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arXiv · 2405.08549

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

Yu-Chen Cheng·Christian Klingenberg·Rony Touma
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Abstract

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.

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Yu-Chen Cheng, Christian Klingenberg, Rony Touma. 2024-05-14. A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case. https://arxiv.org/abs/2405.08549

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