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Volume 17, Issue 4
An Estimate of the Rate of Entropy Dissipation of High Resolution MUSCL Type Godunov Schemes

Hua-Zhong Tang & Ning Zhao

J. Comp. Math., 17 (1999), pp. 369-378.

Published online: 1999-08

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  • Abstract

In this paper, following the paper [7], we analyze the "sharp" estimate of the rate of entropy dissipation of the fully discrete MUSCL type Godunov schemes by the general compact theory introduced by Coquel-LeFloch [1, 2], and find: because of small viscosity of the above schemes, in the vicinity of shock wave, the estimate of the above schemes is more easily obtained, but for rarefaction wave, we must impose a "sharp" condition on limiter function in order to keep its entropy dissipation and its convergence.

  • Keywords

Hyperbolic conservation laws, MUSCL type godunov schemes, Entropy dissipation, shock wave, Rarefaction wave.

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COPYRIGHT: © Global Science Press

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@Article{JCM-17-369, author = {Tang , Hua-Zhong and Zhao , Ning}, title = {An Estimate of the Rate of Entropy Dissipation of High Resolution MUSCL Type Godunov Schemes}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {4}, pages = {369--378}, abstract = {

In this paper, following the paper [7], we analyze the "sharp" estimate of the rate of entropy dissipation of the fully discrete MUSCL type Godunov schemes by the general compact theory introduced by Coquel-LeFloch [1, 2], and find: because of small viscosity of the above schemes, in the vicinity of shock wave, the estimate of the above schemes is more easily obtained, but for rarefaction wave, we must impose a "sharp" condition on limiter function in order to keep its entropy dissipation and its convergence.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9109.html} }
TY - JOUR T1 - An Estimate of the Rate of Entropy Dissipation of High Resolution MUSCL Type Godunov Schemes AU - Tang , Hua-Zhong AU - Zhao , Ning JO - Journal of Computational Mathematics VL - 4 SP - 369 EP - 378 PY - 1999 DA - 1999/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9109.html KW - Hyperbolic conservation laws, MUSCL type godunov schemes, Entropy dissipation, shock wave, Rarefaction wave. AB -

In this paper, following the paper [7], we analyze the "sharp" estimate of the rate of entropy dissipation of the fully discrete MUSCL type Godunov schemes by the general compact theory introduced by Coquel-LeFloch [1, 2], and find: because of small viscosity of the above schemes, in the vicinity of shock wave, the estimate of the above schemes is more easily obtained, but for rarefaction wave, we must impose a "sharp" condition on limiter function in order to keep its entropy dissipation and its convergence.

Tang , Hua-Zhong and Zhao , Ning. (1999). An Estimate of the Rate of Entropy Dissipation of High Resolution MUSCL Type Godunov Schemes. Journal of Computational Mathematics. 17 (4). 369-378. doi:
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