A wave-propagation based volume tracking method for compressible multicomponent flow in two space dimensions

Abstract

We present a simple volume-of-fluid approach to interface tracking for inviscid compressible multicomponent flow problems in two space dimensions. The algorithm uses a uniform Cartesian grid with some grid cells subdivided by tracked interfaces, approximately aligned with the material interfaces in the flow field. A standard volume-moving procedure that consists of two basic steps: (1) the update of a discrete set of volume fractions from the current time to the next and (2) the reconstruction of interfaces from the resulting volume fractions, is employed to find the new location of the tracked interfaces in piecewise linear form at the end of a time step. As in the previous work by LeVeque and the author to front tracking based on a surface-moving procedure (R.J. LeVeque, K.-M. Shyue, Two-dimensional front tracking based on high-resolution wave propagation methods, J. Comput. Phys. 123 (1996) 354–368), a conservative high-resolution wave propagation method is applied on the resulting slightly non-uniform grid to update all the cell values, while the stability of the method is maintained by using a large time step idea even in the presence of small cells and the use of a time step with respect to the uniform grid cells. We validate our algorithm by performing the simulation of a Mach 1.22 shock wave in air over a circular R22 gas bubble, where sensible agreement of some key flow features of the computed solutions are observed when direct comparison of our results are made with the existing experimental and numerical ones that appear in the literature. Other computations are also presented that show the feasibility of the algorithm together with a mixture type of the model equations developed by the author (K.-M. Shyue, A fluid-mixture type algorithm for compressible multicomponent flow with Mie–Grüneisen equation of state, J. Comput. Phys. 171 (2001) 678–707) for practical multicomponent problems with general compressible materials characterized by a Mie–Grüneisen form of the equation of state.