, velocity profiles as well as flow rates can be calculated. However, whenever a cross-section is not highly symmetric (rectangular, elliptical or circular) the Navier-Stokes equation can usually not be solved analytically. In all of these cases, numerical methods are required. However, in many instances it is not necessary to turn to complex numerical solver packages for deriving, e.g., the velocity profile of a more complex microfluidic channel cross-section. In this paper, a simple spreadsheet analysis tool (here: Microsoft Excel) will be used to implement a simple numerical scheme which allows solving the Navier-Stokes equation for arbitrary channel cross-sections.

  15. On bi-grid local mode analysis of solution techniques for 3-D Euler and Navier-Stokes equations

    International Nuclear Information System (INIS)

    Ibraheem, S.O.; Demuren, A.O.

    1996-01-01

    A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection equation, the diffusion equation, and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely spatial, eigenvalue, and combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergences rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central difference scheme, and 3-D Euler solutions with various upwind difference schemes. It is demonstrated that bi-grid analysis can be used as a reliable tool for the prediction of practical multigrid performance. 27 refs., 18 figs., 2 tabs

  16. A GPU-accelerated semi-implicit fractional step method for numerical solutions of incompressible Navier-Stokes equations

    Science.gov (United States)

    Ha, Sanghyun; Park, Junshin; You, Donghyun

    2017-11-01

    Utility of the computational power of modern Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. Due to its serial and bandwidth-bound nature, the present choice of numerical methods is considered to be a good candidate for evaluating the potential of GPUs for solving Navier-Stokes equations using non-explicit time integration. An efficient algorithm is presented for GPU acceleration of the Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution method used in the semi-implicit fractional-step method. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while Navier-Stokes equations are computed on a GPU. Extension to multiple NVIDIA GPUs is implemented using NVLink supported by the Pascal architecture. Performance of the present method is experimented on multiple Tesla P100 GPUs compared with a single-core Xeon E5-2650 v4 CPU in simulations of boundary-layer flow over a flat plate. Supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (Ministry of Science, ICT and Future Planning NRF-2016R1E1A2A01939553, NRF-2014R1A2A1A11049599, and Ministry of Trade, Industry and Energy 201611101000230).

  17. Entropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier--Stokes Equations

    KAUST Repository

    Parsani, Matteo

    2016-10-04

    Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for the compressible Euler and Navier--Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [M. H. Carpenter, T. C. Fisher, E. J. Nielsen, and S. H. Frankel, SIAM J. Sci. Comput., 36 (2014), pp. B835--B867, M. Parsani, M. H. Carpenter, and E. J. Nielsen, J. Comput. Phys., 292 (2015), pp. 88--113], extends the applicable set of points from tensor product, Legendre--Gauss--Lobatto (LGL), to a combination of tensor product Legendre--Gauss (LG) and LGL points. The new semidiscrete operators discretely conserve mass, momentum, energy, and satisfy a mathematical entropy inequality for the compressible Navier--Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly from a theoretical point of view. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinear stability proof for the compressible Navier--Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

  18. Computations on Wings With Full-Span Oscillating Control Surfaces Using Navier-Stokes Equations

    Science.gov (United States)

    Guruswamy, Guru P.

    2013-01-01

    A dual-level parallel procedure is presented for computing large databases to support aerospace vehicle design. This procedure has been developed as a single Unix script within the Parallel Batch Submission environment utilizing MPIexec and runs MPI based analysis software. It has been developed to provide a process for aerospace designers to generate data for large numbers of cases with the highest possible fidelity and reasonable wall clock time. A single job submission environment has been created to avoid keeping track of multiple jobs and the associated system administration overhead. The process has been demonstrated for computing large databases for the design of typical aerospace configurations, a launch vehicle and a rotorcraft.

  19. A Multi-Fluid Compressible System as the Limit of Weak Solutions of the Isentropic Compressible Navier-Stokes Equations

    Science.gov (United States)

    Bresch, D.; Huang, X.

    2011-08-01

    This paper mainly concerns the mathematical justification of a viscous compressible multi-fluid model linked to the Baer-Nunziato model used by engineers, see for instance I shii (Thermo-fluid dynamic theory of two-phase flow, Eyrolles, Paris, 1975), under a "stratification" assumption. More precisely, we show that some approximate finite-energy weak solutions of the isentropic compressible Navier-Stokes equations converge, on a short time interval, to the strong solution of this viscous compressible multi-fluid model, provided the initial density sequence is uniformly bounded with corresponding Young measures which are linear convex combinations of m Dirac measures. To the authors' knowledge, this provides, in the multidimensional in space case, a first positive answer to an open question, see H illairet (J Math Fluid Mech 9:343-376, 2007), with a stratification assumption. The proof is based on the weak solutions constructed by D esjardins (Commun Partial Differ Equ 22(5-6):977-1008, 1997) and on the existence and uniqueness of a local strong solution for the multi-fluid model established by H illairet assuming initial density to be far from vacuum. In a first step, adapting the ideas from H off and S antos (Arch Ration Mech Anal 188:509-543, 2008), we prove that the sequence of weak solutions built by D esjardins has extra regularity linked to the divergence of the velocity without any relation assumption between λ and μ. Coupled with the uniform bound of the density property, this allows us to use appropriate defect measures and their nice properties introduced and proved by H illairet (Aspects interactifs de la m'ecanique des fluides, PhD Thesis, ENS Lyon, 2005) in order to prove that the Young measure associated to the weak limit is the convex combination of m Dirac measures. Finally, under a non-degeneracy assumption of this combination ("stratification" assumption), this provides a multi-fluid system. Using a weak-strong uniqueness argument, we prove that

  20. Pressure correction schemes for compressible flows: application to baro-tropic Navier-Stokes equations and to drift-flux model; Methodes de correction de pression pour les ecoulements compressibles: application aux equations de Navier-Stokes barotropes et au modele de derive

    Energy Technology Data Exchange (ETDEWEB)

    Gastaldo, L

    2007-11-15

    We develop in this PhD thesis a simulation tool for bubbly flows encountered in some late phases of a core-melt accident in pressurized water reactors, when the flow of molten core and vessel structures comes to chemically interact with the concrete of the containment floor. The physical modelling is based on the so-called drift-flux model, consisting of mass balance and momentum balance equations for the mixture (Navier-Stokes equations) and a mass balance equation for the gaseous phase. First, we propose a pressure correction scheme for the compressible Navier-Stokes equations based on mixed non-conforming finite elements. An ad hoc discretization of the advection operator, by a finite volume technique based on a dual mesh, ensures the stability of the velocity prediction step. A priori estimates for the velocity and the pressure yields the existence of the solution. We prove that this scheme is stable, in the sense that the discrete entropy is decreasing. For the conservation equation of the gaseous phase, we build a finite volume discretization which satisfies a discrete maximum principle. From this last property, we deduce the existence and the uniqueness of the discrete solution. Finally, on the basis of these works, a conservative and monotone scheme which is stable in the low Mach number limit, is build for the drift-flux model. This scheme enjoys, moreover, the following property: the algorithm preserves a constant pressure and velocity through moving interfaces between phases (i.e. contact discontinuities of the underlying hyperbolic system). In order to satisfy this property at the discrete level, we build an original pressure correction step which couples the mass balance equation with the transport terms of the gas mass balance equation, the remaining terms of the gas mass balance being taken into account with a splitting method. We prove the existence of a discrete solution for the pressure correction step. Numerical results are presented; they

  1. A frequency domain linearized Navier-Stokes method including acoustic damping by eddy viscosity using RANS

    Science.gov (United States)

    Holmberg, Andreas; Kierkegaard, Axel; Weng, Chenyang

    2015-06-01

    In this paper, a method for including damping of acoustic energy in regions of strong turbulence is derived for a linearized Navier-Stokes method in the frequency domain. The proposed method is validated and analyzed in 2D only, although the formulation is fully presented in 3D. The result is applied in a study of the linear interaction between the acoustic and the hydrodynamic field in a 2D T-junction, subject to grazing flow at Mach 0.1. Part of the acoustic energy at the upstream edge of the junction is shed as harmonically oscillating disturbances, which are conveyed across the shear layer over the junction, where they interact with the acoustic field. As the acoustic waves travel in regions of strong shear, there is a need to include the interaction between the background turbulence and the acoustic field. For this purpose, the oscillation of the background turbulence Reynold's stress, due to the acoustic field, is modeled using an eddy Newtonian model assumption. The time averaged flow is first solved for using RANS along with a k-ε turbulence model. The spatially varying turbulent eddy viscosity is then added to the spatially invariant kinematic viscosity in the acoustic set of equations. The response of the 2D T-junction to an incident acoustic field is analyzed via a plane wave scattering matrix model, and the result is compared to experimental data for a T-junction of rectangular ducts. A strong improvement in the agreement between calculation and experimental data is found when the modification proposed in this paper is implemented. Discrepancies remaining are likely due to inaccuracies in the selected turbulence model, which is known to produce large errors e.g. for flows with significant rotation, which the grazing flow across the T-junction certainly is. A natural next step is therefore to test the proposed methodology together with more sophisticated turbulence models.

  2. SALE-3D, 3-D Fluid Flow, Navier Stokes Equation Using Lagrangian or Eulerian Method

    International Nuclear Information System (INIS)

    Amsden, A.A.; Ruppel, H.M.

    1991-01-01

    1 - Description of problem or function: SALE-3D calculates three- dimensional fluid flows at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held fixed in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a three-dimensional network of arbitrarily shaped, six-sided deformable cells, and a variety of user-selectable boundary conditions are provided in the program. 2 - Method of solution: SALE3D uses an ICED-ALE technique, which combines the ICE method of treating flow speeds and the ALE mesh treatment to calculate three-dimensional fluid flow. The finite- difference approximations to the conservation of mass, momentum, and specific internal energy differential equations are solved in a sequence of time steps on a network of deformable computational cells. The basic hydrodynamic part of each cycle is divided into three phases: (1) an explicit solution of the Lagrangian equations of motion updating the velocity field by the effects of all forces, (2) an implicit calculation using Newton-Raphson iterative scheme that provides time-advanced pressures and velocities, and (3) the addition of advective contributions for runs that are Eulerian or contain some relative motion of grid and fluid. A powerful feature of this three-phases approach is the ease with which

  3. Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua

    Science.gov (United States)

    Brenner, Howard

    2013-01-01

    A critical, albeit simple experimental and/or molecular-dynamic (MD) simulation test is proposed whose outcome would, in principle, establish the viability of the Navier-Stokes-Fourier (NSF) equations for compressible fluid continua. The latter equation set, despite its longevity as constituting the fundamental paradigm of continuum fluid mechanics, has recently been criticized on the basis of its failure to properly incorporate volume transport phenomena—as embodied in the proposed bivelocity paradigm [H. Brenner, Int. J. Eng. Sci.IJESAN0020-722510.1016/j.ijengsci.2012.01.006 54, 67 (2012)]—into its formulation. Were the experimental or simulation results found to accord, even only qualitatively, with bivelocity predictions, the temperature distribution in a gas-filled, thermodynamically and mechanically isolated circular cylinder undergoing steady rigid-body rotation in an inertial reference frame would not be uniform; rather, the temperature would be higher at the cylinder wall than along the axis of rotation. This radial temperature nonuniformity contrasts with the uniformity of the temperature predicted by the NSF paradigm for these same circumstances. Easily attainable rates of rotation in centrifuges and readily available tools for measuring the expected temperature differences render experimental execution of the proposed scheme straightforward in principle. As such, measurement—via experiment or MD simulation—of, say, the temperature difference ΔT between the gas at the wall and along the axis of rotation would provide quantitative tests of both the NSF and bivelocity hydrodynamic models, whose respective solutions for the stated set of circumstances are derived in this paper. Independently of the correctness of the bivelocity model, any temperature difference observed during the proposed experiment or simulation, irrespective of magnitude, would preclude the possibility of the NSF paradigm being correct for fluid continua, except for

  4. Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua.

    Science.gov (United States)

    Brenner, Howard

    2013-01-01

    A critical, albeit simple experimental and/or molecular-dynamic (MD) simulation test is proposed whose outcome would, in principle, establish the viability of the Navier-Stokes-Fourier (NSF) equations for compressible fluid continua. The latter equation set, despite its longevity as constituting the fundamental paradigm of continuum fluid mechanics, has recently been criticized on the basis of its failure to properly incorporate volume transport phenomena-as embodied in the proposed bivelocity paradigm [H. Brenner, Int. J. Eng. Sci. 54, 67 (2012)]-into its formulation. Were the experimental or simulation results found to accord, even only qualitatively, with bivelocity predictions, the temperature distribution in a gas-filled, thermodynamically and mechanically isolated circular cylinder undergoing steady rigid-body rotation in an inertial reference frame would not be uniform; rather, the temperature would be higher at the cylinder wall than along the axis of rotation. This radial temperature nonuniformity contrasts with the uniformity of the temperature predicted by the NSF paradigm for these same circumstances. Easily attainable rates of rotation in centrifuges and readily available tools for measuring the expected temperature differences render experimental execution of the proposed scheme straightforward in principle. As such, measurement-via experiment or MD simulation-of, say, the temperature difference ΔT between the gas at the wall and along the axis of rotation would provide quantitative tests of both the NSF and bivelocity hydrodynamic models, whose respective solutions for the stated set of circumstances are derived in this paper. Independently of the correctness of the bivelocity model, any temperature difference observed during the proposed experiment or simulation, irrespective of magnitude, would preclude the possibility of the NSF paradigm being correct for fluid continua, except for incompressible flows.

  5. Fast chemical reaction in two-dimensional Navier-Stokes flow: initial regime.

    Science.gov (United States)

    Ait-Chaalal, Farid; Bourqui, Michel S; Bartello, Peter

    2012-04-01

    This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional biperiodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one-dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion κ of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution on stratospheric chemistry in climate-chemistry models. Adopting a Lagrangian straining theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it, and of the modulus of the time derivative of the space-average reactant concentrations (here called the chemical speed) to the joint probability density function of the finite-time Lyapunov exponent λ with two times τ and τ[over ̃]. The time 1/λ measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time t, while τ measures it in the recent past before t, and τ[over ̃] in the early part of the trajectory. We show that the chemical speed scales like κ(1/2) and that its time evolution is determined by rare large events in the finite-time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNSs) using a pseudospectral model.

  6. An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

    Science.gov (United States)

    Korte, John J.

