The derivation of macroscopic models for particle-laden gas flows is reviewed.
Semi-implicit and Newton-like finite element methods are developed for the stationary
two-fluid model governing compressible particle-laden gas flows. The
Galerkin discretization of the inviscid fluxes is potentially oscillatory and unstable.
To suppress numerical oscillations, the spatial discretization is performed by
a high-resolution finite element scheme based on algebraic flux correction. Amultidimensional
limiter of TVD type is employed. An important goal is the efficient
computation of stationary solutions in a wide range of Mach numbers, which is
a challenging task due to oscillatory correction factors associated with TVD-type
flux limiters and the additional strong nonlinearity caused by interfacial coupling
terms. A semi-implicit scheme is derived by a time-lagged linearization of the
nonlinear residual, and a Newton-like method is obtained in the limit of infinite
CFL numbers. The original Jacobian is replaced by a low-order approximation.
Special emphasis is laid on the numerical treatment of weakly imposed boundary
conditions. It is shown that the proposed approach offers unconditional stability
and faster convergence rates for increasing CFL numbers. The strongly coupled
solver is compared to operator splitting techniques, which are shown to be less robust