A multiphase SPH model based on Roe's approximate Riemann solver for hydraulic flows with complex interface

A multiphase SPH model based on Roe's approximate Riemann solver is proposed to simulate complex interfacial flows in hydraulics. In this multiphase model, the solution to a one-dimensional Riemann problem is introduced into the SPH governing equations to determine the interaction between particles. The Riemann problem is solved by Roe's approximate Riemann solver which may introduce excessive numerical dissipations. To reduce these dissipations, a dissipation limiter is applied. An equivalent relation between the dissipation term in the dissipation limiter and the Reynolds number is derived to model viscous flows of different Reynolds numbers. For flows of high density ratios (up to 1000), stable and smooth interfacial pressure can be obtained. The realistic compressibility can be considered for the light fluid and a larger time step can be allowed, leading to a decrease of the computational cost. To further make the simulation more efficient, an optimized adaptive linked-list search algorithm is introduced. Using this optimized algorithm, the particle interaction list can be updated every dozen of time steps instead of at each time step, which contributes to a significant reduction of the total computational cost. Seven numerical tests are presented to validate this multiphase model. © 2020 Elsevier B.V.