    1991-01-01

    An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required

  7. An implicit turbulence model for low-Mach Roe scheme using truncated Navier-Stokes equations

    Science.gov (United States)

    Li, Chung-Gang; Tsubokura, Makoto

    2017-09-01

    The original Roe scheme is well-known to be unsuitable in simulations of turbulence because the dissipation that develops is unsatisfactory. Simulations of turbulent channel flow for Reτ = 180 show that, with the 'low-Mach-fix for Roe' (LMRoe) proposed by Rieper [J. Comput. Phys. 230 (2011) 5263-5287], the Roe dissipation term potentially equates the simulation to an implicit large eddy simulation (ILES) at low Mach number. Thus inspired, a new implicit turbulence model for low Mach numbers is proposed that controls the Roe dissipation term appropriately. Referred to as the automatic dissipation adjustment (ADA) model, the method of solution follows procedures developed previously for the truncated Navier-Stokes (TNS) equations and, without tuning of parameters, uses the energy ratio as a criterion to automatically adjust the upwind dissipation. Turbulent channel flow at two different Reynold numbers and the Taylor-Green vortex were performed to validate the ADA model. In simulations of turbulent channel flow for Reτ = 180 at Mach number of 0.05 using the ADA model, the mean velocity and turbulence intensities are in excellent agreement with DNS results. With Reτ = 950 at Mach number of 0.1, the result is also consistent with DNS results, indicating that the ADA model is also reliable at higher Reynolds numbers. In simulations of the Taylor-Green vortex at Re = 3000, the kinetic energy is consistent with the power law of decaying turbulence with -1.2 exponents for both LMRoe with and without the ADA model. However, with the ADA model, the dissipation rate can be significantly improved near the dissipation peak region and the peak duration can be also more accurately captured. With a firm basis in TNS theory, applicability at higher Reynolds number, and ease in implementation as no extra terms are needed, the ADA model offers to become a promising tool for turbulence modeling.

  8. Structure-Preserving Methods for the Navier-Stokes-Cahn-Hilliard System to Model Immiscible Fluids

    KAUST Repository

    Sarmiento, Adel F.

    2017-12-03

    This work presents a novel method to model immiscible incompressible fluids in a stable manner. Here, the immiscible behavior of the flow is described by the incompressible Navier-Stokes-Cahn-Hilliard model, which is based on a diffuse interface method. We introduce buoyancy effects in the model through the Boussinesq approximation in a consistent manner. A structure-preserving discretization is used to guarantee the linear stability of the discrete problem and to satisfy the incompressibility of the discrete solution at every point in space by construction. For the solution of the model, we developed the Portable Extensible Toolkit for Isogeometric Analysis with Multi-Field discretizations (PetIGA-MF), a high-performance framework that supports structure-preserving spaces. PetIGA-MF is built on top of PetIGA and the Portable Extensible Toolkit for Scientific Computation (PETSc), sharing all their user-friendly, performance, and flexibility features. Herein, we describe the implementation of our model in PetIGA-MF and the details of the numerical solution. With several numerical tests, we verify the convergence, scalability, and validity of our approach. We use highly-resolved numerical simulations to analyze the merging and rising of droplets. From these simulations, we detailed the energy exchanges in the system to evaluate quantitatively the quality of our simulations. The good agreement of our results when compared against theoretical descriptions of the merging, and the small errors found in the energy analysis, allow us to validate our approach. Additionally, we present the development of an unconditionally energy-stable generalized-alpha method for the Swift-Hohenberg model that offers control over the numerical dissipation. A pattern formation example demonstrates the energy-stability and convergence of our method.

  9. Analysis of Influence of the Thermal Dependence of Air Thermophysical Properties on the Accuracy of Simulation of Heat Transfer in a Turbulent Flow in Case of Applying Different Methods of Averaging Navier-Stokes Equations

    Directory of Open Access Journals (Sweden)

    A. D. Kliukvin

    2014-01-01

    Full Text Available There is theoretically investigated the influence of thermal dependence of air thermophysical properties on accuracy of heat transfer problems solution in a turbulent flow when using different methods of averaging the Navier-Stokes equations.There is analyzed the practicability of using particular method of averaging the NavierStokes equations when it’s necessary to clarify the solution of heat transfer problem taking into account the variability of air thermophysical properties.It’s shown that Reynolds and Favre averaging (the most common methods of averaging the Navier-Stokes equations are not effective in this case because these methods inaccurately describe behavior of large scale turbulent structures which strongly depends on geometry of particular flow. Thus it’s necessary to use more universal methods of turbulent flow simulation which are not based on averaging of all turbulent scales.In the article it’s shown that instead of Reynold and Favre averaging it’s possible to use large eddy simulation whereby turbulent structures are divided into small-scale and large-scale ones with subsequent modelling of small-scale ones only. But this approach leads to the necessarity of increasing the computational power by 2-3 orders.For different methods of averaging the form of additional terms of averaged Navier-Stokes equations in case of accounting pulsation of thermophysical properties of the air is obtained.On the example of a submerged heated air jet the errors (which occur when neglecting the thermal dependence of air thermophysical properties on averaged flow temperature in determination of convectional and conductive components of heat flux and viscous stresses are evaluated. It’s shown that the greatest increase of solution accuracy can be obtained in case of the flows with high temperature gradients.Finally using infinite Teylor series it’s found that underestimation of convective and conductive components of heat flux and

  10. An adaptive Petrov-Galerkin formulation for solving the compressible Euler and Navier-Stokes; Uma formulacao de Petrov-Galerkin para a resolucao das equacoes de Euler e Navier-Stokes compressivel usando tecnicas adaptativas

    Energy Technology Data Exchange (ETDEWEB)

    Almeida, Regina Celia Cerqueira de

    1993-12-31

    A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) 63 refs., 40 figs.

  11. A GPU-accelerated semi-implicit fractional-step method for numerical solutions of incompressible Navier-Stokes equations

    Science.gov (United States)

    Ha, Sanghyun; Park, Junshin; You, Donghyun

    2018-01-01

    Utility of the computational power of Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. The Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution methods used in the semi-implicit fractional-step method take advantage of multiple tridiagonal matrices whose inversion is known as the major bottleneck for acceleration on a typical multi-core machine. A novel implementation of the semi-implicit fractional-step method designed for GPU acceleration of the incompressible Navier-Stokes equations is presented. Aspects of the programing model of Compute Unified Device Architecture (CUDA), which are critical to the bandwidth-bound nature of the present method are discussed in detail. A data layout for efficient use of CUDA libraries is proposed for acceleration of tridiagonal matrix inversion and fast Fourier transform. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while the Navier-Stokes equations are computed on a GPU. Performance of the present method using CUDA is assessed by comparing the speed of solving three tridiagonal matrices using ADI with the speed of solving one heptadiagonal matrix using a conjugate gradient method. An overall speedup of 20 times is achieved using a Tesla K40 GPU in comparison with a single-core Xeon E5-2660 v3 CPU in simulations of turbulent boundary-layer flow over a flat plate conducted on over 134 million grids. Enhanced performance of 48 times speedup is reached for the same problem using a Tesla P100 GPU.

  12. Viscous properties of isotropic fluids composed of linear molecules: departure from the classical Navier-Stokes theory in nano-confined geometries.

    Science.gov (United States)

    Hansen, J S; Daivis, Peter J; Todd, B D

    2009-10-01

    In this paper we present equilibrium molecular-dynamics results for the shear, rotational, and spin viscosities for fluids composed of linear molecules. The density dependence of the shear viscosity follows a stretched exponential function, whereas the rotational viscosity and the spin viscosities show approximately power-law dependencies. The frequency-dependent shear and spin viscosities are also studied. It is found that viscoelastic behavior is first manifested in the shear viscosity and that the real part of the spin viscosities features a maximum for nonzero frequency. The calculated transport coefficients are used together with the extended Navier-Stokes equations to investigate the effect of the coupling between the intrinsic angular momentum and linear momentum for highly confined fluids. Both steady and oscillatory flows are studied. It is shown, for example, that the fluid flow rate for Poiseuille flow is reduced by up to 10% in a 2 nm channel for a buta-triene fluid at density 236 kg m(-3) and temperature 306 K. The coupling effect may, therefore, become very important for nanofluidic applications.

  13. Design, experimental analysis, and unsteady Reynolds-averaged Navier-Stokes simulation of laboratory-scale counter-rotating vertical-axis turbines in marine environment

    Science.gov (United States)

    Doan, Minh; Padricelli, Claudrio; Obi, Shinnosuke; Totsuka, Yoshitaka

    2017-11-01

    We present the torque and power measurement of laboratory-scale counter-rotating vertical-axis hydrokinetic turbines, built around a magnetic hysteresis brake as the speed controller and a Hall-effect sensor as the rotational speed transducer. A couple of straight-three-bladed turbines were linked through a transmission of spur gears and timing pulleys and coupled to the electronic instrumentation via flexible shaft couplers. A total of 8 experiments in 2 configurations were conducted in the water channel facility (4-m long, 0.3-m wide, and 0.15-m deep). Power generation of the turbines (0.06-m rotor diameter) was measured and compared with that of single turbines of the same size. The wakes generated by these experiments were also measured by particle image velocimetry (PIV) and numerically simulated by unsteady Reynolds-averaged Navier-Stokes (URANS) simulation using OpenFOAM. Preliminary results from wake measurement indicated the mechanism of enhanced power production behind the counter-rotating configuration of vertical-axis turbines. Current address: Politecnico di Milano.

  14. Error estimates for a numerical method for the compressible Navier-Stokes system on sufficiently smooth domains

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Hošek, Radim; Maltese, D.; Novotný, A.

    2017-01-01

    Roč. 51, č. 1 (2017), s. 279-319 ISSN 0764-583X EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.727, year: 2016 http://www.esaim-m2an.org/ articles /m2an/abs/2017/01/m2an150157/m2an150157.html

  15. Error estimates for a numerical method for the compressible Navier-Stokes system on sufficiently smooth domains

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Hošek, Radim; Maltese, D.; Novotný, A.

    2017-01-01

    Roč. 51, č. 1 (2017), s. 279-319 ISSN 0764-583X EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.727, year: 2016 http://www.esaim-m2an.org/articles/m2an/abs/2017/01/m2an150157/m2an150157.html

  16. Synthesis of the scientific activity. Resolution of compressible Navier-Stokes equations for steady supersonic and transonic regimes

    International Nuclear Information System (INIS)

    Angrand, F.

    1990-10-01

    In this HDR (Accreditation to Supervise Researches) report, the author gives an overview of his activities in the field of numerical methods, notably in the field of fluid mechanics and aeronautics. He more particularly addresses the resolution of Euler equations of gas dynamics in transonic and supersonic regimes (equations, centered and off-centered flow calculation, case of one-dimensional and non linear systems), the extension of this work to Navier-Stokes equations (equations, grid adaptation), the study of resolution methods and cost optimisation (Runge-Kutta method, implicit schemes, multi-grid approach). He also addresses the case of hypersonic flows behind a base

  17. A six-mode truncation of the Navier-Stokes equations on a two-dimensional torus: a numerical study

    International Nuclear Information System (INIS)

    Angelo, P.M.; Riela, G.

    1981-01-01

    We study a model obtained from a six-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus. We find that at low values of the Reynolds number R the dynamics is characterized by fixed points and, at large values of R, by two stable periodic orbits; at intermediate values of R two infinite sequences of bifurcations of periodic orbits into periodic orbits of doubled period lead to two regions of ''turbulent'' or ''chaotic'' behaviour. The turbulent regions end up for values of R for which stable periodic orbits appear. (author)

  18. Comment on "Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua".

    Science.gov (United States)

    Felderhof, B U

    2013-08-01

    Recently, a critical test of the Navier-Stokes-Fourier equations for compressible fluid continua was proposed [H. Brenner, Phys. Rev. E 87, 013014 (2013)]. It was shown that the equations of bivelocity hydrodynamics imply that a compressible fluid in an isolated rotating circular cylinder attains a nonequilibrium steady state with a nonuniform temperature increasing radially with distance from the axis. We demonstrate that statistical mechanical arguments, involving Hamiltonian dynamics and ergodicity due to irregularity of the wall, lead instead to a thermal equilibrium state with uniform temperature. This is the situation to be expected in experiment.

  19. An iteration for indefinite and non-symmetric systems and its application to the Navier-Stokes equations

    Energy Technology Data Exchange (ETDEWEB)

    Wathen, A. [Oxford Univ. (United Kingdom); Golub, G. [Stanford Univ., CA (United States)

    1996-12-31

    A simple fixed point linearisation of the Navier-Stokes equations leads to the Oseen problem which after appropriate discretisation yields large sparse linear systems with coefficient matrices of the form (A B{sup T} B -C). Here A is non-symmetric but its symmetric part is positive definite, and C is symmetric and positive semi-definite. Such systems arise in other situations. In this talk we will describe and present some analysis for an iteration based on an indefinite and symmetric preconditioner of the form (D B{sup T} B -C).

  20. A finite-element model in vorticity and current function for the numerical solution of the Navier-Stokes equations

    International Nuclear Information System (INIS)

    Cunha Furtado, F. da; Galeao, A.C.N.R.

    1984-01-01

    A numerical procedure for the integration of the incompressible Navier-Stokes equations, when expressed in terms of a stream function equation and a vorticity transport equation, is presented. This procedure comprises: the variational formulation of the equations, the construction of the approximation spaces by the finite element method and the discretization via the Galerkin method. For the stationary problems, the system of non-linear algebraic equations resulting from the discretization is solved by the Newton-Raphson algorithm. Finally, for the transient problems, the solution of the non-linear ordinary differential equations resulting from the spatial discretization is accomplished through a Crank-Nicolson scheme. (Author) [pt

  1. Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D domains

    Science.gov (United States)

    Brzeźniak, Zdzisław; Motyl, Elżbieta

    Stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains driven by a multiplicative Gaussian noise are considered. The noise term depends on the unknown velocity and its spatial derivatives. The existence of a martingale solution is proved. The construction of the solution is based on the classical Faedo-Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod Theorem for nonmetric spaces. Moreover, some compactness and tightness criteria in nonmetric spaces are proved. Compactness results are based on a certain generalization of the classical Dubinsky Theorem.

  2. Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Medviďová-Lukáčová, M.; Nečasová, Šárka; Novotný, A.; She, Bangwei

    2018-01-01

    Roč. 16, č. 1 (2018), s. 150-183 ISSN 1540-3459 R&D Projects: GA ČR GA16-03230S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method * asymptotic preserving schemes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.865, year: 2016 http://epubs.siam.org/doi/10.1137/16M1094233

  3. Large Eddy/Reynolds-Averaged Navier-Stokes Simulations of CUBRC Base Heating Experiments

    Science.gov (United States)

    Salazar, Giovanni; Edwards, Jack R.; Amar, Adam J.

