A Lagrangian level-set approach for the simulation of incompressible two-fluid flows

摘要

A Lagrangian 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 is employed to decouple the system of non-linear equations. The interface between fluids is represented by the zero level set of a function Φ plus additional marker points of the computational mesh. In the standard Eulerian level-set method, this function is advected through the domain by solving a pure advection equation. To reduce mass conservation errors that can arise from this step, our method employs a Lagrangian technique which moves the nodes of the finite element mesh, and consequently, the information stored in each node. The quality of the mesh is controlled by a remeshing procedure, avoiding bad triangles by flipping edges, inserting or removing vertices from the triangulation. Results of numerical simulations are presented, illustrating the improvements in mass conservation and accuracy of this new methodology.