A new method for moving-boundary hydrodynamic problems in shallow water

Dynamic moving-boundary problems are a common occurrence in shallow-water h ydraulics, yet no generally applicable or computationally efficient framewo rk is available for their solution. In this paper a new scheme is presented that attempts to solve the problem of representing moving-boundary shallow -water hydrodynamics on fixed numerical grids. The scheme consists of three parts: identification of partly wet elements; the development of physicall y appropriate treatments to deal with mass and momentum conservation discre pancies in such areas within a two-dimensional finite-element frame work; a nd the development and testing of a proof of mass conservation for the new scheme. In particular, the algorithm is unique in distinguishing between fl ooding and dam-break partly wet elements, in contrast to previous solutions to this problem which typically treat both types in a similar fashion. In reality, consideration of the problem physics shows that mass and momentum conservation discrepancies can only be positively identified and/corrected on elements of the flooding type. Accordingly, this disaggregation of partl y wet elements into flooding and dam-break types is the approach adopted. T his new scheme is tested against a structured series of numerical experimen ts including objective tests, a newly developed analytical solution for thi s problem and a unique high-resolution topographic dataset recently collect ed for an area of tidal beach on the eastern coast of the UK. The new schem e is shown to be physically realistic, mass conservative and appears to off er a significant improvement over standard finite-element techniques.