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Volume 42, Issue 4
A Cell-Centered Godunov Method Based on Staggered Data Distribution, Part I: One-Dimensional Case

Jiayin Zhai, Xiao Li & Zhijun Shen

DOI: 10.4208/jcm.2301-m2022-0177

J. Comp. Math., 42 (2024), pp. 1172-1196.

Published online: 2024-04

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  • Abstract

This paper presents a cell-centered Godunov method based on staggered data distribution in Eulerian framework. The motivation is to reduce the intrinsic entropy dissipation of classical Godunov methods in the calculation of an isentropic or rarefaction flow. At the same time, the property of accurate shock capturing is also retained. By analyzing the factors that cause nonphysical entropy in the conventional Godunov methods, we introduce two velocities rather than a single velocity in a cell to reduce kinetic energy dissipation. A series of redistribution strategies are adopted to update subcell quantities in order to improve accuracy. Numerical examples validate that the present method can dramatically reduce nonphysical entropy increase.

  • Keywords

Godunov method, Riemann solver, Rarefaction wave, Nonphysical entropy increase.

  • AMS Subject Headings

35Q35, 76N15, 76M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-1172, author = {Zhai , JiayinLi , Xiao and Shen , Zhijun}, title = {A Cell-Centered Godunov Method Based on Staggered Data Distribution, Part I: One-Dimensional Case}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {4}, pages = {1172--1196}, abstract = {

This paper presents a cell-centered Godunov method based on staggered data distribution in Eulerian framework. The motivation is to reduce the intrinsic entropy dissipation of classical Godunov methods in the calculation of an isentropic or rarefaction flow. At the same time, the property of accurate shock capturing is also retained. By analyzing the factors that cause nonphysical entropy in the conventional Godunov methods, we introduce two velocities rather than a single velocity in a cell to reduce kinetic energy dissipation. A series of redistribution strategies are adopted to update subcell quantities in order to improve accuracy. Numerical examples validate that the present method can dramatically reduce nonphysical entropy increase.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2301-m2022-0177}, url = {http://global-sci.org/intro/article_detail/jcm/23051.html} }
TY - JOUR T1 - A Cell-Centered Godunov Method Based on Staggered Data Distribution, Part I: One-Dimensional Case AU - Zhai , Jiayin AU - Li , Xiao AU - Shen , Zhijun JO - Journal of Computational Mathematics VL - 4 SP - 1172 EP - 1196 PY - 2024 DA - 2024/04 SN - 42 DO - http://doi.org/10.4208/jcm.2301-m2022-0177 UR - https://global-sci.org/intro/article_detail/jcm/23051.html KW - Godunov method, Riemann solver, Rarefaction wave, Nonphysical entropy increase. AB -

This paper presents a cell-centered Godunov method based on staggered data distribution in Eulerian framework. The motivation is to reduce the intrinsic entropy dissipation of classical Godunov methods in the calculation of an isentropic or rarefaction flow. At the same time, the property of accurate shock capturing is also retained. By analyzing the factors that cause nonphysical entropy in the conventional Godunov methods, we introduce two velocities rather than a single velocity in a cell to reduce kinetic energy dissipation. A series of redistribution strategies are adopted to update subcell quantities in order to improve accuracy. Numerical examples validate that the present method can dramatically reduce nonphysical entropy increase.

Zhai , JiayinLi , Xiao and Shen , Zhijun. (2024). A Cell-Centered Godunov Method Based on Staggered Data Distribution, Part I: One-Dimensional Case. Journal of Computational Mathematics. 42 (4). 1172-1196. doi:10.4208/jcm.2301-m2022-0177
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