Hybrid Artificial Viscosity-Central-Upwind Scheme for Recirculating Turbulent Shallow Water Flows

Abstract

In this paper, a hybrid artificial viscosity–central-upwind (AV-CU) scheme is proposed for simulating recirculating turbulent shallow water flows by combining the artificial viscosity (AV) technique with the central-upwind (CU) scheme. Two-dimensional (2D) depthaveraged Reynolds-averaged Navier–Stokes (DA-RANS) equations are solved using the AV technique, whereas the CU scheme is employed to compute the κ–ϵ model. The model is spatially and temporally second-order accurate. Scalable wall functions (ScWFs) are employed, thus becoming flexible in generating meshes without having to estimate the wall friction velocity at the initial time step as if the standard wall functions (StWFs) were used. The results benefit strongly from this hybrid approach being more accurate than the CU and Harten-Lax-van Leer-contact (HLLC) schemes—and 1.52× cheaper than the HLLC scheme for modeling recirculating turbulent flows. As such, the proposed approach could become a promising method for practical engineering purposes to simulate turbulent shallow water flows more efficiently and accurately.