A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case
<|reference_start|>A Well-Balanced Method for an Unstaggered Central Scheme, the one-space Dimensional Case: 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.<|reference_end|>
@article{cheng2024a,
    title={A Well-Balanced Method for an Unstaggered Central Scheme, the one-space
  Dimensional Case},
    author={Yu-Chen Cheng, Christian Klingenberg, Rony Touma},
    journal={arXiv preprint arXiv:2405.08549},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.08549},
    primaryClass={math.NA cs.NA}
}