A split scheme for the two-fluid seven-equation model with source terms

Abstract

We develop a numerical solver based on the split scheme for the two-fluid seven-equation model. The solver contains two parts, that are the homogenous partial differential equations (PDEs) system solver and the ordinary differential equations (ODEs) system solver. The homogenous PDEs system solver employs the weak formulation of Roe scheme, and the general equations of state (EOS) are considered. The ODEs system solver employs implicit methods which are backward Euler method, trapezium rule method and TR-BDF2, because the relaxation terms lead to stiffness. The algebraic equations system deduced from the ODEs system is solved by Newton method. The solver is tested to assess two-phase Riemann problem, relaxation terms test problems, faucet flow problem and sedimentation problem. The influence of the number of cells, the performances of ODE solvers and the numerical diffusion are discussed. The solver performs well. But, the prediction of shock solution is not accurate. The numerical diffusion is influenced by the sound speed.