    2012-01-01

    ven with great advances in computational techniques and computing power during recent decades, the modeling of unsteady separated flows, such as those encountered in the wake of a re-entry vehicle, continues to be one of the most challenging problems in CFD. Of most interest to the aerothermodynamics community is accurately predicting transient heating loads on the base of a blunt body, which would result in reduced uncertainties and safety margins when designing a re-entry vehicle. However, the prediction of heat transfer can vary widely depending on the turbulence model employed. Therefore, selecting a turbulence model which realistically captures as much of the flow physics as possible will result in improved results. Reynolds Averaged Navier Stokes (RANS) models have become increasingly popular due to their good performance with attached flows, and the relatively quick turnaround time to obtain results. However, RANS methods cannot accurately simulate unsteady separated wake flows, and running direct numerical simulation (DNS) on such complex flows is currently too computationally expensive. Large Eddy Simulation (LES) techniques allow for the computation of the large eddies, which contain most of the Reynolds stress, while modeling the smaller (subgrid) eddies. This results in models which are more computationally expensive than RANS methods, but not as prohibitive as DNS. By complimenting an LES approach with a RANS model, a hybrid LES/RANS method resolves the larger turbulent scales away from surfaces with LES, and switches to a RANS model inside boundary layers. As pointed out by Bertin et al., this type of hybrid approach has shown a lot of promise for predicting turbulent flows, but work is needed to verify that these models work well in hypersonic flows. The very limited amounts of flight and experimental data available presents an additional challenge for researchers. Recently, a joint study by NASA and CUBRC has focused on collecting heat transfer data

  4. Coupling Two-Phase Fluid Flow with Two-Phase Darcy Flow in Anisotropic Porous Media

    Directory of Open Access Journals (Sweden)

    Jie Chen

    2014-06-01

    Full Text Available This paper reports a numerical study of coupling two-phase fluid flow in a free fluid region with two-phase Darcy flow in a homogeneous and anisotropic porous medium region. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the anisotropic porous medium region. A Robin-Robin domain decomposition method is used for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Obtained results have shown the anisotropic properties effect on the velocity and pressure of the two-phase flow.

  5. Validation Process for LEWICE Coupled by Use of a Navier-stokes Solver

    Science.gov (United States)

    Wright, William B.

    2016-01-01

    A research project is underway at NASA Glenn to produce computer software that can accurately predict ice growth for many meteorological conditions for any aircraft surface. This report will present results from the latest LEWICE release, version 3.5. This program differs from previous releases in its ability to model mixed phase and ice crystal conditions such as those encountered inside an engine. It also has expanded capability to use structured grids and a new capability to use results from unstructured grid flow solvers. An extensive comparison of the results in a quantifiable manner against the database of ice shapes that have been generated in the NASA Glenn Icing Research Tunnel (IRT) has also been performed. This paper will show the differences in ice shape between LEWICE 3.5 and experimental data. In addition, comparisons will be made between the lift and drag calculated on the ice shapes from experiment and those produced by LEWICE. This report will also provide a description of both programs. Quantitative geometric comparisons are shown for horn height, horn angle, icing limit, area and leading edge thickness. Quantitative comparisons of calculated lift and drag will also be shown. The results show that the predicted results are within the accuracy limits of the experimental data for the majority of cases.

  6. A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations

    International Nuclear Information System (INIS)

    Lu, T.; Neittaanmaeki, P.

    1992-01-01

    The traditional splitting-up method or fractional step method is suitable for sequential computing. This means that the computing of the present fractional step needs the value of the previous fractional steps. In this paper we propose a new splitting-up scheme for which the computing of the fractional steps is independent of each other and therefore can be computed by parallel processors. We have proved the convergence estimates of this scheme both for steady state and nonsteady state linear and nonlinear problems. To use finite element method to solve Navier-Stokes problems it is always difficult to handle the zero-divergent finite element spaces. Here, by using the splitting-up method we can use the usual finite element spaces to solve it. Moreover, the proposed method can solve the steady and nonsteady state Navier-Stokes problem by only solving some one dimensional linear systems. All these one dimensional systems are independent of each other, so they can be computed by parallel processors. (author). 20 refs

  7. Developpement of a numerical method for Navier-Stokes equations in anelastic approximation: application to Rayleigh-Taylor instabilities

    International Nuclear Information System (INIS)

    Hammouch, Z.

    2012-01-01

    The 'anelastic' approximation allows us to filter the acoustic waves thanks to an asymptotic development of the Navier-Stokes equations, so increasing the averaged time step, during the numerical simulation of hydrodynamic instabilities development. So, the anelastic equations for a two fluid mixture in case of Rayleigh-Taylor instability are established.The linear stability of Rayleigh-Taylor flow is studied, for the first time, for perfect fluids in the anelastic approximation. We define the Stokes problem resulting from Navier-Stokes equations without the non linear terms (a part of the buoyancy is considered); the ellipticity is demonstrated, the Eigenmodes and the invariance related to the pressure are detailed. The Uzawa's method is extended to the anelastic approximation and shows the decoupling speeds in 3D, the particular case k = 0 and the spurious modes of pressure. Passing to multi-domain allowed to establish the transmission conditions.The algorithms and the implementation in the existing program are validated by comparing the Uzawa's operator in Fortran and Mathematica languages, to an experiment with incompressible fluids and results from anelastic and compressible numerical simulations. The study of the influence of the initial stratification of both fluids on the development of the Rayleigh-Taylor instability is initiated. (author) [fr

  8. Particles at fluid-fluid interfaces: A new Navier-Stokes-Cahn-Hilliard surface- phase-field-crystal model

    Science.gov (United States)

    Aland, Sebastian; Lowengrub, John; Voigt, Axel

    2012-10-01

    Colloid particles that are partially wetted by two immiscible fluids can become confined to fluid-fluid interfaces. At sufficiently high volume fractions, the colloids may jam and the interface may crystallize. The fluids together with the interfacial colloids form an emulsion with interesting material properties and offer an important route to new soft materials. A promising approach to simulate these emulsions was presented in Aland [Phys. FluidsPHFLE61070-663110.1063/1.3584815 23, 062103 (2011)], where a Navier-Stokes-Cahn-Hilliard model for the macroscopic two-phase fluid system was combined with a surface phase-field-crystal model for the microscopic colloidal particles along the interface. Unfortunately this model leads to spurious velocities which require very fine spatial and temporal resolutions to accurately and stably simulate. In this paper we develop an improved Navier-Stokes-Cahn-Hilliard-surface phase-field-crystal model based on the principles of mass conservation and thermodynamic consistency. To validate our approach, we derive a sharp interface model and show agreement with the improved diffuse interface model. Using simple flow configurations, we show that the new model has much better properties and does not lead to spurious velocities. Finally, we demonstrate the solid-like behavior of the crystallized interface by simulating the fall of a solid ball through a colloid-laden multiphase fluid.

  9. Partially-Averaged Navier-Stokes (PANS) approach for study of fluid flow and heat transfer characteristics in Czochralski melt

    Science.gov (United States)

    Verma, Sudeep; Dewan, Anupam

    2018-01-01

    The Partially-Averaged Navier-Stokes (PANS) approach has been applied for the first time to model turbulent flow and heat transfer in an ideal Czochralski set up with the realistic boundary conditions. This method provides variable level of resolution ranging from the Reynolds-Averaged Navier-Stokes (RANS) modelling to Direct Numerical Simulation (DNS) based on the filter control parameter. For the present case, a low-Re PANS model has been developed for Czochralski melt flow, which includes the effect of coriolis, centrifugal, buoyant and surface tension induced forces. The aim of the present study is to assess improvement in results on switching to PANS modelling from unsteady RANS (URANS) approach on the same computational mesh. The PANS computed results were found to be in good agreement with the reported experimental, DNS and Large Eddy Simulation (LES) data. A clear improvement in computational accuracy is observed in switching from the URANS approach to the PANS methodology. The computed results further improved with a reduction in the PANS filter width. Further the capability of the PANS model to capture key characteristics of the Czochralski crystal growth is also highlighted. It was observed that the PANS model was able to resolve the three-dimensional turbulent nature of the melt, characteristic flow structures arising due to flow instabilities and generation of thermal plumes and vortices in the Czochralski melt.

  10. Particles at fluid-fluid interfaces: A new Navier-Stokes-Cahn-Hilliard surface- phase-field-crystal model.

    Science.gov (United States)

    Aland, Sebastian; Lowengrub, John; Voigt, Axel

    2012-10-01

    Colloid particles that are partially wetted by two immiscible fluids can become confined to fluid-fluid interfaces. At sufficiently high volume fractions, the colloids may jam and the interface may crystallize. The fluids together with the interfacial colloids form an emulsion with interesting material properties and offer an important route to new soft materials. A promising approach to simulate these emulsions was presented in Aland et al. [Phys. Fluids 23, 062103 (2011)], where a Navier-Stokes-Cahn-Hilliard model for the macroscopic two-phase fluid system was combined with a surface phase-field-crystal model for the microscopic colloidal particles along the interface. Unfortunately this model leads to spurious velocities which require very fine spatial and temporal resolutions to accurately and stably simulate. In this paper we develop an improved Navier-Stokes-Cahn-Hilliard-surface phase-field-crystal model based on the principles of mass conservation and thermodynamic consistency. To validate our approach, we derive a sharp interface model and show agreement with the improved diffuse interface model. Using simple flow configurations, we show that the new model has much better properties and does not lead to spurious velocities. Finally, we demonstrate the solid-like behavior of the crystallized interface by simulating the fall of a solid ball through a colloid-laden multiphase fluid.

  11. A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions.

    Science.gov (United States)

    Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

    2015-08-15

    In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier-Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.

  12. Uniqueness Results for Weak Leray-Hopf Solutions of the Navier-Stokes System with Initial Values in Critical Spaces

    Science.gov (United States)

    Barker, T.

    2018-03-01

    The main subject of this paper concerns the establishment of certain classes of initial data, which grant short time uniqueness of the associated weak Leray-Hopf solutions of the three dimensional Navier-Stokes equations. In particular, our main theorem that this holds for any solenodial initial data, with finite L_2(R^3) norm, that also belongs to certain subsets of {it{VMO}}^{-1}(R^3). As a corollary of this, we obtain the same conclusion for any solenodial u0 belonging to L2(R^3)\\cap \\dot{B}^{-1+3/p}_{p,∞}(R^3), for any 3Navier-Stokes equations, with these classes of initial data. Such properties seem to be of independent interest. Consequently, we are also able to show if a weak Leray-Hopf solution u satisfies certain extensions of the Prodi-Serrin condition on R^3 × ]0,T[, then it is unique on R^3 × ]0,T[ amongst all other weak Leray-Hopf solutions with the same initial value. In particular, we show this is the case if u\\in L^{q,s}(0,T; L^{p,s}(R^3)) or if it's L^{q,∞}(0,T; L^{p,∞}(R^3)) norm is sufficiently small, where 3

  13. Y spaces and global smooth solution of fractional Navier-Stokes equations with initial value in the critical oscillation spaces

    Science.gov (United States)

    Yang, Qixiang; Yang, Haibo

    2018-04-01

    For fractional Navier-Stokes equations and critical initial spaces X, one used to establish the well-posedness in the solution space which is contained in C (R+ , X). In this paper, for heat flow, we apply parameter Meyer wavelets to introduce Y spaces Y m , β where Y m , β is not contained in C (R+, B˙∞ 1 - 2 β , ∞). Consequently, for 1/2 Navier-Stokes equations with small initial data in all the critical oscillation spaces. The critical oscillation spaces may be any Besov-Morrey spaces (B˙p,q γ1 ,γ2 (Rn)) n or any Triebel-Lizorkin-Morrey spaces (F˙p,q γ1 ,γ2 (Rn)) n where 1 ≤ p , q ≤ ∞ , 0 ≤γ2 ≤ n/p, γ1 -γ2 = 1 - 2 β. These critical spaces include many known spaces. For example, Besov spaces, Sobolev spaces, Bloch spaces, Q-spaces, Morrey spaces and Triebel-Lizorkin spaces etc.

  14. Three-dimensional Navier-Stokes analysis and redesign of an imbedded bellmouth nozzle in a turbine cascade inlet section

    Science.gov (United States)

    VanFossen, G. J.; Lopez, L.; Giel, P. W.; Sirbaugh, J. R.

    1996-01-01

    Experimental measurements in the inlet of a transonic turbine blade cascade showed unacceptable pitchwise flow non-uniformity. A three-dimensional, Navier-Stokes computational fluid dynamics (CFD) analysis of the imbedded bellmouth inlet in the facility was performed to identify and eliminate the source of the flow non-uniformity. The blockage and acceleration effects of the blades were accounted for by specifying a periodic static pressure exit condition interpolated from a separate three-dimensional Navier-Stokes CFD solution of flow around a single blade in an infinite cascade. Calculations of the original inlet geometry showed total pressure loss regions consistent in strength and location to experimental measurements. The results indicate that the distortions were caused by a pair of streamwise vortices that originated as a result of the interaction of the flow with the imbedded bellmouth. Computations were performed for an inlet geometry which eliminated the imbedded bellmouth by bridging the region between it and the upstream wall. This analysis indicated that eliminating the imbedded bellmouth nozzle also eliminates the pair of vortices, resulting in a flow with much greater pitchwise uniformity. Measurements taken with an installed redesigned inlet verify that the flow non-uniformity has indeed been eliminated.

  15. Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence.

    Science.gov (United States)

    Sharma, Ati S; Moarref, Rashad; McKeon, Beverley J; Park, Jae Sung; Graham, Michael D; Willis, Ashley P

    2016-02-01

    We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010)]. This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence.

  16. A stabilized finite element formulation for the solution of the Navier-Stokes equations in axisymmetric geometry; Uma formulacao estabilizada de elementos finitos para solucao das equacoes de Navier-Stokes em geometria axissimetrica

    Energy Technology Data Exchange (ETDEWEB)

    Souza, Altivo Monteiro de

    2008-12-15

    The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS{sub S}OLVER{sub M}PI{sub 2}D{sub A} program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)

  17. Integral transformation of the Navier-Stokes equations for laminar flow in channels of arbitrary two-dimensional geometry; Transformacao integral das equacoes de Navier-Stokes para escoamento laminar em canais de geometria bidimensional arbitraria

    Energy Technology Data Exchange (ETDEWEB)

    Perez Guerrero, Jesus Salvador

    1995-12-31

    Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author) 78 refs., 24 figs., 14 tabs.

  18. Lyapunov analysis and stabilization to the rest state for solutions to the 1D-barotropic compressible Navier-Stokes equations

    Czech Academy of Sciences Publication Activity Database

    Penel, P.; Straškraba, Ivan

    2007-01-01

    Roč. 345, č. 1 (2007), s. 67-72 ISSN 0249-6291 R&D Projects: GA ČR GA201/05/0005 Institutional research plan: CEZ:AV0Z10190503 Keywords : 1D-Navier-Stokes equations * compressible flow * global behavior Subject RIV: BA - General Mathematics

  19. On the Long-Time Behaviour of Solutions to the Navier-Stokes-Fourier System with a Time Dependent Driving Force

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Petzeltová, Hana

    2007-01-01

    Roč. 19, č. 3 (2007), s. 685-707 ISSN 1040-7294 R&D Projects: GA AV ČR IAA1019302 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes-Fourier system * long-time behaviour * time-dependent driving force Subject RIV: BA - General Mathematics

  20. On the steady Navier-Stokes Boundary Value Problem in an Unbounded 2D Domain with Arbitrary Fluxes through the Components of the Boundary

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří

    2009-01-01

    Roč. 55, č. 2 (2009), s. 353-365 ISSN 0430-3202 R&D Projects: GA AV ČR IAA100190905 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes equations Subject RIV: BA - General Mathematics

  1. Renormalization group in the theory of fully developed turbulence. Problem of the infrared relevant corrections to the Navier-Stokes equation

    International Nuclear Information System (INIS)

    Antonov, N.V.; Borisenok, S.V.; Girina, V.I.

