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Volume 26, Issue 2
Asymptotic Preserving Spectral Deferred Correction Methods for Hyperbolic Systems with Relaxation

Chong Sun & Yinhua Xia

DOI: 10.4208/cicp.OA-2018-0067

Commun. Comput. Phys., 26 (2019), pp. 531-557.

Published online: 2019-04

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  • Abstract

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.

  • Keywords

Spectral deferred correction methods, asymptotic preserving schemes, hyperbolic systems with relaxation, stiff systems, weighted essentially non-oscillatory schemes.

  • AMS Subject Headings

65M70, 65B05, 35L45

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-26-531, author = {Chong Sun and Yinhua Xia}, title = {Asymptotic Preserving Spectral Deferred Correction Methods for Hyperbolic Systems with Relaxation}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {2}, pages = {531--557}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0067}, url = {http://global-sci.org/intro/article_detail/cicp/13101.html} }
TY - JOUR T1 - Asymptotic Preserving Spectral Deferred Correction Methods for Hyperbolic Systems with Relaxation AU - Chong Sun & Yinhua Xia 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 -

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.

Chong Sun and Yinhua Xia. (2019). Asymptotic Preserving Spectral Deferred Correction Methods for Hyperbolic Systems with Relaxation. Communications in Computational Physics. 26 (2). 531-557. doi:10.4208/cicp.OA-2018-0067
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