Finite volume simulation of viscous free surface waves using the Cartesian cut cell approach

Abstract

AbstractThe application of the Cartesian cut cell approach in the numerical simulation of two‐dimensional viscous free surface flows is described. The Arbitrary Lagrangian–Eulerian method is adopted to update the moving free water surface in a semi‐Lagrangian scheme, in which a finite volume method of second‐order accuracy in space is used for solving the flow field based on an Eulerian description at each time step. The cut cell approach is employed to track the free surface and solid boundaries across a stationary background Cartesian grid covering the whole fluid, air and solid regions. In this approach, the cells full of air and solid are not calculated explicitly, and apart from the fluid cells, cut cells and merged cells are treated separately in terms of corresponding boundary conditions. In order to validate the present numerical method, current flow past a circular cylinder at various low Reynolds numbers and wave sloshing in a rectangular container are tested first. Further numerical results are obtained for the propagation of regular waves and a wave passing over a submerged dike. The model is also applied to the simulation of radiation waves induced by a forced oscillating submerged circular cylinder. The results indicate that the present numerical model using the Cartesian cut cell approach is highly efficient for solving the wave fields, and fully automatic for generating boundary fitted meshes. These features are particularly useful for moving boundary problems in a larger computational domain and with a longer simulation time. Copyright © 2009 John Wiley & Sons, Ltd.