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Nengchao Wang – 1st expert on this subject based on the ideXlab platform
a unified thermal lattice BGK Model for boussinesq equationsProgress in Computational Fluid Dynamics, 2005Co-Authors: Nanzhong He, Nengchao WangAbstract:
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 equationJournal of Computational Physics, 2000Co-Authors: Nengchao WangAbstract:
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 EquationJournal of Computational Physics, 2000Co-Authors: Zhaoli Guo, Baochang Shi, Nengchao WangAbstract:
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 – 2nd expert on this subject based on the ideXlab platform
convergence estimates of a semi lagrangian scheme for the ellipsoidal BGK Model for polyatomic moleculesarXiv: Numerical Analysis, 2020Co-Authors: Sebastiano Boscarino, Giovanni RussoAbstract:
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 ModelMathematics in Engineering, 2020Co-Authors: Sudarshan Tiwari, Axel Klar, Giovanni RussoAbstract:
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 . 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 dynamicsInternational Journal of Advances in Engineering Sciences and Applied Mathematics, 2019Co-Authors: Sudarshan Tiwari, Axel Klar, Giovanni RussoAbstract:
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.
Sa Jun Park – 3rd expert on this subject based on the ideXlab platform
on a positive decomposition of entropy production functional for the polyatomic BGK ModelApplied Mathematics Letters, 2018Co-Authors: Sa Jun ParkAbstract:
Abstract In this paper, we show that the entropy production functional for the polyatomic ellipsoidal BGK Model can be decomposed into two non-negative parts. Two applications of this property: the H -theorem for the polyatomic BGK Model and the weak compactness of the polyatomic ellipsoidal relaxation operator, are discussed.
cauchy problem for the ellipsoidal BGK Model for polyatomic particlesarXiv: Analysis of PDEs, 2017Co-Authors: Sa Jun ParkAbstract:
We establish the existence and uniqueness of mild solutions for the polyatomic ellipsoidal BGK Model, which is a relaxation type kinetic Model describing the evolution of polyatomic gaseous system at the mesoscopic level.
entropy production estimates for the polyatomic ellipsoidal BGK ModelarXiv: Analysis of PDEs, 2017Co-Authors: Sa Jun ParkAbstract:
We study the entropy production estimate for the polyatomic ellipsoidal BGK Model, which is a relaxation type kinetic Model describing the time evolution of polyatomic particle systems. An interesting dichotomy is observed between $0<\theta\leq 1$ and $\theta=0$: In each case, a distinct target Maxwellians should be chosen to estimate the entropy production functional from below by the relative entropy. The time asymptotic equilibrium state toward which the distribution function stabilizes bifurcates accordingly.