An Entropy-Stable/Double-Flux scheme for the multi-component compressible Navier-Stokes equations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911007322931200 |
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| author | Badrkhani, Vahid Karpowsk, T. Jeremy P. Hasse, Christian |
| author_facet | Badrkhani, Vahid Karpowsk, T. Jeremy P. Hasse, Christian |
| contents | We present a novel combination of numerical techniques to improve the efficiency, accuracy, and robustness of multi-component compressible flow simulations. At the core of our approach is an Entropy-Stable formulation that preserves kinetic energy and integrates a Double-Flux scheme tailored for multi-component flows with variable specific heat ratios. This formulation yields low-dissipation, oscillation-free solutions and enhances stability compared to standard fully conservative methods. To further improve robustness, we introduce a new hybrid dissipation strategy that blends the Entropy-Stable/Double-Flux approach with conventional dissipation mechanisms. We provide a rigorous proof that the resulting numerical flux satisfies a semi-discrete entropy inequality, ensuring consistency with the second law of thermodynamics. For time integration, we employ an explicit Runge-Kutta scheme in combination with adaptive mesh refinement to capture local flow features dynamically. The method is implemented within an existing compressible Navier-Stokes solver based on OpenFOAM. Benchmark cases, including multi-dimensional interface and shock-interface interactions, demonstrate the effectiveness of the proposed framework. The results confirm its favorable stability and robustness, validating the approach as a promising advancement for high-fidelity simulations of supersonic flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Entropy-Stable/Double-Flux scheme for the multi-component compressible Navier-Stokes equations Badrkhani, Vahid Karpowsk, T. Jeremy P. Hasse, Christian Computational Engineering, Finance, and Science We present a novel combination of numerical techniques to improve the efficiency, accuracy, and robustness of multi-component compressible flow simulations. At the core of our approach is an Entropy-Stable formulation that preserves kinetic energy and integrates a Double-Flux scheme tailored for multi-component flows with variable specific heat ratios. This formulation yields low-dissipation, oscillation-free solutions and enhances stability compared to standard fully conservative methods. To further improve robustness, we introduce a new hybrid dissipation strategy that blends the Entropy-Stable/Double-Flux approach with conventional dissipation mechanisms. We provide a rigorous proof that the resulting numerical flux satisfies a semi-discrete entropy inequality, ensuring consistency with the second law of thermodynamics. For time integration, we employ an explicit Runge-Kutta scheme in combination with adaptive mesh refinement to capture local flow features dynamically. The method is implemented within an existing compressible Navier-Stokes solver based on OpenFOAM. Benchmark cases, including multi-dimensional interface and shock-interface interactions, demonstrate the effectiveness of the proposed framework. The results confirm its favorable stability and robustness, validating the approach as a promising advancement for high-fidelity simulations of supersonic flows. |
| title | An Entropy-Stable/Double-Flux scheme for the multi-component compressible Navier-Stokes equations |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2506.13231 |