W. Boscheri, M. Dumbser and M. Righetti A semi-implicit scheme for 3D free surface flows with high-order velocity reconstruction on unstructured Voronoi meshes International Journal for Numerical Methods in Fluids 72
In this paper, we present a computationally efficient semi-implicit scheme for the simulation of hydrostatic three-dimensional free surface flow problems on staggered unstructured Voronoi meshes. A piecewise high-order polynomial vector velocity field is then reconstructed from the scalar normal velocities at the cell faces by using a high-order constrained least-squares reconstruction operator. The reconstructed high-order piecewise polynomial velocity field is used for trajectory integration in a semi-Lagrangian approach to discretize the nonlinear convective terms. For that purpose, a high-order Taylor method is used as ODE integrator. The resulting semi-implicit algorithm is validated on a set of academic test problems and is finally applied to a real-world engineering problem consisting of a curved channel of a hydroelectric power plant.
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