Linear and Unconditionally Energy Stable Schemes for the Multi-Component Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State (Communications in Computational Physics, 2019)
In this paper we consider numerical solutions of the diffuse interface modelwith Peng-Robinson equation of state for the multi-component two-phase fluid system, which describes real states of hydrocarbon fluids in petroleum industry. A majorchallenge is to develop appropriate temporal discretizations to overcome the strongnonlinearity of the source term and preserve the energy dissipation law in the discretesense. Efficient first and second order time stepping schemes are designed based onthe "Invariant Energy Quadratization" approach and the stabilized method. The resulting temporal semi-discretizations by both schemes lead to linear systems that aresymmetric and positive definite at each time step, and their unconditional energy stabilities are rigorously proven. Numerical experiments are presented to demonstrateaccuracy and stability of the proposed schemes.
Keywords: Diffuse interface model; Peng-Robinson equation of state; linear scheme; Invariant Energy Quadratization; energy stability.