scholarly journals Asymptotic-Preserving and Positivity-Preserving Implicit-Explicit Schemes for the Stiff BGK Equation

2018 ◽  
Vol 56 (2) ◽  
pp. 942-973 ◽  
Author(s):  
Jingwei Hu ◽  
Ruiwen Shu ◽  
Xiangxiong Zhang
Keyword(s):  
Positivity Preserving ◽  
Asymptotic Preserving ◽  
Explicit Schemes ◽  
Bgk Equation

scholarly journals Microscopically implicit–macroscopically explicit schemes for the BGK equation

2012 ◽  
Vol 231 (2) ◽  
pp. 299-327 ◽  
Author(s):  
Sandra Pieraccini ◽  
Gabriella Puppo
Keyword(s):  
Explicit Schemes ◽  
Bgk Equation

High-Order Conservative Asymptotic-Preserving Schemes for Modeling Rarefied Gas Dynamical Flows with Boltzmann-BGK Equation

2015 ◽  
Vol 18 (4) ◽  
pp. 1012-1049 ◽  
Author(s):  
Manuel A. Diaz ◽  
Min-Hung Chen ◽  
Jaw-Yen Yang
Keyword(s):  
Rarefied Gas ◽  
Collision Operator ◽  
High Order ◽  
Gas Flows ◽  
Correction Procedure ◽  
Bgk Model ◽  
Time Step ◽  
Asymptotic Preserving ◽  
Bgk Equation ◽  
Rarefied Gas Flows

AbstractHigh-order and conservative phase space direct solvers that preserve the Euler asymptotic limit of the Boltzmann-BGK equation for modelling rarefied gas flows are explored and studied. The approach is based on the conservative discrete ordinate method for velocity space by using Gauss Hermite or Simpsons quadrature rule and conservation of macroscopic properties are enforced on the BGK collision operator. High-order asymptotic-preserving time integration is adopted and the spatial evolution is performed by high-order schemes including a finite difference weighted essentially non-oscillatory method and correction procedure via reconstruction schemes. An artificial viscosity dissipative model is introduced into the Boltzmann-BGK equation when the correction procedure via reconstruction scheme is used. The effects of the discrete velocity conservative property and accuracy of high-order formulations of kinetic schemes based on BGK model methods are provided. Extensive comparative tests with one-dimensional and two-dimensional problems in rarefied gas flows have been carried out to validate and illustrate the schemes presented. Potentially advantageous schemes in terms of stable large time step allowed and higher-order of accuracy are suggested.

A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model

2017 ◽  
Vol 27 (03) ◽  
pp. 549-579 ◽  
Author(s):  
Juntao Huang ◽  
Chi-Wang Shu
Keyword(s):  
Discontinuous Galerkin ◽  
Strong Stability ◽  
Debye Model ◽  
Second Order ◽  
Positivity Preserving ◽  
Asymptotic Preserving ◽  
Runge Kutta ◽  
Numer Anal ◽  
Scalar Conservation ◽  
Unconditional Positivity

In this paper, we develop a second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin (DG) scheme for the Kerr–Debye model. By using the approach first introduced by Zhang and Shu in [Q. Zhang and C.-W. Shu, Error estimates to smooth solutions of Runge–Kutta discontinuous Galerkin methods for scalar conservation laws, SIAM J. Numer. Anal. 42 (2004) 641–666.] with an energy estimate and Taylor expansion, the asymptotic-preserving property of the semi-discrete DG methods is proved rigorously. In addition, we propose a class of unconditional positivity-preserving implicit–explicit (IMEX) Runge–Kutta methods for the system of ordinary differential equations arising from the semi-discretization of the Kerr–Debye model. The new IMEX Runge–Kutta methods are based on the modification of the strong-stability-preserving (SSP) implicit Runge–Kutta method and have second-order accuracy. The numerical results validate our analysis.

scholarly journals Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations

2017 ◽  
Vol 87 (311) ◽  
pp. 1165-1189 ◽  
Author(s):  
Jian-Guo Liu ◽  
Li Wang ◽  
Zhennan Zhou
Keyword(s):  
Positivity Preserving ◽  
Asymptotic Preserving

scholarly journals An asymptotic preserving semi-implicit multiderivative solver

2021 ◽  
Vol 160 ◽  
pp. 84-101 ◽  
Author(s):  
Jochen Schütz ◽  
David C. Seal
Keyword(s):  
Asymptotic Preserving
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