Stabilised finite-element methods for solving the level set equation with mass conservation

摘要

Finite-element methods are studied for solving moving interface flow problems using the level set approach and a stabilised variational formulation proposed in Toure and Soulaimani (2012; Toure and Soulaimani To appear in 0064"> 2016), coupled with a level set correction method. The level set correction is intended to enhance the mass conservation satisfaction property. The stabilised variational formulation (Toure and Soulaimani 2012; Toure and Soulaimani, To appear in 0064"> 2016) 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.