On the approximate Riemann solver for the two-phase two-fluid six equation model and application to real system

A new method is proposed to solve the two-phase two-fluid six-equation model. A Roe-type numerical flux is formulated based on a very structured Jacobian matrix. The Jacobian matrix with arbitrary equation of state is formulated and simplified with the help of a few auxiliary variables, e.g. isentropic speed of sound. Because the Jacobian matrix is very structured, the eigenvalue and eigenvector can be obtained analytically. An explicit Roe-type numerical solver is constructed based on the analytical eigenvalue and eigenvector. A critical feature of the method is that the formulation of the solver does not depend on the form of the equation of state. The proposed method is applicable to realistic two-phase problems. It is applied to the BWR Full-size Fine-mesh Bundle Test (BFBT) benchmark. Considering simplified physical models, the solutions are in very good agreement with those from both existing codes and experiment data. The numerical solver using analytical eigenvalue and eigenvector is shown to be stable and robust.