Primitive Form Godunov-Type Scheme for Two-Phase Homogeneous Water Hammer Flows

The primitive form second-order Godunov-type scheme is developed to simulate two-phase homogeneous water hammer flows. Compared with the previous solution schemes applied to homogeneous flows, the proposed model introduces a conservative scheme using primitive variables within a Godunov approach. Simplifications of the variables using a Riemann solver and second-order scheme are developed and demonstrated. Predictions of the proposed model are compared both with those calculated using a conservative Godunov scheme and with published experimental results. Results show that the primitive form second-order Godunov-type scheme reproduces the experimental pressure histories considerably better than the conservative Godunov scheme. In particular, the proposed primitive scheme converges to the correct solution in the presence of shock waves, and performs better than the traditional conservative Godunov scheme both in computational accuracy and efficiency.