Accommodating Linear and Nonlinear Boundary Conditions in Wave Digital Simulations of PDE Systems

Abstract

The Wave Digital multidimensional discretization technique, recently proposed by A. Fettweis et al., is a potentially important new method for simulating systems of partial differential equations (PDEs), especially those that model processes appearing in nature. To date, no general method has appeared in the literature indicating how to accommodate boundary conditions in Wave Digital simulations. Since the incorporation of a consistent set of boundary conditions within a given PDE system is a necessary condition for that system even to possess a unique solution, it is clear that accounting for boundary conditions within numeric simulations is just as necessary. We present here a method for accommodating lumped, linear or nonlinear boundary conditions into the Wave Digital simulation of either linear or nonlinear PDE systems. Graphic results from the Wave Digital simulation of a simple acoustics problem are also given.