Thermodynamic-consistent multiple-relaxation-time lattice Boltzmann equation model for two-phase hydrocarbon fluids with Peng-Robinson equation of state

In this work, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) equation model with Beam-Warming (B-W) scheme is proposed to simulate a multi-phase fluid system with Peng-Robinson (P-R) equation of state (EOS). The mathematical model of the multi-phase fluid flow is derived based on the NVT-based framework, where the Helmholtz free energy of P-R EOS is introduced. The nonideal force in the multi-phase flow is directly computed from the free energy in order to obtain a more compact formulation of hydrodynamic equations, which is termed as potential form. The MRT-LB model is developed based on the potential form of hydrodynamic equations, which can eliminate spurious currents effectively. In addition, to capture the tiny nonconvex perturbation from the linear trend of P-R model precisely, the B-W scheme is utilized in the present MRT-LB model, which gives rise to an adjustable Courant-Friedrichs-Lewy (CFL) number. Also, the second order accuracy can be naturally achieved by this scheme without any other requirements and numerical boundary conditions. In the numerical experiments, a realistic hydrocarbon component (isobutane) in three dimensional space is simulated by the proposed MRT-LB model. Numerical results show that the magnitude of spurious currents can be significantly reduced by the present MRT-LB model. In addition, our numerical predictions of surface tension agree well with the experimental data, which verify the effectiveness of the proposed MRT-LB model.