The Lagrangian solution of transient problems in hydrodynamics using a triangular mesh

Numerical algorithms for a Lagrangian treatment of incompressible hydrodynamics with free surfaces are developed and applied. The method centers about the use of a triangular general-connectivity finite-difference mesh. The added flexibility arising from this triangular mesh permits accurate long-time solutions of complicated flows with shear and waves in free-surface problems. The techniques discussed here are applied to nonlinear free-surface waves and to unstable shear flow beneath a free surface in two dimensions.