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 bound-ary 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 el-ement 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 ex-ample is provided to confirm the theoretical result.