A low-dissipation numerical method based on boundary variation diminishing principle for compressible gas-liquid two-phase flows with phase change on unstructured grid
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909386202415104 |
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| author | Wakimura, Hiro Aoki, Takayuki Xiao, Feng |
| author_facet | Wakimura, Hiro Aoki, Takayuki Xiao, Feng |
| contents | A low-dissipation numerical method for compressible gas-liquid two-phase flow with phase change on unstructured grids is proposed. The governing equations adopt the six-equation model. The non-conservative terms included in the volume fraction and total energy equations of the six-equation model are defined on cell boundaries using second-order accurate approximations and calculated without interpolating the spatial derivatives. To capture discontinuities such as contact discontinuities and gas-liquid interfaces with low dissipation, the MUSCL-THINC/QQ-BVD scheme, which combines the Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) method and the Tangent Hyperbola for INterface Capturing method with Quadratic surface representation and Gaussian Quadrature (THINC/QQ) method, is employed. The MUSCL method is one of the mainstream numerical solvers for compressible flows, achieving second-order accuracy for smooth solutions, but it introduces excessive numerical dissipation errors near discontinuous solutions. The THINC/QQ method uses a reconstruction function developed for interface capturing on unstructured grids, making use of a sigmoidal function with a quadratic surface. By combining these reconstruction functions according to the Boundary Variation Diminishing (BVD) principle, the MUSCL method is selected for smooth solutions, while the THINC/QQ method is chosen for discontinuous solutions, preserving the solution structure accurately. Several benchmark tests are solved, demonstrating that the MUSCL-THINC/QQ-BVD scheme not only captures contact discontinuities with low dissipation but also resolves dynamically generated gas-liquid interfaces due to phase changes clearly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07704 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A low-dissipation numerical method based on boundary variation diminishing principle for compressible gas-liquid two-phase flows with phase change on unstructured grid Wakimura, Hiro Aoki, Takayuki Xiao, Feng Fluid Dynamics Computational Physics A low-dissipation numerical method for compressible gas-liquid two-phase flow with phase change on unstructured grids is proposed. The governing equations adopt the six-equation model. The non-conservative terms included in the volume fraction and total energy equations of the six-equation model are defined on cell boundaries using second-order accurate approximations and calculated without interpolating the spatial derivatives. To capture discontinuities such as contact discontinuities and gas-liquid interfaces with low dissipation, the MUSCL-THINC/QQ-BVD scheme, which combines the Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) method and the Tangent Hyperbola for INterface Capturing method with Quadratic surface representation and Gaussian Quadrature (THINC/QQ) method, is employed. The MUSCL method is one of the mainstream numerical solvers for compressible flows, achieving second-order accuracy for smooth solutions, but it introduces excessive numerical dissipation errors near discontinuous solutions. The THINC/QQ method uses a reconstruction function developed for interface capturing on unstructured grids, making use of a sigmoidal function with a quadratic surface. By combining these reconstruction functions according to the Boundary Variation Diminishing (BVD) principle, the MUSCL method is selected for smooth solutions, while the THINC/QQ method is chosen for discontinuous solutions, preserving the solution structure accurately. Several benchmark tests are solved, demonstrating that the MUSCL-THINC/QQ-BVD scheme not only captures contact discontinuities with low dissipation but also resolves dynamically generated gas-liquid interfaces due to phase changes clearly. |
| title | A low-dissipation numerical method based on boundary variation diminishing principle for compressible gas-liquid two-phase flows with phase change on unstructured grid |
| topic | Fluid Dynamics Computational Physics |
| url | https://arxiv.org/abs/2411.07704 |