Novel Local Characteristic Decomposition Based Path-Conservative Central-Upwind Schemes
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914783123472384 |
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| author | Chu, Shaoshuai Herty, Michael Kurganov, Alexander |
| author_facet | Chu, Shaoshuai Herty, Michael Kurganov, Alexander |
| contents | 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. Lukáčová-Medvi{\softd}ová}, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_01929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Novel Local Characteristic Decomposition Based Path-Conservative Central-Upwind Schemes Chu, Shaoshuai Herty, Michael Kurganov, Alexander Numerical Analysis 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. Lukáčová-Medvi{\softd}ová}, 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. |
| title | Novel Local Characteristic Decomposition Based Path-Conservative Central-Upwind Schemes |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.01929 |