TY - JOUR
T1 - Asymptotic Preserving Spectral Deferred Correction Methods for Hyperbolic Systems with Relaxation
JO - Communications in Computational Physics
VL - 2
SP - 531
EP - 557
PY - 2019
DA - 2019/04
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0067
UR - https://global-sci.org/intro/article_detail/cicp/13101.html
KW - Spectral deferred correction methods, asymptotic preserving schemes, hyperbolic
systems with relaxation, stiff systems, weighted essentially non-oscillatory schemes.
AB - <p style="text-align: justify;">In this paper, we consider the semi-implicit spectral deferred correction
(SDC) methods for hyperbolic systems of conservation laws with stiff relaxation terms.
The relaxation term is treated implicitly, and the convection terms are treated by explicit schemes. The SDC schemes proposed are asymptotic preserving (AP) in the zero
relaxation limit and can be constructed easily and systematically for any order of accuracy. Weighted essentially non-oscillatory (WENO) schemes are adopted in spatial
discretization to achieve high order accuracy. After a description of the asymptotic preserving property of the SDC schemes, several applications will be presented to demonstrate the stiff accuracy and capability of the schemes.</p>