A positivity preserving second-order scheme for multi-dimensional system of non-local conservation laws
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| Format: | Preprint |
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2024
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| _version_ | 1866909448441692160 |
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| author | Manoj, Nikhil Gowda, G. D. Veerappa K, Sudarshan Kumar |
| author_facet | Manoj, Nikhil Gowda, G. D. Veerappa K, Sudarshan Kumar |
| contents | Non-local systems of conservation laws play a crucial role in modeling flow mechanisms across various scenarios. The well-posedness of such problems is typically established by demonstrating the convergence of robust first-order schemes. However, achieving more accurate solutions necessitates the development of higher-order schemes. In this article, we present a fully discrete, second-order scheme for a general class of non-local conservation law systems in multiple spatial dimensions. The method employs a MUSCL-type spatial reconstruction coupled with Runge-Kutta time integration. The proposed scheme is proven to preserve positivity in all the unknowns and exhibits L-infinity stability. Numerical experiments conducted on both the non-local scalar and system cases illustrate the8 importance of second-order scheme when compared to its first-order counterpart. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_18475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A positivity preserving second-order scheme for multi-dimensional system of non-local conservation laws Manoj, Nikhil Gowda, G. D. Veerappa K, Sudarshan Kumar Numerical Analysis Analysis of PDEs Non-local systems of conservation laws play a crucial role in modeling flow mechanisms across various scenarios. The well-posedness of such problems is typically established by demonstrating the convergence of robust first-order schemes. However, achieving more accurate solutions necessitates the development of higher-order schemes. In this article, we present a fully discrete, second-order scheme for a general class of non-local conservation law systems in multiple spatial dimensions. The method employs a MUSCL-type spatial reconstruction coupled with Runge-Kutta time integration. The proposed scheme is proven to preserve positivity in all the unknowns and exhibits L-infinity stability. Numerical experiments conducted on both the non-local scalar and system cases illustrate the8 importance of second-order scheme when compared to its first-order counterpart. |
| title | A positivity preserving second-order scheme for multi-dimensional system of non-local conservation laws |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2412.18475 |