Linearly Decoupled Energy-Stable Numerical Methods for Multicomponent Two-Phase Compressible Flow

In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multicomponent two-phase compressible flow with a realistic equation of state (e.g., Peng--Robinson equation of state). The methods are constructed based on the scalar auxiliary variable (SAV) approaches for Helmholtz free energy and the intermediate velocities that are designed to decouple the tight relationship between velocity and molar densities. The intermediate velocities are also involved in the discrete momentum equation to ensure consistency with the mass balance equations. Moreover, we propose a componentwise SAV approach for a multicomponent fluid, which requires solving a sequence of linear, separate mass balance equations. The fully discrete schemes are also constructed based on the finite difference/volume methods with the upwind scheme on staggered grids. We prove that the semidiscrete and fully discrete schemes preserve the unconditional energy-dissipation feature. Numerical results are presented to verify the effectiveness of the proposed methods.