Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes
Journal of Computational Physics
Numerical passage from kinetic to fluid equations
SIAM Journal on Numerical Analysis
Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
Numerical schemes for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation
SIAM Journal on Numerical Analysis
Coupling Boltzmann and Navier-Stokes equations by half fluxes
Journal of Computational Physics
Relaxation Schemes for Nonlinear Kinetic Equations
SIAM Journal on Numerical Analysis
An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit
SIAM Journal on Numerical Analysis
Relaxation of Energy and Approximate Riemann Solvers for General Pressure Laws in Fluid Dynamics
SIAM Journal on Numerical Analysis
Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations
SIAM Journal on Numerical Analysis
An implicit Monte Carlo method for rarefied gas dynamics
Journal of Computational Physics
The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: Discrete-Ordinate Method
SIAM Journal on Numerical Analysis
An Asymptotic Preserving Numerical Scheme for Kinetic Equations in the Low Mach Number Limit
SIAM Journal on Numerical Analysis
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
SIAM Journal on Scientific Computing
Discretization of the multiscale semiconductor Boltzmann equation by diffusive relaxation schemes
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
Time Relaxed Monte Carlo Methods for the Boltzmann Equation
SIAM Journal on Scientific Computing
Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
SIAM Journal on Numerical Analysis
High order numerical methods for the space non-homogeneous Boltzmann equation
Journal of Computational Physics
Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion
Journal of Scientific Computing
A Smooth Transition Model between Kinetic and Diffusion Equations
SIAM Journal on Numerical Analysis
Accurate numerical methods for the collisional motion of (heated) granular flows
Journal of Computational Physics
A smooth transition model between kinetic and hydrodynamic equations
Journal of Computational Physics
Solving the Boltzmann Equation in N log2 N
SIAM Journal on Scientific Computing
A finite volume scheme for the Patlak–Keller–Segel chemotaxis model
Numerische Mathematik
An asymptotic preserving scheme for the two-fluid Euler-Poisson model in the quasineutral limit
Journal of Computational Physics
Implicit—Explicit Schemes for BGK Kinetic Equations
Journal of Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
High order resolution of the Maxwell-Fokker-Planck-Landau model intended for ICF applications
Journal of Computational Physics
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II
Journal of Computational Physics
A unified gas-kinetic scheme for continuum and rarefied flows
Journal of Computational Physics
A class of asymptotic-preserving schemes for the Fokker-Planck-Landau equation
Journal of Computational Physics
Microscopically implicit-macroscopically explicit schemes for the BGK equation
Journal of Computational Physics
Exponential Runge-Kutta Methods for Stiff Kinetic Equations
SIAM Journal on Numerical Analysis
Numerical approximation of the Euler-Maxwell model in the quasineutral limit
Journal of Computational Physics
Journal of Computational Physics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Unified gas-kinetic scheme for diatomic molecular simulations in all flow regimes
Journal of Computational Physics
Exponential Runge-Kutta for the inhomogeneous Boltzmann equations with high order of accuracy
Journal of Computational Physics
Hi-index | 31.48 |
In this paper, we propose a general time-discrete framework to design asymptotic-preserving schemes for initial value problem of the Boltzmann kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source) terms induced by small mean free or relaxation time. We propose to penalize the nonlinear collision term by a BGK-type relaxation term, which can be solved explicitly even if discretized implicitly in time. Moreover, the BGK-type relaxation operator helps to drive the density distribution toward the local Maxwellian, thus naturally imposes an asymptotic-preserving scheme in the Euler limit. The scheme so designed does not need any nonlinear iterative solver or the use of Wild Sum. It is uniformly stable in terms of the (possibly small) Knudsen number, and can capture the macroscopic fluid dynamic (Euler) limit even if the small scale determined by the Knudsen number is not numerically resolved. It is also consistent to the compressible Navier-Stokes equations if the viscosity and heat conductivity are numerically resolved. The method is applicable to many other related problems, such as hyperbolic systems with stiff relaxation, and high order parabolic equations.