Entropy conservative discretization of compressible Euler equations with an arbitrary equation of state
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arXiv
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| Format: | Preprint |
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2024
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| author | Aiello, Alessandro De Michele, Carlo Coppola, Gennaro |
| author_facet | Aiello, Alessandro De Michele, Carlo Coppola, Gennaro |
| contents | This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a locally-conservative discretization, guarantees also the spatial conservation of mass, momentum, and total energy and is kinetic energy-preserving. In order to achieve the entropy-conservation property for an arbitrary non-ideal gas, a general strategy is adopted based on the manipulation of discrete balance equations through the imposition of global entropy conservation and the use of a summation by parts rule. The procedure, which is extended to an arbitrary order of accuracy, conducts to a general form of the internal-energy numerical flux which results in a nonlinear function of thermodynamic and dynamic variables and still admits the mass flux as a residual degree of freedom. The effectiveness of the novel entropy-conservative formulation is demonstrated through numerical tests making use of some of the most popular cubic equations of state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01235 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entropy conservative discretization of compressible Euler equations with an arbitrary equation of state Aiello, Alessandro De Michele, Carlo Coppola, Gennaro Fluid Dynamics Numerical Analysis 76N15, 76M25 This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a locally-conservative discretization, guarantees also the spatial conservation of mass, momentum, and total energy and is kinetic energy-preserving. In order to achieve the entropy-conservation property for an arbitrary non-ideal gas, a general strategy is adopted based on the manipulation of discrete balance equations through the imposition of global entropy conservation and the use of a summation by parts rule. The procedure, which is extended to an arbitrary order of accuracy, conducts to a general form of the internal-energy numerical flux which results in a nonlinear function of thermodynamic and dynamic variables and still admits the mass flux as a residual degree of freedom. The effectiveness of the novel entropy-conservative formulation is demonstrated through numerical tests making use of some of the most popular cubic equations of state. |
| title | Entropy conservative discretization of compressible Euler equations with an arbitrary equation of state |
| topic | Fluid Dynamics Numerical Analysis 76N15, 76M25 |
| url | https://arxiv.org/abs/2408.01235 |