A new moving boundary shallow water wave equation numerical model

Abstract

A new moving boundary shallow water wave equation numerical model is presented. The model is adapted from the Selective Lumped Mass (slm) numerical model. The wetting and drying scheme used is different to that in the slm model. The slm model is finite element in space, using fixed triangular elements, finite difference in time and is explicit. The numerical model has been tested against an analytical solution with good agreement between the numerical and analytical solutions. The numerical model proposed is useful for comparing against analytical moving boundary solutions. The analytical solution is presented for the first time, being for the case of frictionless one dimensional moving boundary nonlinear shallow water wave flow with cosine forcing in a bed with quadratically varying depth. The analytical solution, which is explicit, is useful for testing numerical models.

Application of Numerical Techniques to Tsunami Simulation

“…the Aceh Province, Indonesia. Numerical techniques for moving boundary [5]- [6] was incorporated into the previous study [7].…”

“…In the simulation of moving boundary shallow water equations, what is called, wet and dry scheme [5]- [6] were applied. In a simulation, what is called, wet and dry conditions at each node, were checked at the end of each full-time step with step length .…”

“…Exact solutions of the two-dimensional nonlinear shallow water equations, involving linear bottom friction for flow above parabolic bottom topography were reported [5]- [6]. The characteristic feature of those solutions involves moving shoreline.…”

Moving boundary shallow water flow in a region with quadratic bathymetry

“…The numerical model is adapted from the slm (Selective Lumped Mass) numerical model of Kawahara et al [5]. The wetting and drying scheme used, discussed in detail by Sampson et al [12], is different to that in the slm model. The slm model is finite element in space, using fixed triangular elements, finite difference in time and is explicit.…”

“…The work in this article builds on the work of Thacker [13] for unforced flow in a parabolic canal; Thacker's solutions were discussed in detail by Sampson, Easton and Singh [11]. There have been no other analytical solutions of the nonlinear shallow water wave equations as a consequence of the work of Thacker [13] apart from three previous articles by Sampson et al [10,11,12] and the article by Sachdev, Paliannapan and Sarathy [9].…”