Novel Local Characteristic Decomposition Based Path-Conservative Central-Upwind Schemes
<|reference_start|>Novel Local Characteristic Decomposition Based Path-Conservative Central-Upwind Schemes: We introduce local characteristic decomposition based path-conservative central-upwind schemes for (nonconservative) hyperbolic systems of balance laws. The proposed schemes are made to be well-balanced via a flux globalization approach, in which source terms are incorporated into the fluxes: This helps to enforce the well-balanced property when the resulting quasi-conservative system is solved using the local characteristic decomposition based central-upwind scheme recently introduced in [{\sc A. Chertock, S. Chu, M. Herty, A. Kurganov, and M. Luk\'{a}\v{c}ov\'{a}-Medvi{\softd}ov\'{a}}, J. Comput. Phys., 473 (2023), Paper No. 111718]. Nonconservative product terms are also incorporated into the global fluxes using a path-conservative technique. We illustrate the performance of the developed schemes by applying them to one- and two-dimensional compressible multifluid systems and thermal rotating shallow water equations.<|reference_end|>
@article{chu2024novel,
    title={Novel Local Characteristic Decomposition Based Path-Conservative
  Central-Upwind Schemes},
    author={Shaoshuai Chu, Michael Herty, and Alexander Kurganov},
    journal={arXiv preprint arXiv:2405.01929},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.01929},
    primaryClass={math.NA cs.NA}
}