3‐D General Movable Mesh in Water Circulation Modeling

Abstract

Based on the three‐dimensional (3‐D) hydrodynamic Navier‐Stokes equations, a numerical model is developed to simulate circulations in small shallow lakes with particularly irregular geometry. The geometry of the flow field is fitted with a three‐dimensional movable mesh based on a 3‐D coordinate transformation. It conforms to the irregularity of the boundaries and bathymetry and follows at every instant the movement of the free water surface. The equations are integrated over a curvilinear control volume. The discretization process is applied based on MacCormack's fractional step scheme. The surface wind stress is then computed according to Von Karman's approach. A new approximation of the distribution of the eddy viscosity is introduced. The model results are compared against an analytical solution and experimental data. The application of the model to Lake Delaney reveals the effect of the induced circulation on the existing flow pattern. Computed results demonstrate the capability of the model to handle natural complex flow patterns.