A positivity preserving second-order scheme for multi-dimensional system of non-local conservation laws
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In this article, we present and analyze a fully discrete second- order scheme for a general class of non-local system of conservation laws in multiple spatial dimensions. The method employs a MUSCL-type spatial reconstruction coupled with Runge-Kutta time integration. We analytically prove that the proposed scheme preserves the positivity in all the unknowns, a critical property for ensuring the physical validity of quantities like density, which must remain non-negative. Additionally, the scheme is proven to exhibit L∞ -stability. Numerical experiments conducted on both the non-local scalar and system cases illustrate the importance of the second-order scheme when compared to its first-order counterpart and verify the theoretical results.
Recommended citation: Manoj N., Gowda G.D.V., Kenettinkara S.K., (2024). "A positivity preserving second-order scheme for multi-dimensional system of non-local conservation laws." arxiv preprint .
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