A two-fluid spectral-element method Original Research Article

A spectral-element formulation for two-fluid flows is presented which uses arbitrary-Lagrangian–Eulerian mesh movement with an unstructured mesh. The main advantage of this approach is that the spectral elements provide a high order-of-accuracy while the unstructured mesh allows geometric flexibility. The accuracy of this approach is demonstrated for several relatively simple configurations with and without moving interfaces. Another unique feature of the formulation as compared to previous (single-fluid) spectral-element methods is that a fully implicit time advancement scheme is used. This is made possible by the development of a spectral-multigrid iteration which solves the implicit governing equations in a fixed number of iterations insensitive to both the polynomial degree of the spectral elements and the number of elements in the mesh. By using this approach, solutions for both stiff unsteady problems and steady-state problems can be obtained efficiently.