| Abstract: | This paper presents a systematic and theoretically consistent approach for the analysis of free-surface flow, making use of a number of established ideas such as physical component, boundary-fitted co-ordinate (BFC) and Lagrangian front tracking. The approach extends, theoretically as well as numerically, the use of physical component to general non-orthogonal moving grids and provides a numerically stable BFC method with little labour of free-surface positioning, grid generation and grid renewal. The approach conserves mass even at the free surface and allows time step of the order of the Coulant number. The main body of the present paper starts with the definition of analytical space and Riemannian geometry intrinsic to the physical component by applying to it the theorems of differential geometry and manifold theory. Then the governing equations of flow and free surface for the physical component are defined in the general 3D form with the notation of the new Riemannian geometry. Numerical procedures and the fully discrete equations are also presented for the benefit of potential users. Finally, several 2D examples demonstrate the basic performance of the present method by showing the computability of complex free-surface motion. |
