Hybridizing FDM and FVM scheme of high-precision interface fast capture for mixed free-surface-pressurized flow in large cascade water delivery system

In recent years, China has been building several inter-basin water conveyance projects across mountains and deep valleys, leading to the extensive use of long tunnels and inverted siphons. The dynamics of mixed free-surface-pressurized flows are critical for tunnel design and operational safety. However, traditional numerical computation schemes cannot precisely and efficiently capture the pressure interface because the tunnel may be more than 70 km long. This study aims to develop a hybrid scheme that is as fast as the large-time-step Preissmann four-point scheme (FDM) and has the approximate interface accuracy of the finite volume method (FVM) by dynamic grid meshing. A dynamic mesh domain model (DM) is proposed by adopting an FVM mesh with a small time step to dynamically capture the interface and applying an FDM mesh with a large time step to improve computational efficiency. The results show that the method can simulate flow patterns, such as transcritical and pressurized flows, by ignoring the acceleration convection terms and capturing mixed free-surface-pressurized flows conveniently, accurately and efficiently. Furthermore, it can accelerate the computational speed of the transient mixed flow by a factor of approximately 100 when the target tunnel length exceeds 1200 m. The proposed scheme cannot capture the water hammer pressure because of the large time step. However, it can be effectively utilized in large cascade water delivery systems where the flow changes gradually.