Genuinely multi-dimensional stationarity preserving Finite Volume formulation for nonlinear hyperbolic PDEs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908710381551616 |
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| author | Barsukow, Wasilij Ciallella, Mirco Ricchiuto, Mario Torlo, Davide |
| author_facet | Barsukow, Wasilij Ciallella, Mirco Ricchiuto, Mario Torlo, Davide |
| contents | Classical Finite Volume methods for multi-dimensional problems include stabilization (e.g.\ via a Riemann solver), that is derived by considering several one-dimensional problems in different directions. Such methods therefore ignore a possibly existing balance of contributions coming from different directions, such as the one characterizing multi-dimensional stationary states. Instead of being preserved, they are usually diffused away by such methods. Stationarity preserving methods use a better suited stabilization term that vanishes at the stationary state, allowing the method to preserve it. This work presents a general approach to stationarity preserving Finite Volume methods for nonlinear conservation/balance laws. It is based on a multi-dimensional stationarity preserving quadrature strategy that allows to naturally introduce genuinely multi-dimensional numerical fluxes. The new methods are shown to significantly outperform existing ones even if the latter are of higher order of accuracy and even on non-stationary solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Genuinely multi-dimensional stationarity preserving Finite Volume formulation for nonlinear hyperbolic PDEs Barsukow, Wasilij Ciallella, Mirco Ricchiuto, Mario Torlo, Davide Numerical Analysis Computational Physics Classical Finite Volume methods for multi-dimensional problems include stabilization (e.g.\ via a Riemann solver), that is derived by considering several one-dimensional problems in different directions. Such methods therefore ignore a possibly existing balance of contributions coming from different directions, such as the one characterizing multi-dimensional stationary states. Instead of being preserved, they are usually diffused away by such methods. Stationarity preserving methods use a better suited stabilization term that vanishes at the stationary state, allowing the method to preserve it. This work presents a general approach to stationarity preserving Finite Volume methods for nonlinear conservation/balance laws. It is based on a multi-dimensional stationarity preserving quadrature strategy that allows to naturally introduce genuinely multi-dimensional numerical fluxes. The new methods are shown to significantly outperform existing ones even if the latter are of higher order of accuracy and even on non-stationary solutions. |
| title | Genuinely multi-dimensional stationarity preserving Finite Volume formulation for nonlinear hyperbolic PDEs |
| topic | Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2506.21700 |