An Adaptive Spectral Element Method for Two-Fluid Flows

A new mesh adaptation technique for two dimensional deforming domains has been combined with an Arbitrary-Lagrangian-Eulerian, spectral/hp finite element solver. This combination provides a powerful simulation tool for two-fluid flows; With the spectral/hp finite element method, high accuracy solutions can be obtained efficiently, but by itself this technique is limited to problems with moderate interface deformation. By combining it with a mesh adaptation strategy for deforming domains, large deformation problems can be simulated. In addition, solution-based mesh refinement can be performed which is critical for resolving multi-scale two-fluid problems. The capabilities of these techniques together are demonstrated for some preliminary examples.