An Arbitrary Lagrangian-Eulerian Level-Set Method for Incompressible Two-Dimensional Two-Fluid Flows

Abstract

An Arbitrary Lagrangian-Eulerian (ALE) level-set method to solve incompressible two-dimensional two-fluid flows is presented. The Navier-Stokes equations are discretized by a Galerkin Finite Element method. A projection method based on approximated LU decomposi- tion is employed to decouple the system of non-linear equations. The interface between fluids is represented by a discrete Heaviside function plus additional marker points and edges of the computational mesh. Our method employs a technique which moves the nodes of the Finite Element mesh with arbitrary velocity. The quality of the mesh is controlled by a remeshing procedure, avoiding bad triangles by flipping edges, inserting or removing vertices from the triangulation. The relative velocity in the ALE approach is designed to allow for a continuous improvement of the mesh, thus reducing the amount of remeshing required to control the quality of the mesh. Results of numerical simulations are presented, illustrating the improvements in computational cost, mass conservation, and accuracy of this new methodology.