Energy-stable numerical method for compressible flow with generalized Navier boundary condition

In this paper, we derive a dimensionless model for pure-component two-phase compressible flows with Van der Waals equation of state (EoS) and generalized Navier boundary condition (GNBC). We propose three energy-stable numerical schemes. One of them is based on the scalar auxiliary variable (SAV) approach for Helmholtz free energy for bulk and surface free energy, which leads to a modified energy and is proved to be unconditional stable. Another numerical scheme is based on the Lagrange multiplier approach for Helmholtz free energy for bulk and surface free energy, which leads to the original energy and is proved to be unconditional stable. Numerical results are presented to verify the effectiveness of the proposed methods. •A dimensionless model for two-phase compressible flows with GNBC is presented.•Three energy-stable numerical schemes are presented.•The numerical scheme leads to the original energy dissipation.