    1996-01-01

    Within the framework of the renormalization group approach to the theory of fully developed turbulence we consider the problem of possible IR relevant corrections to the Navier-Stokes equation. We formulate an exact criterion of the actual IR relevance of the corrections. In accordance with this criterion we verify the IR relevance for certain classes of composite operators. 17 refs., 2 tabs

  2. A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří

    2014-01-01

    Roč. 139, č. 4 (2014), s. 685-698 ISSN 0862-7959 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * suitable weak solution * regularity Subject RIV: BA - General Mathematics http://hdl.handle.net/10338.dmlcz/144145

  3. 2D and 3D transonic flow computation using finite volume method and model of Euler and Navier-Stokes equations

    Energy Technology Data Exchange (ETDEWEB)

    Fialova, M.; Fuerst, J.; Horak, J.; Kozel, K. [Czech Technical Univ., Faculty of Mechanical Engineering, Dept. of Technical Mathematics, Prague (Czech Republic)

    1997-12-31

    The work deals with numerical solution of 2D and 3D transonic flows using mathematical models of Euler and Navier-Stokes equations. For inviscid flows with a shock wave we tested modern TVD upwind and central methods. For computations of 2D and 3D compressible viscous laminar flows multistage Runge-Kutta methods were used. (orig.)

  4. An Additive Turbulent Decomposition of the Navier-Stokes Equations Implemented on Highly Parallel Computer Systems

    Science.gov (United States)

    1990-05-30

    used in nonlinear multigrid methods ). We describe this technique and also some domain decomposition algorithms that are used in conjunction with this...nonlinear multigrid methods , known as the full approximation scheme. We describe this in a later section. 3 A framework for our studies. The ATD method...the ATD framework a technique commonly used in nonlinear multigrid methods to couple the fine grid and coarse grid problems, namely, the Full

  5. Computational analysis of water entry of a circular section at constant velocity based on Reynold's averaged Navier-Stokes method

    Science.gov (United States)

    Uddin, M. Maruf; Fuad, Muzaddid-E.-Zaman; Rahaman, Md. Mashiur; Islam, M. Rabiul

    2017-12-01

    With the rapid decrease in the cost of computational infrastructure with more efficient algorithm for solving non-linear problems, Reynold's averaged Navier-Stokes (RaNS) based Computational Fluid Dynamics (CFD) has been used widely now-a-days. As a preliminary evaluation tool, CFD is used to calculate the hydrodynamic loads on offshore installations, ships, and other structures in the ocean at initial design stages. Traditionally, wedges have been studied more than circular cylinders because cylinder section has zero deadrise angle at the instant of water impact, which increases with increase of submergence. In Present study, RaNS based commercial code ANSYS Fluent is used to simulate the water entry of a circular section at constant velocity. It is seen that present computational results were compared with experiment and other numerical method.

  6. Homogeneous Solutions of Stationary Navier-Stokes Equations with Isolated Singularities on the Unit Sphere. I. One Singularity

    Science.gov (United States)

    Li, Li; Li, YanYan; Yan, Xukai

    2018-03-01

    We classify all (-1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south pole, parameterize them as a two dimensional surface with boundary, and analyze their pressure profiles near the north pole. Then we prove that there is a curve of (-1)-homogeneous axisymmetric solutions with nonzero swirl, having the same smoothness property, emanating from every point of the interior and one part of the boundary of the solution surface. Moreover we prove that there is no such curve of solutions for any point on the other part of the boundary. We also establish asymptotic expansions for every (-1)-homogeneous axisymmetric solutions in a neighborhood of the singular point on the unit sphere.

  7. Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations.

    Science.gov (United States)

    Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R

    2013-09-01

    We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.

  8. Performance of Reynolds Averaged Navier-Stokes Models in Predicting Separated Flows: Study of the Hump Flow Model Problem

    Science.gov (United States)

    Cappelli, Daniele; Mansour, Nagi N.

    2012-01-01

    Separation can be seen in most aerodynamic flows, but accurate prediction of separated flows is still a challenging problem for computational fluid dynamics (CFD) tools. The behavior of several Reynolds Averaged Navier-Stokes (RANS) models in predicting the separated ow over a wall-mounted hump is studied. The strengths and weaknesses of the most popular RANS models (Spalart-Allmaras, k-epsilon, k-omega, k-omega-SST) are evaluated using the open source software OpenFOAM. The hump ow modeled in this work has been documented in the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control. Only the baseline case is treated; the slot flow control cases are not considered in this paper. Particular attention is given to predicting the size of the recirculation bubble, the position of the reattachment point, and the velocity profiles downstream of the hump.

  9. Evidence for equivalence of diffusion processes of passive scalar and magnetic fields in anisotropic Navier-Stokes turbulence.

    Science.gov (United States)

    Jurčišinová, E; Jurčišin, M

    2017-05-01

    The influence of the uniaxial small-scale anisotropy on the kinematic magnetohydrodynamic turbulence is investigated by using the field theoretic renormalization group technique in the one-loop approximation of a perturbation theory. The infrared stable fixed point of the renormalization group equations, which drives the scaling properties of the model in the inertial range, is investigated as the function of the anisotropy parameters and it is shown that, at least at the one-loop level of approximation, the diffusion processes of the weak passive magnetic field in the anisotropically driven kinematic magnetohydrodynamic turbulence are completely equivalent to the corresponding diffusion processes of passively advected scalar fields in the anisotropic Navier-Stokes turbulent environments.

  10. NSFLEX - An implicit relaxation method for the Navier-Stokes equations for a wide range of Mach numbers

    Science.gov (United States)

    Schmatz, M. A.

    The extension of the NSFLEX method to hypersonic flows is described for simple two-dimensional and complex three-dimensional configurations. Real gas effects were incorporated in the model. The Reynolds-averaged Navier-Stokes equations were employed for turbulent flows with an algebraic turbulence model. To evaluate the inviscid fluxes a Riemann problem was solved at the finite volume faces. For the very strong shocks which occur at hypersonic flow conditions, a hybrid Steger-Warming local characteristic flux was used to avoid negative pressures in the transient phase. The viscous fluxes were made with central differences at each cell face. The infactored implicit equations were solved in time-dependent form by a Gauss-Siedel relaxation technique. The method was applied successfully to the Hermes configuration for several Mach numbers.

  11. NSFLEX: An implicit relaxation method for the Navier-Stokes equations for a wide range of Mach numbers

    Science.gov (United States)

    Schmatz, Manfred A.

    The extension of the NSFLEX method to hypersonic flows is described for simple two-dimensional and complex three-dimensional configurations. Real gas effects were incorporated in the model. The Reynolds-averaged Navier-Stokes equations were employed for turbulent flows with an algebraic turbulence model. To evaluate the inviscid fluxes a Riemann problem was solved at the finite volume faces. For the very strong shocks which occur at hypersonic flow conditions, a hybrid Steger-Warming local characteristic flux was used to avoid negative pressures in the transient phase. The viscous fluxes were made with central differences at each cell face. The infactored implicit equations were solved in time-dependent form by a Gauss-Siedel relaxation technique. The method was applied successfully to the Hermes configuration for several Mach numbers.

  12. A stabilized finite element formulation for the solution of the Navier-Stokes equations in axisymmetric geometry

    International Nuclear Information System (INIS)

    Souza, Altivo Monteiro de

    2008-12-01

    The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS S OLVER M PI 2 D A program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)

  13. An Algorithm for the Numerical Solution of the Pseudo Compressible Navier-stokes Equations Based on the Experimenting Fields Approach

    KAUST Repository

    Salama, Amgad

    2015-06-01

    In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique.

  14. Influence of anisotropy on anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field.

    Science.gov (United States)

    Jurcisinová, E; Jurcisin, M; Remecký, R

    2009-10-01

    The influence of weak uniaxial small-scale anisotropy on the stability of the scaling regime and on the anomalous scaling of the single-time structure functions of a passive scalar advected by the velocity field governed by the stochastic Navier-Stokes equation is investigated by the field theoretic renormalization group and operator-product expansion within one-loop approximation of a perturbation theory. The explicit analytical expressions for coordinates of the corresponding fixed point of the renormalization-group equations as functions of anisotropy parameters are found, the stability of the three-dimensional Kolmogorov-like scaling regime is demonstrated, and the dependence of the borderline dimension d(c) is an element of (2,3] between stable and unstable scaling regimes is found as a function of the anisotropy parameters. The dependence of the turbulent Prandtl number on the anisotropy parameters is also briefly discussed. The influence of weak small-scale anisotropy on the anomalous scaling of the structure functions of a passive scalar field is studied by the operator-product expansion and their explicit dependence on the anisotropy parameters is present. It is shown that the anomalous dimensions of the structure functions, which are the same (universal) for the Kraichnan model, for the model with finite time correlations of the velocity field, and for the model with the advection by the velocity field driven by the stochastic Navier-Stokes equation in the isotropic case, can be distinguished by the assumption of the presence of the small-scale anisotropy in the systems even within one-loop approximation. The corresponding comparison of the anisotropic anomalous dimensions for the present model with that obtained within the Kraichnan rapid-change model is done.

  15. Integral transformation of the Navier-Stokes equations for laminar flow in channels of arbitrary two-dimensional geometry

    International Nuclear Information System (INIS)

    Perez Guerrero, Jesus Salvador

    1995-01-01

    Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author)

  16. A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

    Science.gov (United States)

    Asgharzadeh, Hafez; Borazjani, Iman

    2017-02-15

    The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the

  17. Unsteady Reynolds Averaged Navier-Stokes and Large Eddy Simulations of Flows across Staggered Tube Bundle for a VHTR Lower Plenum Design

    International Nuclear Information System (INIS)

    Choi, Hyeon Kyeong; Park, Jong Woon

    2013-01-01

    In this work, behavior of unsteady and oscillating flow through a typical tube bundle array are analyzed by unsteady computations: 2D unsteady Reynolds averaged Navier-Stokes (URANS) and 3D Large Eddy Simulation (LES) and the results are compared with existing experimental data. In order to confirm appropriateness and limitations of CFD applications in the Korean VHTR design, two types of unsteady computations are performed such as 2D unsteady Reynolds averaged Navier-Stokes (URANS) and 3D Large Eddy Simulation (LES) for the existing tube bundle array. The velocity component profiles are compared with the experimental data and it is concluded that the URANS with the standard k-ω model is reasonably appropriate for cost-effective VHTR lower plenum analysis. Nevertheless, if more accurate results are needed, the LES-Smagorinsky computation is recommended considering limitations in the time averaged RANS in capturing small eddies

  18. A new approach to the existence of weak solutions of the steady Navier-Stokes system with inhomogeneous boundary data in domains with noncompact boundaries

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří

    2010-01-01

    Roč. 198, č. 1 (2010), 331-348 ISSN 0003-9527 R&D Projects: GA ČR GA201/08/0012 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes equations * inhomogeneous boundary data Subject RIV: BA - General Mathematics Impact factor: 2.277, year: 2010 http://link.springer.com/article/10.1007%2Fs00205-010-0297-7

  19. The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří; Al Baba, Hind

    2018-01-01

    Roč. 463, č. 1 (2018), s. 222-234 ISSN 0022-247X R&D Projects: GA ČR(CZ) GA17-01747S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * Navier-type boundary conditions * interior regularity Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 https://www.sciencedirect.com/science/article/pii/S0022247X18302233?via%3Dihub

  20. On a nu-continuous famaly of strong solutions to the Euler or Navier-Stokes equations with the Navier-type boundary condition

    Czech Academy of Sciences Publication Activity Database

    Bellout, H.; Neustupa, Jiří; Penel, P.

    2010-01-01

    Roč. 27, č. 4 (2010), s. 1353-1373 ISSN 1078-0947 R&D Projects: GA AV ČR IAA100190905 Institutional research plan: CEZ:AV0Z10190503 Keywords : Euler equations * Navier-Stokes equations * zero viscosity limit Subject RIV: BA - General Mathematics Impact factor: 0.986, year: 2010 http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5028

  1. Three-dimensional poor man's Navier-Stokes equation: a discrete dynamical system exhibiting k(-5/3) inertial subrange energy scaling.

    Science.gov (United States)

    McDonough, J M

    2009-06-01

    Outline of the derivation and mathematical and physical interpretations are presented for a discrete dynamical system known as the "poor man's Navier-Stokes equation." Numerical studies demonstrate that velocity fields produced by this dynamical system are similar to those seen in laboratory experiments and in detailed simulations, and they lead to scaling for the turbulence kinetic energy spectrum in accord with Kolmogorov K41 theory.

  2. The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Neustupa, Jiří; Al Baba, Hind

    2018-01-01

    Roč. 463, č. 1 (2018), s. 222-234 ISSN 0022-247X R&D Projects: GA ČR(CZ) GA17-01747S Institutional support: RVO:67985840 Keywords : Navier-Stokes equation * Navier-type boundary conditions * interior regularity Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 https://www. science direct.com/ science /article/pii/S0022247X18302233?via%3Dihub

  3. Final Report - High-Order Spectral Volume Method for the Navier-Stokes Equations On Unstructured Tetrahedral Grids

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Z J

    2012-12-06

    The overriding objective for this project is to develop an efficient and accurate method for capturing strong discontinuities and fine smooth flow structures of disparate length scales with unstructured grids, and demonstrate its potentials for problems relevant to DOE. More specifically, we plan to achieve the following objectives: 1. Extend the SV method to three dimensions, and develop a fourth-order accurate SV scheme for tetrahedral grids. Optimize the SV partition by minimizing a form of the Lebesgue constant. Verify the order of accuracy using the scalar conservation laws with an analytical solution; 2. Extend the SV method to Navier-Stokes equations for the simulation of viscous flow problems. Two promising approaches to compute the viscous fluxes will be tested and analyzed; 3. Parallelize the 3D viscous SV flow solver using domain decomposition and message passing. Optimize the cache performance of the flow solver by designing data structures minimizing data access times; 4. Demonstrate the SV method with a wide range of flow problems including both discontinuities and complex smooth structures. The objectives remain the same as those outlines in the original proposal. We anticipate no technical obstacles in meeting these objectives.

