Construction and Performance of Kinetic Schemes for Linear Systems of Conservation Laws
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909951695257600 |
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| author | Audusse, Emmanuel Boyaval, Sébastien Dubos, Virgile Le, Minh-Hoang |
| author_facet | Audusse, Emmanuel Boyaval, Sébastien Dubos, Virgile Le, Minh-Hoang |
| contents | We describe a methodology to build vectorial kinetic schemes, targetting the numerical solution of linear symmetric-hyperbolic systems of conservation laws -a minimal application case for those schemes. Precisely, we fully detail the construction of kinetic schemes that satisfy a discrete equivalent to a convex extension (an additional non-trivial conservation law) of the target system -the (linear) acoustic and elastodynamics systems, specifically -. Then, we evaluate numerically the convergence of various possible kinetic schemes toward smooth solutions, in comparison with standard finite-difference and finite-volume discretizations on Cartesian meshes. Our numerical results confirm the interest of ensuring a discrete equivalent to a convex extension, and show the influence of remaining parameter variations in terms of error magnitude, both for ''first-order'' and ''second-order'' kinetic schemes\,: the parameter choice with largest CFL number (equiv., smallest spurious diffusion in the equivalent equation analysis) has the smallest discretization error. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction and Performance of Kinetic Schemes for Linear Systems of Conservation Laws Audusse, Emmanuel Boyaval, Sébastien Dubos, Virgile Le, Minh-Hoang Numerical Analysis We describe a methodology to build vectorial kinetic schemes, targetting the numerical solution of linear symmetric-hyperbolic systems of conservation laws -a minimal application case for those schemes. Precisely, we fully detail the construction of kinetic schemes that satisfy a discrete equivalent to a convex extension (an additional non-trivial conservation law) of the target system -the (linear) acoustic and elastodynamics systems, specifically -. Then, we evaluate numerically the convergence of various possible kinetic schemes toward smooth solutions, in comparison with standard finite-difference and finite-volume discretizations on Cartesian meshes. Our numerical results confirm the interest of ensuring a discrete equivalent to a convex extension, and show the influence of remaining parameter variations in terms of error magnitude, both for ''first-order'' and ''second-order'' kinetic schemes\,: the parameter choice with largest CFL number (equiv., smallest spurious diffusion in the equivalent equation analysis) has the smallest discretization error. |
| title | Construction and Performance of Kinetic Schemes for Linear Systems of Conservation Laws |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.08479 |