Multiresolution Scheme for Two-Phase Volcanic Flows

The current work addresses a multiresolution scheme for solving two-phase volcanic flow problems. The multiresolution is obtained by a third order interpolating wavelet transform associated to a threshold operator, which allows a sparse representation of the solution in each time step. The spatial operator is solved by the Lax-Friedrich flux splitting approach in which the flux derivatives are approximated by the standard WENO scheme. Two-phase volcanic flows benefit from this type of adaptive schemes since they can accurately capture the formation of shocks and the evolution of rarefaction waves. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions.