Implicit dual time-stepping positivity-preserving entropy-stable schemes for the compressible Navier-Stokes equations
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| Format: | Preprint |
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2025
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| author | Sayyari, Mohammed Yamaleev, Nail K. |
| author_facet | Sayyari, Mohammed Yamaleev, Nail K. |
| contents | We generalize the explicit high-order positivity-preserving entropy stable spectral collocation schemes developed in Upperman 2023 and Yamaleev 2023 for the three-dimensional (3D) compressible Navier Stokes equations to a time implicit formulation. The time derivative terms are discretized by using the first- and second-order implicit backward difference formulas (BDF1 and BDF2) that are well suited for solving steady-state and time-dependent viscous flows at high Reynolds numbers, respectively. The nonlinear system of discrete equations at each physical time step is solved by using a dual time-stepping technique. The proposed scheme is provably entropy stable and positivity-preserving and provides unconditional stability properties in the physical time. Numerical results demonstrating the accuracy and positivity-preserving properties of the new dual time-stepping scheme are presented for supersonic viscous flows with strong shock waves and contact discontinuities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_11333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Implicit dual time-stepping positivity-preserving entropy-stable schemes for the compressible Navier-Stokes equations Sayyari, Mohammed Yamaleev, Nail K. Numerical Analysis 65L06, 65M12, 65M70, 76J20, 76M25 We generalize the explicit high-order positivity-preserving entropy stable spectral collocation schemes developed in Upperman 2023 and Yamaleev 2023 for the three-dimensional (3D) compressible Navier Stokes equations to a time implicit formulation. The time derivative terms are discretized by using the first- and second-order implicit backward difference formulas (BDF1 and BDF2) that are well suited for solving steady-state and time-dependent viscous flows at high Reynolds numbers, respectively. The nonlinear system of discrete equations at each physical time step is solved by using a dual time-stepping technique. The proposed scheme is provably entropy stable and positivity-preserving and provides unconditional stability properties in the physical time. Numerical results demonstrating the accuracy and positivity-preserving properties of the new dual time-stepping scheme are presented for supersonic viscous flows with strong shock waves and contact discontinuities. |
| title | Implicit dual time-stepping positivity-preserving entropy-stable schemes for the compressible Navier-Stokes equations |
| topic | Numerical Analysis 65L06, 65M12, 65M70, 76J20, 76M25 |
| url | https://arxiv.org/abs/2504.11333 |