Development of a WENO-type numerical solver for two-phase two-fluid six-equation model

Abstract

Advanced discretization methods are pursued to improve accuracy of numerical solver for two-phase two-fluid six-equation model. The Weighted Essentially-Non-Oscillatory (WENO) method was a popular high-order discretization one and was successfully applied to many applications. However, development of the WENO-type numerical solver for two-phase two-fluid six-equation model was limited, which was partly due to the lack of analytical eigenvalues and eigenvectors. In previous work, the author derived an approximate analytical eigenvalues and eigenvectors for the two-phase flow model. The analytical eigenvalues and eigenvectors were formulated in a compact and structured way and were valid for arbitrary form of equation of state. The analytical eigenvalues and eigenvectors enable the development of a new WENO-type numerical solver for the two-phase flow model. In this work, a new WENO-type numerical solver is developed. Numerical tests show that the newly developed WENO-type solver works very well and is capable of capturing all the characteristic waves and sharp discontinuities. The order of accuracy study shows that the accuracy of WENO is at least third-order for a smooth solution.