Three‐dimensional mesh embedding for the Navier–Stokes equations using upwind control volumes

Abstract

AbstractA numerical model for the compressible Navier–Stokes equations using local mesh embedding is presented. The model solves for three‐dimensional turbulent flow using an algebraic mixing length model of turbulence. The technique of control volume upwinding is used to produce a novel treatment, whereby the hanging nodes on the mesh interfaces are left with null control volumes. This yields an efficient discretization scheme which ensures second‐order accuracy, flux conservation and stability at the mesh interfaces, whilst retaining a simple interpolative treatment for the hanging nodes. The discrete flow equations are solved using the semi‐implicit pressure correction method. The accuracy of the embedded mesh solver is demonstrated by modelling the three‐dimensional flow through a cascade of turbine vanes at design and off‐design conditions. Mesh embedding gives a saving of 48% in the number of nodes. The embedded mesh solutions compare well with fine structured mesh solutions and experimental measurements. The capability of the embedded mesh solver to perform solution adaptive calculations is demonstrated using a two‐dimensional mid‐height section of the cascade at the off‐design flow conditions.