Approach to simulating acoustics in supersonic flow by means of multidimensional vector-WDFs

Algorithms based on multidimensional wave digital filters (MDWDFs) can be used to numerically integrate partial differential equations (PDEs) governing a physical system. The method consists in replacing the original physical system by a discrete passive dynamical system. This system behaves in the same way as the original one, except that it is governed by difference equations instead of differential equations. In this paper an MDWDF will be derived that models the propagation of acoustic waves in supersonic flow in an inviscid homentropic fluid. Starting from a set of partial differential equations (PDEs) of fluid dynamics, the EULER equations, a multidimensional KIRCHHOFF circuit (MD-K) that is described by a set of linearized PDEs will be developed. Choosing a matched coordinate transformation problems occur concerning the realizability of a scalar structure of the MDWDF. Hence a vector representation of the reference network will be given and the theory of vector MDWDFs will be applied