Two-Dimensional Two-phase Flow Riemann Problem Simulations Using WENO Wavelet Methods

In the current work a WENO multiresolution scheme is considered for solving a seven-equation model of two-dimensional two-phase flow problems. A third order interpolating wavelet transform associated to a threshold operator is the main tool for obtaining the sparse representation of the solution at each time step. The spatial operator is solved on the sparse grid by the Lax-Friedrich flux splitting scheme in which the flux derivatives are approximated by the standard WENO scheme. A parallel formulation of the code based on OpenMP allows long term simulations to be obtained with shorter computational times. This type of adaptive parallel scheme can accurately capture the formation of shocks and the evolution of rarefaction waves. As a consequence, more detailed structures of the solution are identified, enriching the understanding of the analyzed two-phase flow phenomena.