  In the present paper we propose a reduced temperature non-equilibrium model
for simulating multicomponent flows with inter-phase heat transfer, diffusion
processes (including the viscosity and the heat conduction) and external energy
sources. We derive three equivalent formulations for the proposed model. All
the three formulations assume velocity and pressure equilibrium across the
material interface. These equivalent forms provide different physical
perspectives and numerical conveniences. Temperature equilibration and
continuity across the material interfaces are achieved with the instantaneous
thermal relaxation. Temperature equilibrium is maintained during the heat
conduction process. The proposed models are proved to respect the
thermodynamical laws. For numerical solution, the model is split into a
hyperbolic partial differential equation (PDE) system and parabolic PDE
systems. The former is solved with the high-order Godunov finite volume method
that ensures the pressure-velocity-temperature (PVT) equilibrium conduction.
The parabolic PDEs are solved with both the implicit and the explicit locally
iterative method (LIM) based on Chebyshev parameters. Numerical results are
presented for several multicomponent flow problems with diffusion processes.
Furthermore, we apply the proposed model to simulate the target ablation
problem that is of significance to inertial confinement fusion. Comparisons
with one-temperature models in literature demonstrate the ability to maintain
the PVT property and superior convergence performance of the proposed model in
solving multicomponent problems with diffusions.
