  The present article proposes a diffuse interface model for compressible
multicomponent flows with transport phenomena of mass, momentum and energy
(i.e., mass diffusion, viscous dissipation and heat conduction). The model is
reduced from the seven-equation Baer-Nuziato type model with asymptotic
analysis in the limit of instantaneous mechanical relaxations. The main
difference between the present model and the Kapila's five-equation model
consists in that different time scales for pressure and velocity relaxations
are assumed, the former being much smaller than the latter. Thanks to this
assumption, the velocity disequilibrium is retained to model the mass diffusion
process. Aided by the diffusion laws, the final model still formally consists
of five equations. The proposed model satisfy two desirable properties : (1) it
respects the laws of thermodynamics, (2) it is free of the spurious oscillation
problem in the vicinity of the diffused interface zone. The mass diffusion,
viscous dissipation and heat conduction processes contribute parabolic partial
differential equations that are solved with the Chebyshev method of local
iterations. Numerical results show that the proposed model maintains pressure,
velocity and temperature equilibrium near the diffused interface. Convergence
tests demonstrate that the numerical methods achieve second order in space and
time. The proposed model and numerical methods are applied to simulate the
laser-driven RM instability problem in inertial confinement fusion, good
agreement with experimental results are observed.
