The integrated space-time finite volume method

Abstract

The integrated space-time finite volume method for predicting time-dependent fluid flow problems is developed. By enforcing discrete conservation over space-time control volumes hich fill the space-time domain, this method satisfies global conservation in space-time. Unlike traditional finite volume methods, there is no need to incorporate the Leibnitz Rule or the geometrical conservation law into the discretization. The method is validated using a variety of two-dimensional problems featuring both prescribed and free boundary motion. Advances in other aspects of cell-centered finite volume discretization - most notably in the modelling of diffusion terms and free surface flows - are also described.