Multidimensional wave digital filtering approach for numerical integration of non-linear shallow water equations

An alternative approach based on principles of multidimensional (MD) digital signal processing is presented for the solution of a nonlinear physical system. In essence, it consists in the modelling of a continuous (time-dependent) shallow water system by an equivalent discrete passive dynamical system, i.e. system described by difference equations instead of differential equations having the same behaviour as the original one. Details for arriving at the desired discrete system represented by a MD-WDF model are described. In addition, the nonlinearity of the original PDEs is transformed into a system of nonlinear algebraic equations which can be solved without major difficulty by a least-squares method. Graphical results are given to illustrate physical effects of nonlinear water wave propagation including radiation, reflection, refraction, and crest lines from and across the hard boundaries.