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

We propose a new solution method to the two-phase two-fluid six-equation model, which involves six conservation equations. A Roe-type numerical flux is formulated based on a very structured Jacobian matrix. We formulate the Jacobian matrix with arbitrary equation of state and simplify the Jacobian matrix 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 our solver does not depend on the form of the equation of state. The proposed method is applicable to realistic two-phase problems. We applied the numerical solver to the BWR Full-size Fine-mesh Bundle Test (BFBT) benchmark. Considering simplified physical models, the solutions are in very good agreement with solutions from either existing codes and experiment data. The numerical solver using analytical eigenvalue and eigenvector is shown to be stable and robust.