Mathematical modelling of transport phenomena in compressible multicomponent flows

TL;DR

This paper introduces a thermodynamically consistent diffuse interface model for compressible multicomponent flows that captures mass diffusion, viscous dissipation, and heat conduction, and demonstrates its effectiveness through numerical simulations.

Contribution

It develops a novel five-equation model with different pressure and velocity relaxation time scales, improving the accuracy of multicomponent flow simulations.

Findings

Model respects thermodynamics and avoids spurious oscillations.

Achieves second-order accuracy in space and time.

Successfully simulates laser-driven RM instability with good agreement to experiments.

Abstract

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.