A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case

Fuente: arXiv
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Main Authors: Cheng, Yu-Chen, Klingenberg, Christian, Touma, Rony
Format: Preprint
Published: 2024
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author Cheng, Yu-Chen
Klingenberg, Christian
Touma, Rony
author_facet Cheng, Yu-Chen
Klingenberg, Christian
Touma, Rony
contents In this paper, we propose a new MUSCL scheme by combining the ideas of the Kurganov and Tadmor scheme and the so-called Deviation method which results in a well-balanced finite volume method for the hyperbolic balance laws, by evolving the difference between the exact solution and a given stationary solution. After that, we derive a semi-discrete scheme from this new scheme and it can be shown to be essentially TVD when applied to a scalar conservation law. In the end, we apply and validate the developed methods by numerical experiments and solve classical problems featuring Euler equations with gravitational source term.
format Preprint
id arxiv_https___arxiv_org_abs_2405_08549
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case
Cheng, Yu-Chen
Klingenberg, Christian
Touma, Rony
Numerical Analysis
In this paper, we propose a new MUSCL scheme by combining the ideas of the Kurganov and Tadmor scheme and the so-called Deviation method which results in a well-balanced finite volume method for the hyperbolic balance laws, by evolving the difference between the exact solution and a given stationary solution. After that, we derive a semi-discrete scheme from this new scheme and it can be shown to be essentially TVD when applied to a scalar conservation law. In the end, we apply and validate the developed methods by numerical experiments and solve classical problems featuring Euler equations with gravitational source term.
title A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case
topic Numerical Analysis
url https://arxiv.org/abs/2405.08549