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Summary: A SIMPLE METHOD FOR COMPRESSIBLE MULTIFLUID FLOWS
RICHARD SAUREL AND R´EMI ABGRALL
SIAM J. SCI. COMPUT. c 1999 Society for Industrial and Applied Mathematics
Vol. 21, No. 3, pp. 11151145
Abstract. A simple second order accurate and fully Eulerian numerical method is presented for
the simulation of multifluid compressible flows, governed by the stiffened gas equation of state, in
hydrodynamic regime. Our numerical method relies on a second order Godunov-type scheme, with
approximate Riemann solver for the resolution of conservation equations, and a set of nonconservative
equations. It is valid for all mesh points and allows the resolution of interfaces. This method works
for an arbitrary number of interfaces, for breakup and coalescence. It allows very high density ratios
(up to 1000). It is able to compute very strong shock waves (pressure ratio up to 105). Contrary
to all existing schemes (which consider the interface as a discontinuity) the method considers the
interface as a numerical diffusion zone as contact discontinuities are computed in compressible single
phase flows, but the variables describing the mixture zone are computed consistently with the density,
momentum and energy. Several test problems are presented in one, two, and three dimensions. This
method allows, for example, the computation of the interaction of a shock wave propagating in a
liquid with a gas cylinder, as well as RichtmeyerMeshkov instabilities, or hypervelocity impact,
with realistic initial conditions. We illustrate our method with the Rusanov flux. However, the same
principle can be applied to a more general class of schemes.
Key words. compressible multicomponents flows, compressible multifluid flows, Godunov
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