Asymptotic preserving and positive schemes for radiation hydrodynamics
Journal of Computational Physics
Upwinding of the source term at interfaces for Euler equations with high friction
Computers & Mathematics with Applications
Journal of Computational Physics
Numerical Schemes of Diffusion Asymptotics and Moment Closures for Kinetic Equations
Journal of Scientific Computing
An Asymptotic Preserving scheme for the Euler equations in a strong magnetic field
Journal of Computational Physics
Journal of Computational Physics
Analysis of an Asymptotic Preserving Scheme for Linear Kinetic Equations in the Diffusion Limit
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
On Stability, Monotonicity, and Construction of Difference Schemes II: Applications
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
Asymptotic-preserving Projective Integration Schemes for Kinetic Equations in the Diffusion Limit
SIAM Journal on Scientific Computing
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Many transport equations, such as the neutron transport, radiative transfer, and transport equations for waves in random media, have a diffusive scaling that leads to the diffusion equations. In many physical applications, the scaling parameter (mean free path) may differ in several orders of magnitude from the rarefied regimes to the hydrodynamic (diffusive) regimes within one problem, and it is desirable to develop a class of robust numerical schemes that can work uniformly with respect to this relaxation parameter. In an earlier work [Jin, Pareschi, and Toscani, SIAM J. Numer. Anal., 35 (1998), pp. 2405--2439] we handled this numerical problem for discrete-velocity kinetic models by reformulating the system into a form commonly used for a relaxation scheme for conservation laws [Jin and Xin, Comm. Pure Appl. Math., 48 (1995), pp. 235--277]. Such a reformulation allows us to use the splitting technique for relaxation schemes to design a class of implicit, yet explicitly implementable, schemes that work with high resolution uniformly with respect to the relaxation parameter. In this paper we show that such a numerical technique can be applied to a large class of transport equations with continuous velocities, when one uses the even and odd parities of the transport equation.