SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions

. In this paper, the Peng-Robinson equation of state with dynamic boundary conditions is discussed, which considers the interactions with solid walls. At ﬁrst, the model is introduced and the regularization method on the nonlinear term is adopted. Next, The scalar auxiliary variable (SAV) method in temporal and ﬁnite element method in spatial are used to handle the Peng-Robinson equation of state. Then, the energy dissipation law of the numerical method is obtained. Also, we acquire the convergence of the discrete SAV ﬁnite element method (FEM). Finally, a numerical example is provided to conﬁrm the theoretical result.