WENO Wavelet Method for a Hyperbolic Model of Two-Phase Flow in Conservative Form

The current work presents a WENO wavelet adaptive method for solving multiphase flow problems. The grid adaptivity in each time step is obtained by the application of a thresholded interpolating wavelet transform, which allows the construction of a small yet effective sparse point representation of the solution. The spatial operator is solved by the Lax-Friedrich flux splitting approach in which the flux derivatives are approximated by the WENO scheme. Hyperbolic models of two-phase flow in conservative form are efficiently solved since shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions.