Towards parallel WENO wavelet methods for the simulation of compressible two-fluid models

In the current work a seven-equation model of two-dimensional two-phase flow problems is analyzed by a parallel formulation of a WENO multiresolution scheme. The scheme adaptivity is obtained by a third order interpolating wavelet transform associated to a threshold operator. In this way, a sparse representation of the vector solution is obtained at each time step. The evolution in time is performed by a third order TVD Runge-Kutta scheme. For the spatial integration on the sparse grid, the Lax-Friedrich flux splitting scheme is considered in which the flux derivatives are approximated by the standard fifth-order WENO scheme. The parallel formulation of the code is based on OpenMP, which is crucial for the computation of long term simulations with shorter computational times. The considered adaptive parallel WENO scheme has the capability of accurately capturing the formation of shocks and the evolution of rarefaction waves, as evinced by the presented numerical simulations.