  Typical multispecies compressible Navier-Stokes computations employ
conservative equations for mass fraction transport. Upwind discretisations of
these governing equations produce spurious pressure oscillations at diffuse
contact surfaces between gases of differing ratio of specific heat capacities
which degrade the convergence rate of the algorithm. Adding quasi-conservative
equations for volume fraction can solve this error, however this approach has
been derived only for immiscible fluids. Here, a five-equation
quasi-conservative model is proposed that includes the effects of species
diffusion, viscosity and thermal conductivity. The derivation of the model is
presented, along with a numerical method to solve the governing equations at
second order accuracy in space and time. Formal convergence studies demonstrate
the expected order of accuracy is achieved for three benchmark problems,
cross-validated against two standard mass fraction models. In these test cases,
the new model has between 2 and 10 times lower error for a given grid size.
Simulations of a two-dimensional air-SF_6 Richtmyer-Meshkov instability
demonstrate that the new model converges to the solution with four times fewer
points in each direction when compared to the mass fraction model in an
identical numerical framework. This represents an ~40 times lower computational
cost for an equivalent error in two-dimensional computations. The proposed
model is thus very suitable for Direct Numerical Simulation and Large Eddy
Simulation of compressible mixing.
