Numerical study of a high order 3D FEM-Level Set approach for immiscible flow simulation

Numerical simulation of incompressible multiphase flows with immiscible fluids is still a challenging field, particularly for 3D configurations undergoing complex topological changes. In this paper, we discuss a 3D FEM approach with a high-order Stokes elements (Q2/P1) for velocity and pressure on general hexahedral meshes. A discontinuous Galerkin approach with piecewise linear polynomials (dG(1)) is used to treat the Level Set function. The developed methodology allows the application of special redistancing algorithms which do not change the position of the interface. We explain the corresponding FEM techniques for treating the advection steps and surface tension effects, and validate the corresponding 3D code with respect to both numerical test cases and experimental data. The corresponding applications describe the classical rising bubble problem for various parameters and the generation of droplets from a viscous liquid jet in a coflowing surrounding fluid. Both of these applications can be used for rigorous benchmarking of 3D multiphase flow simulations. Stefan Turek Institut für Angewandte Mathematik, TU Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany, e-mail: [email protected] Otto Mierka Institut für Angewandte Mathematik, TU Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany, e-mail: [email protected] Shuren Hysing Department of Mathematics, Shanghai Jiaotong University, Shanghai, China, e-mail: [email protected] Dmitri Kuzmin Lehrstuhl für Angewandte Mathematik III, Universität Erlangen-Nürnberg, Cauerstraße 11, 91058 Erlangen, Germany, e-mail: [email protected]