The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform

Nengchao Wang - One of the best experts on this subject based on the ideXlab platform.

  • a unified thermal lattice BGK Model for boussinesq equations
    Progress in Computational Fluid Dynamics, 2005
    Co-Authors: Nanzhong He, Nengchao Wang
    Abstract:

    A unified thermal Lattice Bhatnagar-Gross-Krook (LBGK) Model for the Boussinesq incompressible fluids is introduced. In the Model, the velocity and temperature fields are solved by two independent LBGK equations which are combined into a coupled one for the whole system. Numerical simulations of three-dimensional natural convection flow in rectangular enclosures with differentially heated vertical walls are performed at Rayleigh numbers 1.5 × 103 – 7.5 × 104 and Prandtl numbers 0.015 and 0.025. The numerical results are compared with those of a previous study.

  • lattice BGK Model for incompressible navier stokes equation
    Journal of Computational Physics, 2000
    Co-Authors: Nengchao Wang
    Abstract:

    Abstract Most of the existing lattice Boltzmann BGK Models (LBGK) can be viewed as compressible schemes to simulate incompressible fluid flows. The compressible effect might lead to some undesirable errors in numerical simulations. In this paper a LBGK Model without compressible effect is designed for simulating incompressible flows. The incompressible Navier–Stokes equations are exactly recovered from this incompressible LBGK Model. Numerical simulations of the plane Poiseuille flow, the unsteady 2-D shear decaying flow, the driven cavity flow, and the flow around a circular cylinder are performed. The results agree well with the analytic solutions and the results of previous studies.

  • Lattice BGK Model for Incompressible Navier-Stokes Equation
    Journal of Computational Physics, 2000
    Co-Authors: Zhaoli Guo, Baochang Shi, Nengchao Wang
    Abstract:

    Most of the existing lattice Boltzmann BGK Models (LBGK) can be viewed as compressible schemes to simulate incompressible fluid flows. The compressible effect might lead to some undesirable errors in numerical simulations. In this paper a LBGK Model without compressible effect is designed for simulating incompressible flows. The incompressible Navier-Stokes equations are exactly recovered from this incompressible LBGK Model. Numerical simulations of the plane Poiseuille flow, the unsteady 2-D shear decaying flow, the driven cavity flow, and the flow around a circular cylinder are performed. The results agree well with the analytic solutions and the results of previous studies. © 2000 Academic Press.

Giovanni Russo - One of the best experts on this subject based on the ideXlab platform.

  • convergence estimates of a semi lagrangian scheme for the ellipsoidal BGK Model for polyatomic molecules
    arXiv: Numerical Analysis, 2020
    Co-Authors: Sebastiano Boscarino, Giovanni Russo
    Abstract:

    In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK Model. In order to avoid time step restrictions coming from convection term and small Knudsen number, we combine a semi-Lagrangian approach for the convection term with an implicit treatment for the relaxation term. We show how to explicitly solve the implicit step, thus obtaining an efficient and stable scheme for any Knudsen number. We also derive an explicit error estimate on the convergence of the proposed scheme for every fixed value of the Knudsen number.

  • Interaction of rigid body motion and rarefied gas dynamics based on the BGK Model
    Mathematics in Engineering, 2020
    Co-Authors: Sudarshan Tiwari, Axel Klar, Giovanni Russo
    Abstract:

    In this paper we present simulations of moving rigid bodies immersed in a rarefied gas. The rarefied gas is simulated by solving the Bhatnager-Gross-Krook (BGK) Model for the Boltzmann equation. The Newton-Euler equations are solved to simulate the rigid body motion. The force and the torque on the rigid body is computed from the surrounded gas. An explicit Euler scheme is used for the time integration of the Newton-Euler equations. The BGK Model is solved by the semi-Lagrangian method suggested by Russo & Filbet [22]. Due to the motion of the rigid body, the computational domain for the rarefied gas (and the interface between the rigid body and the gas domain) changes with respect to time. To allow a simpler handling of the interface motion we have used a meshfree method for the interpolation procedure in the semi-Lagrangian scheme. We have considered a one way, as well as a two-way coupling of rigid body and gas flow. We use diffuse reflection boundary conditions on the rigid body and also on the boundary of the computational domain. In one space dimension the numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann equation. In the two-dimensional case results are compared with DSMC simulations for the Boltzmann equation and with results obtained by other researchers. Several test problems and applications illustrate the versatility of the approach.

