  We have developed a high-order numerical method for the 3D simulation of
viscous and inviscid multiphase flow described by a homogeneous equilibrium
model and a general equation of state. Here we focus on single-phase, two-phase
(gas-liquid or gas-solid) and three-phase (gas-liquid-solid) flow of CO2 whose
thermodynamic properties are calculated using the Span-Wagner reference
equation of state. The governing equations are spatially discretized on a
uniform Cartesian grid using the finite-volume method with a fifth-order
weighted essentially non-oscillatory (WENO) scheme and the robust first-order
centered (FORCE) flux. The solution is integrated in time using a third-order
strong-stability-preserving Runge-Kutta method. We demonstrate close to
fifth-order convergence for advection-diffusion and for smooth single- and
two-phase flows. Quantitative agreement with experimental data is obtained for
a direct numerical simulation of an air jet flowing from a rectangular nozzle.
Quantitative agreement is also obtained for the shape and dimensions of the
barrel shock in two highly underexpanded CO2 jets.
