Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes
Journal of Computational Physics
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Numerical schemes for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
A linear-discontinuous spatial differencing scheme for Sn radiative transfer calculations
Journal of Computational Physics
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
SIAM Journal on Scientific Computing
Central Schemes for Balance Laws of Relaxation Type
SIAM Journal on Numerical Analysis
Journal of Computational Physics
On solutions to the Pn equations for thermal radiative transfer
Journal of Computational Physics
Semi-implicit time integration for PN thermal radiative transfer
Journal of Computational Physics
Robust and accurate filtered spherical harmonics expansions for radiative transfer
Journal of Computational Physics
A second order self-consistent IMEX method for radiation hydrodynamics
Journal of Computational Physics
Numerical approximation of the Euler-Maxwell model in the quasineutral limit
Journal of Computational Physics
Asymptotic-preserving Projective Integration Schemes for Kinetic Equations in the Diffusion Limit
SIAM Journal on Scientific Computing
Journal of Computational Physics
Hi-index | 31.47 |
Many hyperbolic systems of equations with stiff relaxation terms reduce to a parabolic description when relaxation dominates. An asymptotic-preserving numerical method is a discretization of the hyperbolic system that becomes a valid discretization of the parabolic system in the asymptotic limit. We explore the consequences of applying a slope limiter to the discontinuous Galerkin (DG) method, with linear elements, for hyperbolic systems with stiff relaxation terms. Without a limiter, the DG method gives an accurate discretization of the Chapman-Enskog approximation of the system when the relaxation length scale is not resolved. It is well known that the first-order upwind (or ''step'') method fails to obtain the proper asymptotic limit. We show that using the minmod slope limiter also fails, but that using double minmod gives the proper asymptotic limit. Despite its effectiveness in the asymptotic limit, the double minmod limiter allows artificial extrema at cell interfaces, referred to as ''sawteeth''. We present a limiter that eliminates the sawteeth, but maintains the proper asymptotic limit. The systems that we analyze are the hyperbolic heat equation and the P"n thermal radiation equations. Numerical examples are used to verify our analysis.