  • A meshfree method for the BGK Model for rarefied gas dynamics
    International Journal of Advances in Engineering Sciences and Applied Mathematics, 2019
    Co-Authors: Sudarshan Tiwari, Axel Klar, Giovanni Russo
    Abstract:

    In this paper, we have applied semi-Lagrangian schemes with meshfree interpolation, based on a moving least squares method, to solve the BGK Model for rarefied gas dynamics. Sod’s shock tube problems are presented for a large range of mean free paths in one-dimensional physical space and three-dimensional velocity space. In order to validate the solutions obtained from the meshfree method, we have used the piecewise linear spline interpolation. Furthermore, we have compared the solutions of the BGK Model with the solutions obtained from direct simulation Monte Carlo method. In the case of a very small mean free path, the numerical solutions are compared with the exact solutions of the compressible Euler equations. Overall, we found that the meshfree interpolation gives better approximation than the piecewise linear spline interpolation.

  • high order conservative semi lagrangian scheme for the BGK Model of the boltzmann equation
    arXiv: Numerical Analysis, 2019
    Co-Authors: Sebastiano Boscarino, Giovanni Russo
    Abstract:

    In this paper, we present a conservative semi-Lagrangian finite-difference scheme for the BGK Model. Classical semi-Lagrangian finite difference schemes, coupled with an L-stable treatment of the collision term, allow large time steps, for all the range of Knudsen number. Unfortunately, however, such schemes are not conservative. There are two main sources of lack of conservation. First, when using classical continuous Maxwellian, conservation error is negligible only if velocity space is resolved with sufficiently large number of grid points. However, for a small number of grids in velocity space such error is not negligible, because the parameters of the Maxwellian do not coincide with the discrete moments. Secondly, the non-linear reconstruction used to prevent oscillations destroys the translation invariance which is at the basis of the conservation properties of the scheme. As a consequence the schemes show a wrong shock speed in the limit of small Knudsen number. To treat the first problem and ensure machine precision conservation of mass, momentum and energy with a relatively small number of velocity grid points, we replace the continuous Maxwellian with the discrete Maxwellian introduced by Mieussens. The second problem is treated by implementing a conservative correction procedure based on the flux difference form. In this way we can construct a conservative semi-Lagrangian scheme which is Asymptotic Preserving (AP) for the underlying Euler limit, as the Knudsen number vanishes. The effectiveness of the proposed scheme is demonstrated by extensive numerical tests.

  • convergence of a semi lagrangian scheme for the ellipsoidal BGK Model of the boltzmann equation
    SIAM Journal on Numerical Analysis, 2018
    Co-Authors: Giovanni Russo
    Abstract:

    The ellipsoidal Bhatnagar--Greene--Kruskal (BGK) Model is a generalized version of the original BGK Model designed to reproduce the physical Prandtl number in the Navier--Stokes limit. In this paper, we propose a new implicit semi-Lagrangian scheme for the ellipsoidal BGK Model, which, by exploiting special structures of the ellipsoidal Gaussian, can be transformed into a semiexplicit form, guaranteeing the stability of the implicit methods and the efficiency of the explicit methods at the same time. We then derive an error estimate of this scheme in a weighted $L^{\infty}$ norm. Our convergence estimate holds uniformly in the whole range of relaxation parameter $\nu$ including $\nu=0$, which corresponds to the original BGK Model.

