A Wave-Propagation Based Volume Tracking Method for Compressible Multicomponent Flow in Two Space Dimensions

We present a simple volume-of- uid approach to interface tracking for inviscid compressible
multicomponent ow problems in two space dimensions. The algorithm uses a uniform Carte-
sian grid with some grid cells subdivided by tracked interfaces, approximately aligned with the
material interfaces in the ow 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 (J. Comput. Phys., 123 (1996), pp. 354-368), a conservative high-resolution
wave propagation method is applied on the resulting slightly nonuniform 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 ow features of
the computed solutions are observed when direct comparison of our results are made with
the existing experimental and numerical ones appeared 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 (J. Comput. Phys., 171 (2001), pp. 678-707)
for practical multicomponent problems with general compressible materials characterized by
a Mie-Gr¨ uneisen form of the equation of state.