Stabilised finite-element methods for solving the level set equation with mass conservation
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Bibliographic record
Abstract
Finite-element methods are studied for solving moving interface flow problems using the level set approach and a stabilised variational formulation proposed in Touré and Soulaïmani (2012; Touré and Soulaïmani To appear in 2016 Touré, Mamadou Kabirou, and Azzeddine Soulaïmani. To appear in 2016. “Stabilized Finite Element Methods for Solving the Level Set Equation without Renitialization.” Computers & Mathematics with Applications. doi:10.1016/j.camwa.2016.02.028[Crossref] , [Google Scholar]), coupled with a level set correction method. The level set correction is intended to enhance the mass conservation satisfaction property. The stabilised variational formulation (Touré and Soulaïmani 2012; Touré and Soulaïmani, To appear in 2016 Touré, Mamadou Kabirou, and Azzeddine Soulaïmani. To appear in 2016. “Stabilized Finite Element Methods for Solving the Level Set Equation without Renitialization.” Computers & Mathematics with Applications. doi:10.1016/j.camwa.2016.02.028[Crossref] , [Google Scholar]) constrains the level set function to remain close to the signed distance function, while the mass conservation is a correction step which enforces the mass balance. The eXtended finite-element method (XFEM) is used to take into account the discontinuities of the properties within an element. XFEM is applied to solve the Navier–Stokes equations for two-phase flows. The numerical methods are numerically evaluated on several test cases such as time-reversed vortex flow, a rigid-body rotation of Zalesak's disc, sloshing flow in a tank, a dam-break over a bed, and a rising bubble subjected to buoyancy. The numerical results show the importance of satisfying global mass conservation to accurately capture the interface position.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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