Wave equation hydrodynamics on deforming elements

Abstract

Abstract The shallow water wave equation is derived in a general deforming co‐ordinate system. A weak form is developed which displays the natural boundary condition prominently and which may be implemented on C 0 elements. A time‐stepping algorithm is implemented with clastic mapping of interior node motion. Lossless test cases show agreement with analytic solutions. A simple hypothetical test case shows intuitively good behaviour at length scales approaching those required of estuarine simulations.