Space-time mesh refinement method for simulating transient mixed flows

For design and management of large scale tunnels, it is important to model the transitions between pressurized and free-surface flows inside them. The pressurized and free-surface flow regimes are separated by a discontinuity with different wave speeds on two sides, which makes efficient and accurate simulations still challenging. A robust and conservative space-time adaptive mesh refinement (AMR) strategy is proposed to simulate such transient mixed flow. In the present AMR, the mesh resolution is refined adaptively near the interface between two flow regimes, and the flow states at child meshes are determined by a conservative approach which can avoid numerical oscillations. The numerical results from the AMR strategy are validated with analytical and experimental results, which indicates its good ability to capture the interface between two flow regimes and prevent numerical oscillations. The numerical test in a field scale tunnel shows that AMR can speed up simulations of transient mixed flow by 60 times.