Numerical Study Of Peng-Robinson Equation Of State

This thesis mainly studies the numerical simulation of the Peng-Robinson equation of state.We study the Peng-Robinson equation of state with dynamic boundary conditions,and construct a scalar auxiliary variation-finite element scheme(SAV-FEM).Then we analyze the SAV-FEM scheme,and obtain first-order convergence results.At the same time,the time exponential difference scheme(ETD)is used for the Peng-Robinson equation of state with periodic boundary conditions.In the end,three numerical simulations with different initial values are given.In the chapter 2 of this paper,we use the SAV-FEM method to carry out error analysis and numerical simulation for Peng-Robinson equation of state with dynamic boundary conditions.Firstly,we introduce the Peng-Robinson equation of state,and regularize the nonlinear term to eliminating the singularity at the points.Then,the SAV method is used in temporal and the finite element method is used in space to deal with the PengRobinson equation of state.Next,the energy dissipation law of discrete scheme is obtained.At the same time,we obtain the convergence of the discrete SAV-FEM scheme.Finally,a numerical example verifies the theoretical results.In the chapter 3 of the paper,we use the ETD scheme of the difference method to discretizing the Peng-Robinson equation of state with periodic boundary conditions.In chapter 3,the discrete Fourier transform and its inverse transform are introduced.Then the first and second order ETD Runge-Kutta schemes are described and we give the corresponding algorithms.Finally,three numerical examples are given to simulate the dynamic evolution of the gas-liquid two-phase flow systems.