On the Construction of High-Order and Exact Pressure Equilibrium Schemes for Arbitrary Equations of State
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911301559648256 |
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| author | DeGrendele, Christopher Ly, Nguyen Cadieux, Francois Barad, Michael Lee, Dongwook Duensing, Jared |
| author_facet | DeGrendele, Christopher Ly, Nguyen Cadieux, Francois Barad, Michael Lee, Dongwook Duensing, Jared |
| contents | Typical fully conservative discretizations of the Euler compressible single or multi-component fluid equations governed by a real-fluid equation of state exhibit spurious pressure oscillations due to the nonlinearity of the thermodynamic relation between pressure, density, and internal energy. A fully conservative, pressure-equilibrium preserving method and a high-order, fully conservative, approximate pressure-equilibrium preserving method are presented. Both methods are general and can handle an arbitrary equation of state and arbitrary number of species. Unlike existing approaches to discretize the multi-component Euler equations, we do not introduce non conservative updates, overspecified equations, or design for a specific equation of state. The proposed methods are demonstrated on inviscid smooth interface advection problems governed by three equations of state: ideal-gas, stiffened-gas, and van der Waals where we show orders of magnitude reductions in spurious pressure oscillations compared to existing schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Construction of High-Order and Exact Pressure Equilibrium Schemes for Arbitrary Equations of State DeGrendele, Christopher Ly, Nguyen Cadieux, Francois Barad, Michael Lee, Dongwook Duensing, Jared Computational Physics Numerical Analysis Typical fully conservative discretizations of the Euler compressible single or multi-component fluid equations governed by a real-fluid equation of state exhibit spurious pressure oscillations due to the nonlinearity of the thermodynamic relation between pressure, density, and internal energy. A fully conservative, pressure-equilibrium preserving method and a high-order, fully conservative, approximate pressure-equilibrium preserving method are presented. Both methods are general and can handle an arbitrary equation of state and arbitrary number of species. Unlike existing approaches to discretize the multi-component Euler equations, we do not introduce non conservative updates, overspecified equations, or design for a specific equation of state. The proposed methods are demonstrated on inviscid smooth interface advection problems governed by three equations of state: ideal-gas, stiffened-gas, and van der Waals where we show orders of magnitude reductions in spurious pressure oscillations compared to existing schemes. |
| title | On the Construction of High-Order and Exact Pressure Equilibrium Schemes for Arbitrary Equations of State |
| topic | Computational Physics Numerical Analysis |
| url | https://arxiv.org/abs/2512.04450 |