Multi-material mixing

In the study of multi-material mixing,
we are currently implementing and validating multifluid algorithms.
Based on the problems of interest (turbulent mixing in multi-material
flows, *e.g.*, compressible Rayleigh-Taylor instability,
Richtmyer-Meshkov instability), flows of multiple non-reacting fluid
components are considered. A certain class of schemes is selected;
specific properties of the schemes are identified as essential to
carry out direct numerical simulations and a suite of benchmark is
defined to test these properties.

In accelerated multi-material flows (*e.g.*,
Rayleigh-Taylor and Richtmyer-Meshkov instabilities), the turbulence
evolution is different from the classical shear-dominated turbulence
of aeronautical applications. Interactions between shock waves and
density variations (*e.g.*, interface) lead to baroclinic
vorticity generation along the interfaces. Instabilities are active on
multiple scales: at the macroscopic level, they lead to the
deformation of certain flow structures, while they drive the turbulent
mixing at the microscopic level. Regions of high vorticity then evolve
into turbulent mixing zones. Material interfaces are thin regions over
which the composition changes from one fluid to another. Because the
focus of the present work is on *mixing*, an interface-*capturing*
approach is pursued, as opposed to interface-tracking and in analogy
to shock-capturing. Because the interface is smeared over a few grid
points, it is important that the dissipation of the scheme is low.
Additional properties essential for stable and accurate simulations
include discrete conservation and the prevention of oscillations at
discontinuities (interfaces and shocks) that may have large jumps in
pressure and/or density across them.

Quasi-conservative schemes extended to
high-order accuracy are considered here in the context of the *
Hybrid* method. In these scheme, supplementary
advection equations (for the mass fraction and/or for a function of
the ratio of specific heats) are solved in conjunction with the
equations of motion. These schemes have currently been implemented in
a multi-dimensional finite volume shock-capturing framework and can be
used to simulate various multicomponent flow problems. An example
thereof includes the two-dimensional shock-bubble interaction shown in
figure 1. In this problem, the baroclinic vorticity generated by the
passage of the shock leads to the formation of a re-entrant jet;
complex flow features can be observed and regions of low pressure
(high vorticity) are present.

Figure 1. Interaction of a left-moving Mach 1.22 shock wave in air with
a
helium cylinder (top: numerical Schlieren; bottom: pressure). |

The quasi-conservative schemes are
currently being implemented in a finite difference framework into the
*Hybrid* code. The treatment of interface is similar to that of
shockwaves, in that an interface sensor (*e.g.*, based on the mass fraction field) is required.
Thus a high-order accurate WENO scheme is used near interfaces,
similarly to shock waves, in order to prevent the generation of
spurious oscillations. Each of the codes considered in the present
SciDAC project will undergo a series of stringent test
problems to evaluate its performance in multifluid problems. The
careful development of the multifluid algorithm and its verification
via the stringent suite of test problems is crucial in order to
successfully simulate the multi-material problems of interest, *i.e.*,
compressible Rayleigh-Taylor instability and Richtmyer-Meshkov
instability, and to study certain specific aspects, *e.g.*,
turbulent mixing and sub-grid modeling.