A Well-Balanced Method for an Unstaggered Central Scheme, the two-space Dimensional Case
<|reference_start|>A Well-Balanced Method for an Unstaggered Central Scheme, the two-space Dimensional Case: We develop a second-order accurate central scheme for the two-dimensional hyperbolic system of in-homogeneous conservation laws. The main idea behind the scheme is that we combine the well-balanced deviation method with the Kurganov-Tadmor (KT) scheme. The approach satisfies the well-balanced property and retains the advantages of KT scheme: Riemann-solver-free and the avoidance of oversampling on the regions between Riemann-fans. The scheme is implemented and applied to a number of numerical experiments for the Euler equations with gravitational source term and the results are non-oscillatory. Based on the same idea, we construct a semi-discrete scheme where we combine the above two methods and illustrate the maximum principle.<|reference_end|>
@article{cheng2024a,
    title={A Well-Balanced Method for an Unstaggered Central Scheme, the two-space
  Dimensional Case},
    author={Yu-Chen Cheng, Christian Klingenberg, Rony Touma},
    journal={arXiv preprint arXiv:2406.07185},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.07185},
    primaryClass={math.NA cs.NA}
}