An Energy Stable Nonlinear Incompressible Multi-Phase Flow Formulation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915082836901888 |
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| author | Nordström, Jan Malan, Arnaud. G. |
| author_facet | Nordström, Jan Malan, Arnaud. G. |
| contents | We show that a reformulation of the governing equations for incompressible multi-phase flow in the volume of fluid setting leads to a well defined energy rate. Weak nonlinear inflow-outflow and solid wall boundary conditions complement the development and lead to an energy estimate in terms of external data. The new formulation combined with summation-by-parts operators lead to provably nonlinear energy stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19525 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Energy Stable Nonlinear Incompressible Multi-Phase Flow Formulation Nordström, Jan Malan, Arnaud. G. Analysis of PDEs Numerical Analysis 65M12 G.1.8 We show that a reformulation of the governing equations for incompressible multi-phase flow in the volume of fluid setting leads to a well defined energy rate. Weak nonlinear inflow-outflow and solid wall boundary conditions complement the development and lead to an energy estimate in terms of external data. The new formulation combined with summation-by-parts operators lead to provably nonlinear energy stability. |
| title | An Energy Stable Nonlinear Incompressible Multi-Phase Flow Formulation |
| topic | Analysis of PDEs Numerical Analysis 65M12 G.1.8 |
| url | https://arxiv.org/abs/2406.19525 |