• triangle to triangle intersection;
  • Cartesian cut cell;
  • free surface capturing;
  • 3D Euler equations;
  • artificial compressibility method


A Cartesian cut cell mesh generation procedure is developed together with a finite volume Euler solver for a two-fluid system with a free surface. A fast and robust triangle to triangle overlap scheme is used to determine the intersection of a body-surface with the background Cartesian mesh. Improvements to the cut cell routines include a new treatment for multiple cuts within a single cell and a surface trimming procedure to ensure a good quality mesh around solid boundaries. The formulae for calculating all necessary information about a cut cell are also presented. These are generic and can be used for arbitrarily irregular boundary elements. A collocated finite volume method with a high resolution Godunov-type scheme in space is used for discretization of the governing flow equations. By computing in both the air and water regions simultaneously in a consistent manner, the free surface is automatically captured as a contact discontinuity in the density field without the need for any special free surface tracking method. The algorithm incorporates the artificial compressibility method with a dual time stepping strategy to maintain a divergence free velocity field. The mathematical formulation including its numerical implementation of the method is reviewed and results for a number of test cases are also presented. Copyright © 2012 John Wiley & Sons, Ltd.