Compressible Two-Phase Flow Using a Fourth Order Time-Accurate TVD-SLIC Method

The numerical simulation of compressible two-phase flow is investigated in the context of the mixture model with non-zero relative velocity. A fourth-order time accurate method is adapted to a TVD-SLIC flux using a superbee limiter. Initial conditions are chosen using volcanic magma interacting with air and the numerical results are compared with those found from other numerical methods. The most important of these is the use of Mathematica for the direct numerical simulations of the approximate Riemann solution. The numerical methods are shown to be in close agreement with the exception of oscillations brought on by the introduction of numerical dispersion in the case of the fourth order method.