  4. Applying the expansion method in hierarchical functions to the solution of Navier-Stokes equations for incompressible fluids

    International Nuclear Information System (INIS)

    Sabundjian, Gaiane

    1999-01-01

    This work presents a novel numeric method, based on the finite element method, applied for the solution of the Navier-Stokes equations for incompressible fluids in two dimensions in laminar flow. The method is based on the expansion of the variables in almost hierarchical functions. The used expansion functions are based on Legendre polynomials, adjusted in the rectangular elements in a such a way that corner, side and area functions are defined. The order of the expansion functions associated with the sides and with the area of the elements can be adjusted to the necessary or desired degree. This novel numeric method is denominated by Hierarchical Expansion Method. In order to validate the proposed numeric method three well-known problems of the literature in two dimensions are analyzed. The results show the method capacity in supplying precise results. From the results obtained in this thesis it is possible to conclude that the hierarchical expansion method can be applied successfully for the solution of fluid dynamic problems that involve incompressible fluids. (author)

  5. Transient cavitating vortical flows around a hydrofoil using k-ω partially averaged Navier-Stokes model

    Science.gov (United States)

    Luo, Xianwu; Huang, Renfang; Ji, Bin

    2016-01-01

    For accurate simulations of wall-bounded turbulent cavitating flows, the present paper proposed a partially averaged Navier-Stokes (PANS) method derived from the k-ω turbulence model. Transient cavitating vortical flows around a NACA66 hydrofoil were simulated by using the k-ω PANS model with various filter parameters (fk = 0.2, 0.5 and 1, while fω = 1/fk) and a mass transfer cavitation model based on the Rayleigh-Plesset equation. Compared with the available experimental data, the k-ω PANS model with fk = 0.2 can accurately reproduce the cavitation evolution with more complicated structures due to the reduction in the predicted eddy viscosity. Further analyses, using the vorticity transport equation, indicate that the transition of cavitation structure from two dimension to three dimension is associated with strong vortex-cavitation interaction, where vortex stretching and dilation may play a major role. Therefore, the k-ω PANS model with the filter parameter of fk = 0.2 is an effective method to numerically predict the transient cavitating vortical flows around hydrofoils. The results obtained in this paper are helpful to provide a physical insight into the mechanisms of cavitation shedding dynamics.

  6. A well-posed and stable stochastic Galerkin formulation of the incompressible Navier-Stokes equations with random data

    Science.gov (United States)

    Pettersson, Per; Nordström, Jan; Doostan, Alireza

    2016-02-01

    We present a well-posed stochastic Galerkin formulation of the incompressible Navier-Stokes equations with uncertainty in model parameters or the initial and boundary conditions. The stochastic Galerkin method involves representation of the solution through generalized polynomial chaos expansion and projection of the governing equations onto stochastic basis functions, resulting in an extended system of equations. A relatively low-order generalized polynomial chaos expansion is sufficient to capture the stochastic solution for the problem considered. We derive boundary conditions for the continuous form of the stochastic Galerkin formulation of the velocity and pressure equations. The resulting problem formulation leads to an energy estimate for the divergence. With suitable boundary data on the pressure and velocity, the energy estimate implies zero divergence of the velocity field. Based on the analysis of the continuous equations, we present a semi-discretized system where the spatial derivatives are approximated using finite difference operators with a summation-by-parts property. With a suitable choice of dissipative boundary conditions imposed weakly through penalty terms, the semi-discrete scheme is shown to be stable. Numerical experiments in the laminar flow regime corroborate the theoretical results and we obtain high-order accurate results for the solution variables and the velocity divergence converges to zero as the mesh is refined.

  7. Numerical resolution of the Navier-Stokes equations for a low Mach number by a spectral method

    International Nuclear Information System (INIS)

    Frohlich, Jochen

    1990-01-01

    The low Mach number approximation of the Navier-Stokes equations, also called isobar, is an approximation which is less restrictive than the one due to Boussinesq. It permits strong density variations while neglecting acoustic phenomena. We present a numerical method to solve these equations in the unsteady, two dimensional case with one direction of periodicity. The discretization uses a semi-implicit finite difference scheme in time and a Fourier-Chebycheff pseudo-spectral method in space. The solution of the equations of motion is based on an iterative algorithm of Uzawa type. In the Boussinesq limit we obtain a direct method. A first application is concerned with natural convection in the Rayleigh-Benard setting. We compare the results of the low Mach number equations with the ones in the Boussinesq case and consider the influence of variable fluid properties. A linear stability analysis based on a Chebychev-Tau method completes the study. The second application that we treat is a case of isobaric combustion in an open domain. We communicate results for the hydrodynamic Darrieus-Landau instability of a plane laminar flame front. [fr

  8. A stable and high-order accurate discontinuous Galerkin based splitting method for the incompressible Navier-Stokes equations

    Science.gov (United States)

    Piatkowski, Marian; Müthing, Steffen; Bastian, Peter

    2018-03-01

    In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order rotational incremental pressure correction scheme. The major focus of the paper is threefold: i) We propose a modified upwind scheme based on the Vijayasundaram numerical flux that has favourable properties in the context of DG. ii) We present a novel postprocessing technique in the Helmholtz projection step based on H (div) reconstruction of the pressure correction that is computed locally, is a projection in the discrete setting and ensures that the projected velocity satisfies the discrete continuity equation exactly. As a consequence it also provides local mass conservation of the projected velocity. iii) Numerical results demonstrate the properties of the scheme for different polynomial degrees applied to two-dimensional problems with known solution as well as large-scale three-dimensional problems. In particular we address second-order convergence in time of the splitting scheme as well as its long-time stability.

  9. Electroosmotic flow in capillary channels filled with nonconstant viscosity electrolytes: exact solution of the Navier-Stokes equation.

    Science.gov (United States)

    Otevrel, Marek; Klepárník, Karel

    2002-10-01

    The partial differential equation describing unsteady velocity profile of electroosmotic flow (EOF) in a cylindrical capillary filled with a nonconstant viscosity electrolyte was derived. Analytical solution, based on the general Navier-Stokes equation, was found for constant viscosity electrolytes using the separation of variables (Fourier method). For the case of a nonconstant viscosity electrolyte, the steady-state velocity profile was calculated assuming that the viscosity decreases exponentially in the direction from the wall to the capillary center. Since the respective equations with nonconstant viscosity term are not solvable in general, the method of continuous binding conditions was used to solve this problem. In this method, an arbitrary viscosity profile can be modeled. The theoretical conclusions show that the relaxation times at which an EOF approaches the steady state are too short to have an impact on a separation process in any real systems. A viscous layer at the wall affects EOF significantly, if it is thicker than the Debye length of the electric double layer. The presented description of the EOF dynamics is applicable to any microfluidic systems.

  10. Navier-Stokes Computations of a Wing-Flap Model With Blowing Normal to the Flap Surface

    Science.gov (United States)

    Boyd, D. Douglas, Jr.

    2005-01-01

    A computational study of a generic wing with a half span flap shows the mean flow effects of several blown flap configurations. The effort compares and contrasts the thin-layer, Reynolds averaged, Navier-Stokes solutions of a baseline wing-flap configuration with configurations that have blowing normal to the flap surface through small slits near the flap side edge. Vorticity contours reveal a dual vortex structure at the flap side edge for all cases. The dual vortex merges into a single vortex at approximately the mid-flap chord location. Upper surface blowing reduces the strength of the merged vortex and moves the vortex away from the upper edge. Lower surface blowing thickens the lower shear layer and weakens the merged vortex, but not as much as upper surface blowing. Side surface blowing forces the lower surface vortex farther outboard of the flap edge by effectively increasing the aerodynamic span of the flap. It is seen that there is no global aerodynamic penalty or benefit from the particular blowing configurations examined.

  11. Analysis of wall shear stress around a competitive swimmer using 3D Navier-Stokes equations in CFD.

    Science.gov (United States)

    Popa, C V; Zaidi, H; Arfaoui, A; Polidori, G; Taiar, R; Fohanno, S

    2011-01-01

    This paper deals with the flow dynamics around a competitive swimmer during underwater glide phases occurring at the start and at every turn. The influence of the head position, namely lifted up, aligned and lowered, on the wall shear stress and the static pressure distributions is analyzed. The problem is considered as 3D and in steady hydrodynamic state. Three velocities (1.4 m/s, 2.2 m/s and 3.1 m/s) that correspond to inter-regional, national and international swimming levels are studied. The flow around the swimmer is assumed turbulent. The Reynolds-averaged Navier-Stokes (RANS) equations are solved with the standard k-ω turbulent model by using the CFD (computational fluid dynamics) numerical method based on a volume control approach. Numerical simulations are carried out with the ANSYS FLUENT® CFD code. The results show that the wall shear stress increases with the velocity and consequently the drag force opposing the movement of the swimmer increases as well. Also, high wall shear stresses are observed in the areas where the body shape, globally rigid in form, presents complex surface geometries such as the head, shoulders, buttocks, heel and chest.

  12. Parametric Study of Flow Control Over a Hump Model Using an Unsteady Reynolds- Averaged Navier-Stokes Code

    Science.gov (United States)

    Rumsey, Christopher L.; Greenblatt, David

    2007-01-01

    This is an expanded version of a limited-length paper that appeared at the 5th International Symposium on Turbulence and Shear Flow Phenomena by the same authors. A computational study was performed for steady and oscillatory flow control over a hump model with flow separation to assess how well the steady and unsteady Reynolds-averaged Navier-Stokes equations predict trends due to Reynolds number, control magnitude, and control frequency. As demonstrated in earlier studies, the hump model case is useful because it clearly demonstrates a failing in all known turbulence models: they under-predict the turbulent shear stress in the separated region and consequently reattachment occurs too far downstream. In spite of this known failing, three different turbulence models were employed to determine if trends can be captured even though absolute levels are not. Overall the three turbulence models showed very similar trends as experiment for steady suction, but only agreed qualitatively with some of the trends for oscillatory control.

  13. Improved mesh sequencing method for the accelerated solution of the compressible Euler and Navier-Stokes equations

    Science.gov (United States)

    Tsangaris, S.; Drikakis, D.

    The solution of the compressible Euler and Navier-Stokes equations via an upwind finite volume scheme is obtained. For the inviscid fluxes the monotone, upstream centered scheme for conservation laws (MUSCL) has been incorporated into a Riemann solver. The flux vector splitting method of Steger and Warming is used with some modifications. The MUSCL scheme is used for the unfactored implicit equations which are solved by a Newton form and relaxation is performed with a Gauss-Seidel technique. The solution on the fine grid is obtained by iterating first on a sequence of coarse grids and then interpolating the solution up to the next refined grid. Because the distribution of the numerical error is not uniform, the local solution of the equations in regions where the numerical error is large can be obtained. The choice of the partial meshes, in which the iterations will be continued, is determined by the use of an adaptive procedure taking into account some convergence criteria. Reduction of the iterations for the two-dimensional problem is obtained via the local adaptive mesh solution which is expected to be more effective in three-dimensional complex flow computations.

  14. Upscaling the Navier-Stokes Equation for Turbulent Flows in Porous Media Using a Volume Averaging Method

    Science.gov (United States)

    Wood, Brian; He, Xiaoliang; Apte, Sourabh

    2017-11-01

    Turbulent flows through porous media are encountered in a number of natural and engineered systems. Many attempts to close the Navier-Stokes equation for such type of flow have been made, for example using RANS models and double averaging. On the other hand, Whitaker (1996) applied volume averaging theorem to close the macroscopic N-S equation for low Re flow. In this work, the volume averaging theory is extended into the turbulent flow regime to posit a relationship between the macroscale velocities and the spatial velocity statistics in terms of the spatial averaged velocity only. Rather than developing a Reynolds stress model, we propose a simple algebraic closure, consistent with generalized effective viscosity models (Pope 1975), to represent the spatial fluctuating velocity and pressure respectively. The coefficients (one 1st order, two 2nd order and one 3rd order tensor) of the linear functions depend on averaged velocity and gradient. With the data set from DNS, performed with inertial and turbulent flows (pore Re of 300, 500 and 1000) through a periodic face centered cubic (FCC) unit cell, all the unknown coefficients can be computed and the closure is complete. The macroscopic quantity calculated from the averaging is then compared with DNS data to verify the upscaling. NSF Project Numbers 1336983, 1133363.

  15. N3S project of fluid mechanics. High order in time methods by operator splitting. Application to Navier-Stokes equations

    International Nuclear Information System (INIS)

    Boukir, K.

    1994-06-01

    This thesis deals with the extension to higher order in time of two splitting methods for the Navier-Stokes equations: the characteristics method and the projection one. The first consists in decoupling the convection operator from the Stokes one. The second decomposes this latter into a diffusion problem and a pressure-continuity one. Concerning the characteristics method, numerical and theoretical study is developed for the second order scheme together with a finite element spatial discretization. The case of a spectral spatial discretization is also treated and theoretical analysis are given respectively for second and third order schemes. For both spatial discretizations, we obtain good error estimates, unconditionally or under non stringent stability conditions, for both velocity and pressure. Numerical results illustrate the interest of the second order scheme comparing to the first order one. Extensions of the second order scheme to the K-epsilon turbulence model are proposed and tested, in the case of a finite element spatial discretization. Concerning the projection method, we define the order schemes. The theoretical study deals with stability and convergence of first and second order projection schemes, for the incompressible Navier-Stokes equations and with a finite element spatial discretization. The numerical study concerns mainly the second order scheme applied to the Navier-Stokes equations with varying density. (authors). 63 refs., figs

  16. The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations.

    Science.gov (United States)

    Thamareerat, N; Luadsong, A; Aschariyaphotha, N

    2016-01-01

    In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier-Stokes equations in two dimensions. We first employ the meshless local Petrov-Galerkin (MLPG) method based on a local weak formulation to form the system of discretized equations and then we will approximate the time fractional derivative interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging interpolation which possesses the Kronecker delta property is applied to construct shape functions. This research aims to extend and develop further the applicability of the truly MLPG method to the generalized incompressible Navier-Stokes equations. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed algorithm. Very good agreement between the numerically and analytically computed solutions can be observed in the verification. The present MLPG method has proved its efficiency and reliability for solving the two-dimensional time fractional Navier-Stokes equations arising in fluid dynamics as well as several other problems in science and engineering.

  17. Multilocality and fusion rules on the generalized structure functions in two-dimensional and three-dimensional Navier-Stokes turbulence.

    Science.gov (United States)

    Gkioulekas, Eleftherios

    2016-09-01

    Using the fusion-rules hypothesis for three-dimensional and two-dimensional Navier-Stokes turbulence, we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences. We call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator "multilocality." The resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry. Our main result is that the fusion-rules hypothesis implies both locality and multilocality in both the IR and UV limits for the downscale energy cascade of three-dimensional Navier-Stokes turbulence and the downscale enstrophy cascade and inverse energy cascade of two-dimensional Navier-Stokes turbulence. We stress that these claims relate to nonperturbative locality of generalized structure functions on all orders and not the term-by-term perturbative locality of diagrammatic theories or closure models that involve only two-point correlation and response functions.

  18. Retrospective cost adaptive Reynolds-averaged Navier-Stokes k-ω model for data-driven unsteady turbulent simulations

    Science.gov (United States)

    Li, Zhiyong; Hoagg, Jesse B.; Martin, Alexandre; Bailey, Sean C. C.

    2018-03-01

    This paper presents a data-driven computational model for simulating unsteady turbulent flows, where sparse measurement data is available. The model uses the retrospective cost adaptation (RCA) algorithm to automatically adjust the closure coefficients of the Reynolds-averaged Navier-Stokes (RANS) k- ω turbulence equations to improve agreement between the simulated flow and the measurements. The RCA-RANS k- ω model is verified for steady flow using a pipe-flow test case and for unsteady flow using a surface-mounted-cube test case. Measurements used for adaptation of the verification cases are obtained from baseline simulations with known closure coefficients. These verification test cases demonstrate that the RCA-RANS k- ω model can successfully adapt the closure coefficients to improve agreement between the simulated flow field and a set of sparse flow-field measurements. Furthermore, the RCA-RANS k- ω model improves agreement between the simulated flow and the baseline flow at locations at which measurements do not exist. The RCA-RANS k- ω model is also validated with experimental data from 2 test cases: steady pipe flow, and unsteady flow past a square cylinder. In both test cases, the adaptation improves agreement with experimental data in comparison to the results from a non-adaptive RANS k- ω model that uses the standard values of the k- ω closure coefficients. For the steady pipe flow, adaptation is driven by mean stream-wise velocity measurements at 24 locations along the pipe radius. The RCA-RANS k- ω model reduces the average velocity error at these locations by over 35%. For the unsteady flow over a square cylinder, adaptation is driven by time-varying surface pressure measurements at 2 locations on the square cylinder. The RCA-RANS k- ω model reduces the average surface-pressure error at these locations by 88.8%.

  19. Error Estimate of the Ares I Vehicle Longitudinal Aerodynamic Characteristics Based on Turbulent Navier-Stokes Analysis

    Science.gov (United States)

    Abdol-Hamid, Khaled S.; Ghaffari, Farhad

    2011-01-01

    Numerical predictions of the longitudinal aerodynamic characteristics for the Ares I class of vehicles, along with the associated error estimate derived from an iterative convergence grid refinement, are presented. Computational results are based on the unstructured grid, Reynolds-averaged Navier-Stokes flow solver USM3D, with an assumption that the flow is fully turbulent over the entire vehicle. This effort was designed to complement the prior computational activities conducted over the past five years in support of the Ares I Project with the emphasis on the vehicle s last design cycle designated as the A106 configuration. Due to a lack of flight data for this particular design s outer mold line, the initial vehicle s aerodynamic predictions and the associated error estimates were first assessed and validated against the available experimental data at representative wind tunnel flow conditions pertinent to the ascent phase of the trajectory without including any propulsion effects. Subsequently, the established procedures were then applied to obtain the longitudinal aerodynamic predictions at the selected flight flow conditions. Sample computed results and the correlations with the experimental measurements are presented. In addition, the present analysis includes the relevant data to highlight the balance between the prediction accuracy against the grid size and, thus, the corresponding computer resource requirements for the computations at both wind tunnel and flight flow conditions. NOTE: Some details have been removed from selected plots and figures in compliance with the sensitive but unclassified (SBU) restrictions. However, the content still conveys the merits of the technical approach and the relevant results.

  20. CCM Continuity Constraint Method: A finite-element computational fluid dynamics algorithm for incompressible Navier-Stokes fluid flows

    Energy Technology Data Exchange (ETDEWEB)

    Williams, P. T. [Univ. of Tennessee, Knoxville, TN (United States)

    1993-09-01

    As the field of computational fluid dynamics (CFD) continues to mature, algorithms are required to exploit the most recent advances in approximation theory, numerical mathematics, computing architectures, and hardware. Meeting this requirement is particularly challenging in incompressible fluid mechanics, where primitive-variable CFD formulations that are robust, while also accurate and efficient in three dimensions, remain an elusive goal. This dissertation asserts that one key to accomplishing this goal is recognition of the dual role assumed by the pressure, i.e., a mechanism for instantaneously enforcing conservation of mass and a force in the mechanical balance law for conservation of momentum. Proving this assertion has motivated the development of a new, primitive-variable, incompressible, CFD algorithm called the Continuity Constraint Method (CCM). The theoretical basis for the CCM consists of a finite-element spatial semi-discretization of a Galerkin weak statement, equal-order interpolation for all state-variables, a 0-implicit time-integration scheme, and a quasi-Newton iterative procedure extended by a Taylor Weak Statement (TWS) formulation for dispersion error control. Original contributions to algorithmic theory include: (a) formulation of the unsteady evolution of the divergence error, (b) investigation of the role of non-smoothness in the discretized continuity-constraint function, (c) development of a uniformly H1 Galerkin weak statement for the Reynolds-averaged Navier-Stokes pressure Poisson equation, (d) derivation of physically and numerically well-posed boundary conditions, and (e) investigation of sparse data structures and iterative methods for solving the matrix algebra statements generated by the algorithm.

  1. Weak solutions to the full Navier-Stokes-Fourier system with slip boundary conditions in time dependent domains

    Czech Academy of Sciences Publication Activity Database

    Kreml, Ondřej; Mácha, Václav; Nečasová, Šárka; Wróblewska-Kamińska, A.

    2018-01-01

    Roč. 109, January (2018), s. 67-92 ISSN 0021-7824 R&D Projects: GA ČR GA13-00522S; GA MŠk(CZ) 7AMB16PL060 Institutional support: RVO:67985840 Keywords : compressible Navier–Stokes–Fourier equations * time-varying domain * slip boundary conditions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.802, year: 2016 http://www. science direct.com/ science /article/pii/S0021782417301381?via%3Dihub

  2. Weak solutions to the full Navier-Stokes-Fourier system with slip boundary conditions in time dependent domains

    Czech Academy of Sciences Publication Activity Database

    Kreml, Ondřej; Mácha, Václav; Nečasová, Šárka; Wróblewska-Kamińska, A.

    2018-01-01

    Roč. 109, January (2018), s. 67-92 ISSN 0021-7824 R&D Projects: GA ČR GA13-00522S; GA MŠk(CZ) 7AMB16PL060 Institutional support: RVO:67985840 Keywords : compressible Navier–Stokes–Fourier equations * time-varying domain * slip boundary conditions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.802, year: 2016 http://www.sciencedirect.com/science/article/pii/S0021782417301381?via%3Dihub

  3. Navier-Stokes Equation and Computational Scheme for Non-Newtonian Debris Flow

    Directory of Open Access Journals (Sweden)

    Ignazio Licata

    2014-01-01

    Full Text Available This paper proposes a computational approach to debris flow model. In recent years, the theoretical activity on the classical Herschel-Bulkley model (1926 has been very intense, but it was in the early 80s that the opportunity to explore the computational model has enabled considerable progress in identifying the subclasses of applicability of different sets of boundary conditions and their approximations. Here we investigate analytically the problem of the simulation of uniform motion for heterogeneous debris flow laterally confined taking into account mainly the geological data and methodological suggestions derived from simulation with cellular automata and grid systems, in order to propose a computational scheme able to operate a compromise between “global” predictive capacities and computing effort.

  4. Ergodicity of Truncated Stochastic Navier Stokes with Deterministic Forcing and Dispersion

    Science.gov (United States)

    Majda, Andrew J.; Tong, Xin T.

    2016-10-01

    Turbulence in idealized geophysical flows is a very rich and important topic. The anisotropic effects of explicit deterministic forcing, dispersive effects from rotation due to the β -plane and F-plane, and topography together with random forcing all combine to produce a remarkable number of realistic phenomena. These effects have been studied through careful numerical experiments in the truncated geophysical models. These important results include transitions between coherent jets and vortices, and direct and inverse turbulence cascades as parameters are varied, and it is a contemporary challenge to explain these diverse statistical predictions. Here we contribute to these issues by proving with full mathematical rigor that for any values of the deterministic forcing, the β - and F-plane effects and topography, with minimal stochastic forcing, there is geometric ergodicity for any finite Galerkin truncation. This means that there is a unique smooth invariant measure which attracts all statistical initial data at an exponential rate. In particular, this rigorous statistical theory guarantees that there are no bifurcations to multiple stable and unstable statistical steady states as geophysical parameters are varied in contrast to claims in the applied literature. The proof utilizes a new statistical Lyapunov function to account for enstrophy exchanges between the statistical mean and the variance fluctuations due to the deterministic forcing. It also requires careful proofs of hypoellipticity with geophysical effects and uses geometric control theory to establish reachability. To illustrate the necessity of these conditions, a two-dimensional example is developed which has the square of the Euclidean norm as the Lyapunov function and is hypoelliptic with nonzero noise forcing, yet fails to be reachable or ergodic.

  5. Stabilization of the solution of a two-dimensional system of Navier-Stokes equations in an unbounded domain with several exits to infinity

    International Nuclear Information System (INIS)

    Khisamutdinova, N A

    2003-01-01

    The behaviour as t→∞ of the solution of the mixed problem for the system of Navier-Stokes equations with a Dirichlet condition at the boundary is studied in an unbounded two-dimensional domain with several exits to infinity. A class of domains is distinguished in which an estimate characterizing the decay of solutions in terms of the geometry of the domain is proved for exponentially decreasing initial velocities. A similar estimate of the solution of the first mixed problem for the heat equation is sharp in a broad class of domains with several exits to infinity

  6. Well-posed two-temperature constitutive equations for stable dense fluid shock waves using molecular dynamics and generalizations of Navier-Stokes-Fourier continuum mechanics.

    Science.gov (United States)

    Hoover, Wm G; Hoover, Carol G

    2010-04-01

    Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.

  7. Stabilizing a solution of the 2D Navier-Stokes system in the exterior of a bounded domain by means of a control on the boundary

    International Nuclear Information System (INIS)

    Gorshkov, Aleksei V

    2012-01-01

    The problem of stabilizing a solution of the 2D Navier-Stokes system defined in the exterior of a bounded domain with smooth boundary is investigated. For a given initial velocity field a control on the boundary of the domain must be constructed such that the solution stabilizes to a prescribed vortex solution or trivial solution at the rate of 1/t k . On the way, related questions are investigated, concerning the behaviour of the spectrum of an operator under a relatively compact perturbation and the existence of attracting invariant manifolds. Bibliography: 21 titles.

  8. Global existence of strong solutions to the three- dimensional incompressible Navier-Stokes equations with special boundary conditions

    Science.gov (United States)

    Riley, Douglas A.

    We study the three-dimensional incompressible Navier- Stokes equations in a domain of the form W'×(0,e) . First, we assume W' is a C3 bounded domain and impose no-slip boundary conditions on 6W'×(0,e ) , and periodic conditions on W'×0,e . Physically, this models fluid flow through a pipe with cross-section W' where the inlet and outlet conditions are assumed periodic. Secondly, we assume W'=(0,l4) ×(0,l5) and impose periodic boundary conditions. This problem is of interest mathematically, and has been more widely considered than the pipe flow problem. For both sets of boundary conditions, we show that a strong solution exists for all time with conditions on the initial data and forcing. We start by recalling that if the forcing function and initial condition do not depend on x3, then a global strong solution exists which also does not depend on x3. Here (x1,x2,x3) ∈W≡W'×( 0,e) . With this observation as motivation, and using an additive decomposition introduced by Raugel and Sell, we split the initial data and forcing into a portion independent of x3 and a remainder. In our first result, we impose a smallness condition on the remainder and assume the forcing function is square- integrable in time as a function into L2(W) . With these assumptions, we prove a global existence theorem that does not require a smallness condition on e or on the portion of the initial condition and forcing independent of x3. However, these quantities do affect the allowable size of the remainder. For our second result, we assume the forcing is only bounded in time as a function into L2(W) . In this case, we need a smallness condition on the initial data, the forcing, and e to obtain global existence. The interesting observation is that the allowable sizes for the initial data and forcing grow as e-->0 . Thus, we obtain a `thin-domain' result as originally obtained by Raugel and Sell. In fact, our results allow the portion of the initial data and forcing independent of x3 to

  9. N3S project of fluid mechanics. High order in time methods by operator splitting. Application to Navier-Stokes equations; Projet N3S. Methode en temps d`ordre eleve par decomposition d`operateurs. Application aux equations de Navier-Stokes

    Energy Technology Data Exchange (ETDEWEB)

    Boukir, K.

    1994-06-01

    This thesis deals with the extension to higher order in time of two splitting methods for the Navier-Stokes equations: the characteristics method and the projection one. The first consists in decoupling the convection operator from the Stokes one. The second decomposes this latter into a diffusion problem and a pressure-continuity one. Concerning the characteristics method, numerical and theoretical study is developed for the second order scheme together with a finite element spatial discretization. The case of a spectral spatial discretization is also treated and theoretical analysis are given respectively for second and third order schemes. For both spatial discretizations, we obtain good error estimates, unconditionally or under non stringent stability conditions, for both velocity and pressure. Numerical results illustrate the interest of the second order scheme comparing to the first order one. Extensions of the second order scheme to the K-epsilon turbulence model are proposed and tested, in the case of a finite element spatial discretization. Concerning the projection method, we define the order schemes. The theoretical study deals with stability and convergence of first and second order projection schemes, for the incompressible Navier-Stokes equations and with a finite element spatial discretization. The numerical study concerns mainly the second order scheme applied to the Navier-Stokes equations with varying density. (authors). 63 refs., figs.

  10. Large time periodic solutions to coupled chemotaxis-fluid models

    Science.gov (United States)

    Jin, Chunhua

    2017-12-01

    In this paper, we deal with the time periodic problem to coupled chemotaxis-fluid models. We prove the existence of large time periodic strong solutions for the full chemotaxis-Navier-Stokes system in spatial dimension N=2, and the existence of large time periodic strong solutions for the chemotaxis-Stokes system in spatial dimension N=3. On the basis of these, the regularity of the solutions can be further improved. More precisely speaking, if the time periodic source g and the potential force \

  11. A Newton-Krylov method with approximate Jacobian for implicit solution of Navier-Stokes on staggered overset-curvilinear grids with immersed boundaries

    Science.gov (United States)

    Asgharzadeh, Hafez; Borazjani, Iman

    2014-11-01

    Time step-size restrictions and low convergence rates are major bottle necks for implicit solution of the Navier-Stokes in simulations involving complex geometries with moving boundaries. Newton-Krylov method (NKM) is a combination of a Newton-type method for super-linearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations, which can theoretically address both bottle necks. The efficiency of this method vastly depends on the Jacobian forming scheme e.g. automatic differentiation is very expensive and Jacobian-free methods slow down as the mesh is refined. A novel, computationally efficient analytical Jacobian for NKM was developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered curvilinear grids with immersed boundaries. The NKM was validated and verified against Taylor-Green vortex and pulsatile flow in a 90 degree bend and efficiently handles complex geometries such as an intracranial aneurysm with multiple overset grids, pulsatile inlet flow and immersed boundaries. The NKM method is shown to be more efficient than the semi-implicit Runge-Kutta methods and Jabobian-free Newton-Krylov methods. We believe NKM can be applied to many CFD techniques to decrease the computational cost. This work was supported partly by the NIH Grant R03EB014860, and the computational resources were partly provided by Center for Computational Research (CCR) at University at Buffalo.

  12. New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

    Science.gov (United States)

    Chang, Sin-Chung

    1993-01-01

    A new numerical framework for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods--i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

  13. A Study on GPU Computing of Bi-conjugate Gradient Method for Finite Element Analysis of the Incompressible Navier-Stokes Equations

    International Nuclear Information System (INIS)

    Yoon, Jong Seon; Choi, Hyoung Gwon; Jeon, Byoung Jin; Jung, Hye Dong

    2016-01-01

    A parallel algorithm of bi-conjugate gradient method was developed based on CUDA for parallel computation of the incompressible Navier-Stokes equations. The governing equations were discretized using splitting P2P1 finite element method. Asymmetric stenotic flow problem was solved to validate the proposed algorithm, and then the parallel performance of the GPU was examined by measuring the elapsed times. Further, the GPU performance for sparse matrix-vector multiplication was also investigated with a matrix of fluid-structure interaction problem. A kernel was generated to simultaneously compute the inner product of each row of sparse matrix and a vector. In addition, the kernel was optimized to improve the performance by using both parallel reduction and memory coalescing. In the kernel construction, the effect of warp on the parallel performance of the present CUDA was also examined. The present GPU computation was more than 7 times faster than the single CPU by double precision.

  14. A systematic comparison of two-equation Reynolds-averaged Navier-Stokes turbulence models applied to shock-cloud interactions

    Science.gov (United States)

    Goodson, Matthew D.; Heitsch, Fabian; Eklund, Karl; Williams, Virginia A.

    2017-07-01

    Turbulence models attempt to account for unresolved dynamics and diffusion in hydrodynamical simulations. We develop a common framework for two-equation Reynolds-averaged Navier-Stokes turbulence models, and we implement six models in the athena code. We verify each implementation with the standard subsonic mixing layer, although the level of agreement depends on the definition of the mixing layer width. We then test the validity of each model into the supersonic regime, showing that compressibility corrections can improve agreement with experiment. For models with buoyancy effects, we also verify our implementation via the growth of the Rayleigh-Taylor instability in a stratified medium. The models are then applied to the ubiquitous astrophysical shock-cloud interaction in three dimensions. We focus on the mixing of shock and cloud material, comparing results from turbulence models to high-resolution simulations (up to 200 cells per cloud radius) and ensemble-averaged simulations. We find that the turbulence models lead to increased spreading and mixing of the cloud, although no two models predict the same result. Increased mixing is also observed in inviscid simulations at resolutions greater than 100 cells per radius, which suggests that the turbulent mixing begins to be resolved.

  15. From model conception to verification and validation, a global approach to multiphase Navier-Stoke models with an emphasis on volcanic explosive phenomenology

    Energy Technology Data Exchange (ETDEWEB)

    Dartevelle, Sebastian

    2007-10-01

    Large-scale volcanic eruptions are hazardous events that cannot be described by detailed and accurate in situ measurement: hence, little to no real-time data exists to rigorously validate current computer models of these events. In addition, such phenomenology involves highly complex, nonlinear, and unsteady physical behaviors upon many spatial and time scales. As a result, volcanic explosive phenomenology is poorly understood in terms of its physics, and inadequately constrained in terms of initial, boundary, and inflow conditions. Nevertheless, code verification and validation become even more critical because more and more volcanologists use numerical data for assessment and mitigation of volcanic hazards. In this report, we evaluate the process of model and code development in the context of geophysical multiphase flows. We describe: (1) the conception of a theoretical, multiphase, Navier-Stokes model, (2) its implementation into a numerical code, (3) the verification of the code, and (4) the validation of such a model within the context of turbulent and underexpanded jet physics. Within the validation framework, we suggest focusing on the key physics that control the volcanic clouds—namely, momentum-driven supersonic jet and buoyancy-driven turbulent plume. For instance, we propose to compare numerical results against a set of simple and well-constrained analog experiments, which uniquely and unambiguously represent each of the key-phenomenology. Key

  16. Large Eddy Simulation and Reynolds-Averaged Navier-Stokes modeling of flow in a realistic pharyngeal airway model: an investigation of obstructive sleep apnea.

    Science.gov (United States)

    Mihaescu, Mihai; Murugappan, Shanmugam; Kalra, Maninder; Khosla, Sid; Gutmark, Ephraim

    2008-07-19

    Computational fluid dynamics techniques employing primarily steady Reynolds-Averaged Navier-Stokes (RANS) methodology have been recently used to characterize the transitional/turbulent flow field in human airways. The use of RANS implies that flow phenomena are averaged over time, the flow dynamics not being captured. Further, RANS uses two-equation turbulence models that are not adequate for predicting anisotropic flows, flows with high streamline curvature, or flows where separation occurs. A more accurate approach for such flow situations that occur in the human airway is Large Eddy Simulation (LES). The paper considers flow modeling in a pharyngeal airway model reconstructed from cross-sectional magnetic resonance scans of a patient with obstructive sleep apnea. The airway model is characterized by a maximum narrowing at the site of retropalatal pharynx. Two flow-modeling strategies are employed: steady RANS and the LES approach. In the RANS modeling framework both k-epsilon and k-omega turbulence models are used. The paper discusses the differences between the airflow characteristics obtained from the RANS and LES calculations. The largest discrepancies were found in the axial velocity distributions downstream of the minimum cross-sectional area. This region is characterized by flow separation and large radial velocity gradients across the developed shear layers. The largest difference in static pressure distributions on the airway walls was found between the LES and the k-epsilon data at the site of maximum narrowing in the retropalatal pharynx.

  17. Lattice Boltzmann scheme for mixture modeling: analysis of the continuum diffusion regimes recovering Maxwell-Stefan model and incompressible Navier-Stokes equations.

    Science.gov (United States)

    Asinari, Pietro

    2009-11-01

    A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.

  18. On Parametric Sensitivity of Reynolds-Averaged Navier-Stokes SST Turbulence Model: 2D Hypersonic Shock-Wave Boundary Layer Interactions

    Science.gov (United States)

    Brown, James L.

    2014-01-01

    Examined is sensitivity of separation extent, wall pressure and heating to variation of primary input flow parameters, such as Mach and Reynolds numbers and shock strength, for 2D and Axisymmetric Hypersonic Shock Wave Turbulent Boundary Layer interactions obtained by Navier-Stokes methods using the SST turbulence model. Baseline parametric sensitivity response is provided in part by comparison with vetted experiments, and in part through updated correlations based on free interaction theory concepts. A recent database compilation of hypersonic 2D shock-wave/turbulent boundary layer experiments extensively used in a prior related uncertainty analysis provides the foundation for this updated correlation approach, as well as for more conventional validation. The primary CFD method for this work is DPLR, one of NASA's real-gas aerothermodynamic production RANS codes. Comparisons are also made with CFL3D, one of NASA's mature perfect-gas RANS codes. Deficiencies in predicted separation response of RANS/SST solutions to parametric variations of test conditions are summarized, along with recommendations as to future turbulence approach.

  19. A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid

    International Nuclear Information System (INIS)

    Kirkpatrick, M.P.; Armfield, S.W.; Kent, J.H.

    2003-01-01

    A method is presented for representing curved boundaries for the solution of the Navier-Stokes equations on a non-uniform, staggered, three-dimensional Cartesian grid. The approach involves truncating the Cartesian cells at the boundary surface to create new cells which conform to the shape of the surface. We discuss in some detail the problems unique to the development of a cut cell method on a staggered grid. Methods for calculating the fluxes through the boundary cell faces, for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second-order accuracy in space. In addition, a novel 'cell-linking' method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell-merging approaches. Techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces. The new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at Re=40 and is shown to give significant improvement over a staircase boundary formulation. Finally, it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a Reynolds number of 800. Good agreement is obtained with experimental results for this flow

  20. Decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio.

    Science.gov (United States)

    Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan

    2016-10-01

    A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.

  1. Can a numerically stable subgrid-scale model for turbulent flow computation be ideally accurate?: a preliminary theoretical study for the Gaussian filtered Navier-Stokes equations.

    Science.gov (United States)

    Ida, Masato; Taniguchi, Nobuyuki

    2003-09-01

    This paper introduces a candidate for the origin of the numerical instabilities in large eddy simulation repeatedly observed in academic and practical industrial flow computations. Without resorting to any subgrid-scale modeling, but based on a simple assumption regarding the streamwise component of flow velocity, it is shown theoretically that in a channel-flow computation, the application of the Gaussian filtering to the incompressible Navier-Stokes equations yields a numerically unstable term, a cross-derivative term, which is similar to one appearing in the Gaussian filtered Vlasov equation derived by Klimas [J. Comput. Phys. 68, 202 (1987)] and also to one derived recently by Kobayashi and Shimomura [Phys. Fluids 15, L29 (2003)] from the tensor-diffusivity subgrid-scale term in a dynamic mixed model. The present result predicts that not only the numerical methods and the subgrid-scale models employed but also only the applied filtering process can be a seed of this numerical instability. An investigation concerning the relationship between the turbulent energy scattering and the unstable term shows that the instability of the term does not necessarily represent the backscatter of kinetic energy which has been considered a possible origin of numerical instabilities in large eddy simulation. The present findings raise the question whether a numerically stable subgrid-scale model can be ideally accurate.

  2. A hybridized discontinuous Galerkin framework for high-order particle-mesh operator splitting of the incompressible Navier-Stokes equations

    Science.gov (United States)

    Maljaars, Jakob M.; Labeur, Robert Jan; Möller, Matthias

    2018-04-01

    A generic particle-mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier-Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an advection operator, and an Eulerian mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to formulate the projections between the Lagrangian particle space and the Eulerian finite element space in terms of local (i.e. cellwise) ℓ2-projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder.

  3. Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: effects of strong compressibility and large-scale anisotropy.

    Science.gov (United States)

    Antonov, N V; Kostenko, M M

    2014-12-01

    The field theoretic renormalization group and the operator product expansion are applied to two models of passive scalar quantities (the density and the tracer fields) advected by a random turbulent velocity field. The latter is governed by the Navier-Stokes equation for compressible fluid, subject to external random force with the covariance ∝δ(t-t')k(4-d-y), where d is the dimension of space and y is an arbitrary exponent. The original stochastic problems are reformulated as multiplicatively renormalizable field theoretic models; the corresponding renormalization group equations possess infrared attractive fixed points. It is shown that various correlation functions of the scalar field, its powers and gradients, demonstrate anomalous scaling behavior in the inertial-convective range already for small values of y. The corresponding anomalous exponents, identified with scaling (critical) dimensions of certain composite fields ("operators" in the quantum-field terminology), can be systematically calculated as series in y. The practical calculation is performed in the leading one-loop approximation, including exponents in anisotropic contributions. It should be emphasized that, in contrast to Gaussian ensembles with finite correlation time, the model and the perturbation theory presented here are manifestly Galilean covariant. The validity of the one-loop approximation and comparison with Gaussian models are briefly discussed.

  4. Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

    Science.gov (United States)

    Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

    2014-07-01

    In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

  5. Artificial dissipation models applied to Navier-Stokes equations for analysis of supersonic flow of helium gas around a geometric configuration ramp type

    Energy Technology Data Exchange (ETDEWEB)

    Rocha, Jussie Soares da, E-mail: jussie.soares@ifpi.edu.br [Instituto Federal de Educacao, Ciencia e Tecnologia do Piaui (IFPI), Valenca, PI (Brazil); Maciel, Edisson Savio de G., E-mail: edissonsavio@yahoo.com.br [Instituto Tecnologico de Aeronautica (ITA), Sao Paulo, SP (Brazil); Lira, Carlos A.B. de O., E-mail: cabol@ufpe.edu.br [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil)

    2015-07-01

    Very High Temperature Gas Cooled Reactors - VHTGRs are studied by several research groups for the development of advanced reactors that can meet the world's growing energy demand. The analysis of the flow of helium coolant around the various geometries at the core of these reactors through computational fluid dynamics techniques is an essential tool in the development of conceptual designs of nuclear power plants that provide added safety. This analysis suggests a close analogy with aeronautical cases widely studied using computational numerical techniques to solve systems of governing equations for the flow involved. The present work consists in solving the Navier-Stokes equations in a conservative form, in two-dimensional space employing a finite difference formulation for spatial discretization using the Euler method for explicit marching in time. The physical problem of supersonic laminar flow of helium gas along a ramp configuration is considered. For this, the Jameson and Mavriplis algorithm and the artificial dissipations models linear and nonlinear of Pulliam was implemented. A spatially variable time step is employed aiming to accelerate the convergence to the steady state solution. The main purpose of this work is to study the cited dissipation models and describe their characteristics in relation to the overall quality of the solution, aiming preliminary results for the development of computational tools of dynamic analysis of helium flow for the VHTGR core. (author)

  6. Cell-Averaged discretization for incompressible Navier-Stokes with embedded boundaries and locally refined Cartesian meshes: a high-order finite volume approach

    Science.gov (United States)

    Bhalla, Amneet Pal Singh; Johansen, Hans; Graves, Dan; Martin, Dan; Colella, Phillip; Applied Numerical Algorithms Group Team

    2017-11-01

    We present a consistent cell-averaged discretization for incompressible Navier-Stokes equations on complex domains using embedded boundaries. The embedded boundary is allowed to freely cut the locally-refined background Cartesian grid. Implicit-function representation is used for the embedded boundary, which allows us to convert the required geometric moments in the Taylor series expansion (upto arbitrary order) of polynomials into an algebraic problem in lower dimensions. The computed geometric moments are then used to construct stencils for various operators like the Laplacian, divergence, gradient, etc., by solving a least-squares system locally. We also construct the inter-level data-transfer operators like prolongation and restriction for multi grid solvers using the same least-squares system approach. This allows us to retain high-order of accuracy near coarse-fine interface and near embedded boundaries. Canonical problems like Taylor-Green vortex flow and flow past bluff bodies will be presented to demonstrate the proposed method. U.S. Department of Energy, Office of Science, ASCR (Award Number DE-AC02-05CH11231).