Sa Jun Park - One of the best experts on this subject based on the ideXlab platform.

Xiaowen Shan - One of the best experts on this subject based on the ideXlab platform.

  • lattice ellipsoidal statistical BGK Model for thermal non equilibrium flows
    Journal of Fluid Mechanics, 2013
    Co-Authors: Jianping Meng, Yonghao Zhang, Nicolas G Hadjiconstantinou, Gregg A Radtke, Xiaowen Shan
    Abstract:

    A thermal lattice Boltzmann Model is constructed on the basis of the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK Model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this Model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small Mach number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK Model, direct Monte Carlo and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately 0:5. On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations that have been chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased.

Benoit Perthame - One of the best experts on this subject based on the ideXlab platform.

  • Numerical comparison between the Boltzmann and ES-BGK Models for rarefied gases ☆
    Computer Methods in Applied Mechanics and Engineering, 2002
    Co-Authors: Pierre Andries, Jean-françois Bourgat, Patrick Le Tallec, Benoit Perthame
    Abstract:

    Abstract Rarefied gas flows obey the Boltzmann equation, but numerical simulations of this equation are not always possible, so that simpler Models have been introduced. The ES-BGK equation is one of these Models. It gives the correct transport coefficients for the Navier–Stokes approximation, so that Boltzmann or ES-BGK simulations are expected to give the same results for dense gases, but in the case of a rarefied flow, complete numerical comparisons are needed. In this paper we present numerical comparisons between the two Models in transitional regimes (where the ES-BGK Model is expected to be useful) for reentry flows around a compression ramp and a plate. We also emphasize that the ES-BGK Model gives flow predictions closer to the Boltzmann result than the simpler BGK Model.

  • the es BGK Model equation with correct prandtl number
    RAREFIED GAS DYNAMICS: 22nd International Symposium, 2002
    Co-Authors: Pierre Andries, Benoit Perthame
    Abstract:

    To avoid the complexity of the Boltzmann collision operator, the BGK Model Equation is widely used, but it is well known that one of its shortcoming is that it gives a Prandtl number of one in the fluid limit. The ES-BGK was introduced to obtain the correct Prandtl number, but the entropy property for this Model was an open problem. In this talk we prove that this Model actually verify an H theorem. Moreover we show in a simple case that computations with this Model are of the same order of complexity and cost as with the BGK Model, so that it appears as a valid alternative of the BGK Model.

  • the gaussian BGK Model of boltzmann equation with small prandtl number
    European Journal of Mechanics B-fluids, 2000
    Co-Authors: Pierre Andries, Patrick Le Tallec, J P Perlat, Benoit Perthame
    Abstract:

    Abstract In this paper we prove the entropy inequality for the Gaussian-BGK Model of Boltzmann equation. This Model, also called ellipsoidal statistical Model, was introduced in order to fit realistic values of the transport coefficients (Prandtl number, second viscosity) in the Navier–Stokes approximation, which cannot be achieved by the usual relaxation towards isotropic Maxwellians introduced in standard BGK Models. Moreover, we introduce new entropic kinetic Models for polyatomic gases which suppress the internal energy variable in the phase space by using two distribution functions (one for particles mass and one for their internal energy). This reduces the cost of their numerical solution while keeping a kinetic description well adapted to desequilibrium regions.

  • a BGK Model for small prandtl number in the navier stokes approximation
    Journal of Statistical Physics, 1993
    Co-Authors: Francois Bouchut, Benoit Perthame
    Abstract:

    We present a BGK-type collision Model which approximates, by a Chapman-Enskog expansion, the compressible Navier-Stokes equations with a Prandtl number that can be chosen arbitrarily between 0 and 1. This Model has the basic properties of the Boltzmann equation, including theH-theorem, but contains an extra parameter in comparison with the standard BGK Model. This parameter is introduced multiplying the collision operator by a nonlinear functional of the distribution function. It is adjusted to the Prandtl number.