A semi-implicit scheme for 3D free surface flows with high-order velocity reconstruction on unstructured Voronoi meshes

In this paper, we present a computationally efficient semi-implicit scheme for the simulation of three-dimensional hydrostatic free surface flow problems on staggered unstructured Voronoi meshes. For eachpolygonal control volume, the pressure is defined in the cell center, whereas the discrete velocity fieldis given by the normal velocity component at the cell faces. A piecewise high-order polynomialvectorvelocity field is then reconstructed from thescalarnormal velocities at the cell faces by using a new high-order constrained least-squares reconstruction operator. The reconstructed high-order piecewise polynomialvelocity field is used for trajectory integration in a semi-Lagrangian approach to discretize the nonlinearconvective terms in the governing PDE. For that purpose, a high-order Taylor method is used as ODEintegrator. The resulting semi-implicit algorithm is extensively validated on a large set of different academictest problems with exact analytical solution and is finally applied to a real-world engineering problemconsisting of a curved channel upstream of two micro-turbines of a hydroelectric power plant. For thisrealistic case, some experimental reference data are available from field measurements. Copyright © 2012John Wiley & Sons, Ltd.