Simplex space-time meshes in two-phase flow simulations
For engineers simulating two-phase flows, this method provides a way to locally refine in time near interfaces, improving efficiency without sacrificing accuracy.
The paper presents a space-time finite element method with adaptive temporal refinement for two-phase flow problems, using the interface position to guide refinement. The method achieves efficient and accurate simulations of engineering-relevant two-phase flows.
In this paper, we present the numerical solution of two-phase flow problems of engineering significance with a space-time finite element method that allows for local temporal refinement. Our basis is the method presented in [3], which allows for arbitrary temporal refinement in preselected regions of the mesh. It has been extended to adaptive temporal refinement that is governed by a quantity that is part of the solution process, namely, the interface position in two-phase flow. Due to local effects such as surface tension, jumps in material properties, etc., the interface can, in general, be considered a region that requires high flexibility and high resolution, both in space and in time. The new method, which leads to tetrahedral (for 2D problems) and pentatope (for 3D problems) meshes, offers an efficient yet accurate approach to the underlying two-phase flow problems.