Amacroscopic two-fluid model of compressible particle-laden gas flows is
considered. The governing equations are discretized by a high-resolution
finite element method based on algebraic flux correction. A multidimensional
limiter of TVD type is employed to constrain the local characteristic
variables for the continuous gas phase and conservative fluxes for a suspension
of solid particles. Special emphasis is laid on the efficient computation
of steady state solutions at arbitrary Mach numbers. To avoid
stability restrictions and convergence problems, the characteristic boundary
conditions are imposed weakly and treated in a fully implicit manner.
A two-way coupling via the interphase drag force is implemented using
operator splitting. The Douglas-Rachford scheme is found to provide a
robust treatment of the interphase exchange terms within the framework
of a fractional-step solution strategy. Two-dimensional simulation results
are presented for a moving shock wave and for a steady nozzle flow.