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Volume 18, Issue 3
On the Central Relaxing Schemes I: Single Conservation Laws

Hua-Zhong Tang

J. Comp. Math., 18 (2000), pp. 313-324.

Published online: 2000-06

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  • Abstract

In this first paper we present a central relaxing scheme for scalar conservation laws, based on using the local relaxation approximation. Our scheme is obtained without using linear or nonlinear Riemann solvers. A cell entropy inequality is studied for the semidiscrete central relaxing scheme, and a second order MUSCL scheme is shown to be TVD in the zero relaxation limit. The next paper will extend the central relaxing scheme to multi-dimensional systems of conservation laws in curvilinear coordinates, including numerical experiments for 1D and 2D problems.

  • Keywords

Hyperbolic conservation laws, the relaxing scheme, TVD, cell entropy inequality.

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COPYRIGHT: © Global Science Press

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@Article{JCM-18-313, author = {Tang , Hua-Zhong}, title = {On the Central Relaxing Schemes I: Single Conservation Laws}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {3}, pages = {313--324}, abstract = {

In this first paper we present a central relaxing scheme for scalar conservation laws, based on using the local relaxation approximation. Our scheme is obtained without using linear or nonlinear Riemann solvers. A cell entropy inequality is studied for the semidiscrete central relaxing scheme, and a second order MUSCL scheme is shown to be TVD in the zero relaxation limit. The next paper will extend the central relaxing scheme to multi-dimensional systems of conservation laws in curvilinear coordinates, including numerical experiments for 1D and 2D problems.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9045.html} }
TY - JOUR T1 - On the Central Relaxing Schemes I: Single Conservation Laws AU - Tang , Hua-Zhong JO - Journal of Computational Mathematics VL - 3 SP - 313 EP - 324 PY - 2000 DA - 2000/06 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9045.html KW - Hyperbolic conservation laws, the relaxing scheme, TVD, cell entropy inequality. AB -

In this first paper we present a central relaxing scheme for scalar conservation laws, based on using the local relaxation approximation. Our scheme is obtained without using linear or nonlinear Riemann solvers. A cell entropy inequality is studied for the semidiscrete central relaxing scheme, and a second order MUSCL scheme is shown to be TVD in the zero relaxation limit. The next paper will extend the central relaxing scheme to multi-dimensional systems of conservation laws in curvilinear coordinates, including numerical experiments for 1D and 2D problems.

Hua-Zhong Tang. (1970). On the Central Relaxing Schemes I: Single Conservation Laws. Journal of Computational Mathematics. 18 (3). 313-324. doi:
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