Improved HLL Riemann Solver Including Source Term for Transient Mixed Flow

Abstract

The increasing number of interbasin diversion projects place high demands on fine-grained simulation and control of free-surface and transient mixed flow. Since the numerical oscillation of the transient mixed flow generates more with higher-order finite volume method (FVM), the study is based on a high-precision first-order Harten, Lax, and van Leer (HLL) Riemann solver that considers the source term (HLLS). This study modifies the original HLLS solver and introduces numerical viscosity in the vicinity of filling bores to suppress the numerical oscillations. Furthermore, this study explores the selection of wave velocity calculation methods. A first-order scheme with high accuracy of the free surface and transient flow was developed and verified through various experiments. The results show that the proposed scheme can deal with the bottom slope both in constant free-surface and mixed flow. This is because of the perfect conservation properties of this scheme. Furthermore, the formula shows good performance in transient mixed flow. Therefore, this method can satisfy the requirements for modelling a long-distance complex channel tunnel system.