A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case
Numerical Analysis
2024-05-15 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2405.08549,
title = {A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case},
author = {Yu-Chen Cheng and Christian Klingenberg and Rony Touma},
journal= {arXiv preprint arXiv:2405.08549},
year = {2024}
}