  7. Investigating dynamic stall, 3-D and rotational effects on wind turbine blades by means of an unsteady quasi-3D Navier-Stokes solver

    Energy Technology Data Exchange (ETDEWEB)

    Chaviaropoulos, P.K. [CRES-Center for Renewable Energy Sources, Pikermi Attiki (Greece)

    1997-08-01

    The blade element codes provide surprisingly accurate predictions of the aerodynamic loads provided that they are `fed` with proper lift and drag - incidence curves for the profiles mounted on the rotor blades. The evident question is how one can obtain such data. It is common experience that the use of the mostly available steady two-dimensional profile data may lead to serious discrepancies between measured and simulated loads. Although several correction techniques have been proposed as a remedy during the last years, from simplified dynamic stall models suitably tuned for wind turbines to 3-D correction schemes for profile data, the problem is by no means over-passed. Especially for the three-dimensional effects it seems that part of the difficulty is due to our limited understanding of the physical mechanism which is responsible for the extra loading of the inner part of the blades. Recognizing the importance of the above aspects two relevant Joule projects have been launched, the concluded `Dynamic Stall and 3-D Effects` JOU2-CT93-0345 and the ongoing `VISCWIND` JOR3-CT95-0007 project. Part of the activities in the first and all the activities in the second project are devoted to the identification and quantification of the dynamic stall and three-dimensional effects experienced by the wind turbine blades using Navier-Stokes computations. The contribution of CRES in these two projects is briefly presented in this paper. (EG)

  8. Progress on Multicomponent Reynolds-Averaged Navier-Stokes Model Development and Validation for Rayleigh-Taylor and Reshocked Richtmyer-Meshkov Turbulent Mixing

    Science.gov (United States)

    Schilling, Oleg

    2014-11-01

    Recent progress on the development and validation of a new K- ɛ multicomponent Reynolds-averaged Navier-Stokes model is discussed. The model includes mixture molecular dissipation and diffusion terms, molecular and turbulent enthalpy diffusion terms, and models for pressure-dilatation and dilatation dissipation. The model has successfully been applied to a set of ten reshocked Richtmyer-Meshkov mixing experiments, and more recently to experiments with larger Mach numbers and various Atwood numbers. An extension of the model to include a modeled density variance transport equation is described. The three-equation model is applied to various Rayleigh-Taylor mixing cases with complex accelerations. The evolution of various turbulence statistics, fields, and turbulent transport equation budgets are compared among these cases to elucidate differences in the turbulence production, dissipation and diffusion mechanisms. It is also shown that the mechanical turbulence timescale is poorly correlated with the molecular mixing timescale determined by the time-evolution of the molecular mixing parameter. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  9. Three-Dimensional Navier-Stokes Simulations with Two-Equation Turbulence Models of Intersecting Shock-Waves/Turbulent Boundary Layer at Mach 8.3

    Science.gov (United States)

    Bardina, J. E.; Coakley, T. J.

    1994-01-01

    An investigation of the numerical simulation with two-equation turbulence models of a three-dimensional hypersonic intersecting (SWTBL) shock-wave/turbulent boundary layer interaction flow is presented. The flows are solved with an efficient implicit upwind flux-difference split Reynolds-averaged Navier-Stokes code. Numerical results are compared with experimental data for a flow at Mach 8.28 and Reynolds number 5.3x10(exp 6) with crossing shock-waves and expansion fans generated by two lateral 15 fins located on top of a cold-wall plate. This experiment belongs to the hypersonic database for modeling validation. Simulations show the development of two primary counter-rotating cross-flow vortices and secondary turbulent structures under the main vortices and in each corner singularity inside the turbulent boundary layer. A significant loss of total pressure is produced by the complex interaction between the main vortices and the uplifted jet stream of the boundary layer. The overall agreement between computational and experimental data is generally good. The turbulence modeling corrections show improvements in the predictions of surface heat transfer distribution and an increase in the strength of the cross-flow vortices. Accurate predictions of the outflow flowfield is found to require accurate modeling of the laminar/turbulent boundary layers on the fin walls.

  10. 3D analysis of Navier-Stokes in steady state of the behavior of the flow in the Inter stage 1 of a gas turbine Frame 7; Analisis de navier-stokes tridimensional en estado estable del comportamiento del flujo en la inter etapa 1 de una turbina de gas frame 7

    Energy Technology Data Exchange (ETDEWEB)

    Henandez Rosete, Alejandro; Mazur C, Zdzislaw [Instituto de Investigaciones Electricas, Cuernavaca, Morelos (Mexico)

    2007-11-15

    The results of the simulation by CFD (Computacional Fluid Dynamics) realized to the first stage of a gas turbine GE Frame 7 are presented. The analysis includes the 3D modeling of the flow channel in the nozzle and the movable blade to know the velocities distributions, temperatures and pressures of the main hot gas flow that are developed in the Inter stage. The results are influenced by the imposed border conditions in the properties of the main flow, the rotation of the movable blade, as well as the simulation of cooling air injection in the nozzle. The present study focuses in the validation of the model of the meshes of the ensemble nozzle-blade, for later realize an analysis of conjugated heat transfer in a model with ceramic lining type heat barrier (THB) in the movable blade. The analysis is realized in a CFD commercial code oriented to turbo-machinery using the equations of unstable flows 3D of Navier Stokes. [Spanish] Se presentan los resultados de la simulacion por CFD (Computacional Fluid Dynamics) realizada a la primera etapa de una turbina de gas GE Frame 7. El analisis incluye la modelacion tridimensional del canal de flujo en la tobera y el alabe movil para conocer las distribuciones de las velocidades, temperaturas y presiones del flujo principal de gases calientes que se desarrollan en la inter etapa. Los resultados son influenciados por las condiciones de frontera impuestos en las propiedades del flujo principal, la rotacion del alabe movil, asi como la simulacion de inyeccion de aire de enfriamiento en la tobera. El presente estudio se enfoca en la validacion del modelo de la malla del conjunto tobera-alabe, para posteriormente realizar un analisis de transferencia de calor conjugada en un modelo con recubrimiento ceramico tipo barrera termica (TBC) en el alabe movil. El analisis es realizado en un codigo de CFD comercial orientado a turbomaquinaria utilizando las ecuaciones de flujos inestables 3D de Navier Stokes.

  11. 2-D left ventricular flow estimation by combining speckle tracking with Navier-Stokes-based regularization: an in silico, in vitro and in vivo study.

    Science.gov (United States)

    Gao, Hang; Bijnens, Nathalie; Coisne, Damien; Lugiez, Mathieu; Rutten, Marcel; D'hooge, Jan

    2015-01-01

    Despite the availability of multiple ultrasound approaches to left ventricular (LV) flow characterization in two dimensions, this technique remains in its childhood and further developments seem warranted. This article describes a new methodology for tracking the 2-D LV flow field based on ultrasound data. Hereto, a standard speckle tracking algorithm was modified by using a dynamic kernel embedding Navier-Stokes-based regularization in an iterative manner. The performance of the proposed approach was first quantified in synthetic ultrasound data based on a computational fluid dynamics model of LV flow. Next, an experimental flow phantom setup mimicking the normal human heart was used for experimental validation by employing simultaneous optical particle image velocimetry as a standard reference technique. Finally, the applicability of the approach was tested in a clinical setting. On the basis of the simulated data, pointwise evaluation of the estimated velocity vectors correlated well (mean r = 0.84) with the computational fluid dynamics measurement. During the filling period of the left ventricle, the properties of the main vortex obtained from the proposed method were also measured, and their correlations with the reference measurement were also calculated (radius, r = 0.96; circulation, r = 0.85; weighted center, r = 0.81). In vitro results at 60 bpm during one cardiac cycle confirmed that the algorithm properly measures typical characteristics of the vortex (radius, r = 0.60; circulation, r = 0.81; weighted center, r = 0.92). Preliminary qualitative results on clinical data revealed physiologic flow fields. Copyright © 2015 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

  12. Application of the FUN3D Unstructured-Grid Navier-Stokes Solver to the 4th AIAA Drag Prediction Workshop Cases

    Science.gov (United States)

    Lee-Rausch, Elizabeth M.; Hammond, Dana P.; Nielsen, Eric J.; Pirzadeh, S. Z.; Rumsey, Christopher L.

    2010-01-01

    FUN3D Navier-Stokes solutions were computed for the 4th AIAA Drag Prediction Workshop grid convergence study, downwash study, and Reynolds number study on a set of node-based mixed-element grids. All of the baseline tetrahedral grids were generated with the VGRID (developmental) advancing-layer and advancing-front grid generation software package following the gridding guidelines developed for the workshop. With maximum grid sizes exceeding 100 million nodes, the grid convergence study was particularly challenging for the node-based unstructured grid generators and flow solvers. At the time of the workshop, the super-fine grid with 105 million nodes and 600 million elements was the largest grid known to have been generated using VGRID. FUN3D Version 11.0 has a completely new pre- and post-processing paradigm that has been incorporated directly into the solver and functions entirely in a parallel, distributed memory environment. This feature allowed for practical pre-processing and solution times on the largest unstructured-grid size requested for the workshop. For the constant-lift grid convergence case, the convergence of total drag is approximately second-order on the finest three grids. The variation in total drag between the finest two grids is only 2 counts. At the finest grid levels, only small variations in wing and tail pressure distributions are seen with grid refinement. Similarly, a small wing side-of-body separation also shows little variation at the finest grid levels. Overall, the FUN3D results compare well with the structured-grid code CFL3D. The FUN3D downwash study and Reynolds number study results compare well with the range of results shown in the workshop presentations.

  13. Comparative Analysis of Natural Convection Flows Simulated by both the Conservation and Incompressible Forms of the Navier-Stokes Equations in a Differentially-Heated Square Cavity

    Energy Technology Data Exchange (ETDEWEB)

    Richard C. Martineau; Ray A. Berry; Aurélia Esteve; Kurt D. Hamman; Dana A. Knoll; Ryosuke Park; William Taitano

    2009-01-01

    This report illustrates a comparative study to analyze the physical differences between numerical simulations obtained with both the conservation and incompressible forms of the Navier-Stokes equations for natural convection flows in simple geometries. The purpose of this study is to quantify how the incompressible flow assumption (which is based upon constant density advection, divergence-free flow, and the Boussinesq gravitational body force approximation) differs from the conservation form (which only assumes that the fluid is a continuum) when solving flows driven by gravity acting upon density variations resulting from local temperature gradients. Driving this study is the common use of the incompressible flow assumption in fluid flow simulations for nuclear power applications in natural convection flows subjected to a high heat flux (large temperature differences). A series of simulations were conducted on two-dimensional, differentially-heated rectangular geometries and modeled with both hydrodynamic formulations. From these simulations, the selected characterization parameters of maximum Nusselt number, average Nusselt number, and normalized pressure reduction were calculated. Comparisons of these parameters were made with available benchmark solutions for air with the ideal gas assumption at both low and high heat fluxes. Additionally, we generated body force, velocity, and divergence of velocity distributions to provide a basis for further analysis. The simulations and analysis were then extended to include helium at the Very High Temperature gas-cooled Reactor (VHTR) normal operating conditions. Our results show that the consequences of incorporating the incompressible flow assumption in high heat flux situations may lead to unrepresentative results. The results question the use of the incompressible flow assumption for simulating fluid flow in an operating nuclear reactor, where large temperature variations are present. The results show that the use of

  14. Multiscale Modeling of Blood Flow: Coupling Finite Elements with Smoothed Dissipative Particle Dynamics

    KAUST Repository

    Moreno Chaparro, Nicolas

    2013-06-01

    A variational multi scale approach to model blood flow through arteries is proposed. A finite element discretization to represent the coarse scales (macro size), is coupled to smoothed dissipative particle dynamics that captures the fine scale features (micro scale). Blood is assumed to be incompressible, and flow is described through the Navier Stokes equation. The proposed cou- pling is tested with two benchmark problems, in fully coupled systems. Further refinements of the model can be incorporated in order to explicitly include blood constituents and non-Newtonian behavior. The suggested algorithm can be used with any particle-based method able to solve the Navier-Stokes equation.

  15. A numerical method for a model of two-phase flow in a coupled free flow and porous media system

    KAUST Repository

    Chen, Jie

    2014-07-01

    In this article, we study two-phase fluid flow in coupled free flow and porous media regions. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the porous medium region. We propose a Robin-Robin domain decomposition method for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Numerical examples are presented to illustrate the effectiveness of this method. © 2014 Elsevier Inc.

  16. Eulerian derivation of non-inertial Navier-Stokes equations for compressible flow in constant, pure rotation

    CSIR Research Space (South Africa)

    Combrinck, ML

    2015-07-01

    Full Text Available such that any vector observed from the inertial frame O can be related to the vector observed from the orientation preserving frame O’ as: ),(=),'(' tGt xuxu M (4) This definition will lead to a mathematical description to directly relate the vector... fields in the inertial frame O, to the vector fields in the orientation preserving frame O’: ),(=),'(' tGt xuxu M xȍxu ),(= t (5) Rotational Transform Since frame Ô shares an origin with the frame O’ the vector components in Ô is related...

  17. On the Coupling of Incompressible Stokes or Navier–Stokes and Darcy Flows Through Porous Media

    KAUST Repository

    Girault, V.

    2012-11-03

    In this chapter, we present the theoretical analysis of coupled incompressible Navier-Stokes (or Stokes) flows and Darcy flows with the Beavers-Joseph-Saffman interface condition. We discuss alternative interface and porous media models. We review some finite element methods used by several authors in this coupling and present numerical experiments.

  18. Development of the Glenn-Heat-Transfer (Glenn-HT) Computer Code to Enable Time-Filtered Navier Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

    Science.gov (United States)

    Ameri, Ali A.; Shyam, Vikram; Rigby, David; Poinsatte, Phillip; Thurman, Douglas; Steinthorsson, Erlendur

    2014-01-01

    Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.

  19. Development of the Glenn Heat-Transfer (Glenn-HT) Computer Code to Enable Time-Filtered Navier-Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

    Science.gov (United States)

    Ameri, Ali; Shyam, Vikram; Rigby, David; Poinsatte, Phillip; Thurman, Douglas; Steinthorsson, Erlendur

    2014-01-01

    Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30deg holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described.

  20. Development of the Glenn-HT Computer Code to Enable Time-Filtered Navier-Stokes (TFNS) Simulations and Application to Film Cooling on a Flat Plate Through Long Cooling Tubes

    Science.gov (United States)

    Ameri, Ali; Shyam, Vikram; Rigby, David; Poinsatte, Philip; Thurman, Douglas; Steinthorsson, Erlendur

    2014-01-01

    Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related flows has enabled improved engine component designs. RANS methodology has limitations which are related to its inability to accurately describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS include phenomena such as laminarturbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes which take advantage of both unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn-HT code and applied to film cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 30 holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and four blowing ratios of 0.5, 1.0, 1.5 and 2.0 are shown. Flow features under those conditions are also described.