Modelling of Compressible Multi-Component Two-Phase Flow with Multi-Component Navier Boundary Condition (Communications in Computational Physics, 2024)
In this paper, we derive a dimensionless model for compressible multi-component two-phase flows with Peng-Robinson equation of state (EoS), incorporatedwith the multi-component Navier boundary condition (MNBC). We propose three linearly decoupled and energy-stable numerical schemes for this model. These schemesare developed based on the Lagrange multiplier approach for bulk Helmholtz free energy and surface free energy. One of them is based on a component-wise approach,which requires solving a sequence of linear, separate mass balance equations andleads to an original discrete energy that unconditionally dissipates. Another numerical scheme is based on a component-separate approach, which requires solving a sequence of linear, separate mass balance equations but leads to a modified discrete energy dissipating under certain conditions. Numerical results are presented to verifythe effectiveness of the proposed methods.
Keywords: Compressible; Helmholtz free energy; energy-stable; Lagrange multiplier; multi-component; Peng-Robinson EoS.