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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.21076 |
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| _version_ | 1866910850660433920 |
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| author | Chen, Tuowei Du, Zhifang |
| author_facet | Chen, Tuowei Du, Zhifang |
| contents | In the finite volume framework, a Lax-Wendrof type second-order flux solver for the compressible Navier-Stokes equations is proposed by utilizing a hyperbolic relaxation model. The flux solver is developed by applying the generalized Riemann problem (GRP) method to the relaxation model that approximates the compressible Navier-Stokes equations. The GRP-based flux solver includes the effects of source terms in numerical fluxes and treats the stiff source terms implicitly, allowing a CFL condition conventionally used for the Euler equations. The trade-off is to solve linear systems of algebraic equations. The resulting numerical scheme achieves second-order accuracy within a single stage, and the linear systems are solved only once in a time step. The parameters to establish the relaxation model are allowed to be locally determined at each cell interface, improving the adaptability to diverse flow regions. Numerical tests with a wide range of flow problems, from nearly incompressible to supersonic flows with strong shocks, for both inviscid and viscous problems, demonstrate the high resolution of the current second-order scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Second-Order Relaxation Flux Solver for Compressible Navier-Stokes Equations based on Generalized Riemann Problem Method Chen, Tuowei Du, Zhifang Numerical Analysis In the finite volume framework, a Lax-Wendrof type second-order flux solver for the compressible Navier-Stokes equations is proposed by utilizing a hyperbolic relaxation model. The flux solver is developed by applying the generalized Riemann problem (GRP) method to the relaxation model that approximates the compressible Navier-Stokes equations. The GRP-based flux solver includes the effects of source terms in numerical fluxes and treats the stiff source terms implicitly, allowing a CFL condition conventionally used for the Euler equations. The trade-off is to solve linear systems of algebraic equations. The resulting numerical scheme achieves second-order accuracy within a single stage, and the linear systems are solved only once in a time step. The parameters to establish the relaxation model are allowed to be locally determined at each cell interface, improving the adaptability to diverse flow regions. Numerical tests with a wide range of flow problems, from nearly incompressible to supersonic flows with strong shocks, for both inviscid and viscous problems, demonstrate the high resolution of the current second-order scheme. |
| title | A Second-Order Relaxation Flux Solver for Compressible Navier-Stokes Equations based on Generalized Riemann Problem Method |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2502.21076 |