On the derivation of the nonlinear discrete equations numerically integrating the Euler PDEs (Q1303525)

Summary: The Euler equations, namely a set of nonlinear partial differential equations (PDEs) mathematically describing the dynamics of inviscid fluids, are numerically integrated by directly modeling the original continuous-domain physical system by means of a discrete multi-dimensional passive (MD-passive) dynamic system, using principles of MD nonlinear digital filtering. The resulting integration algorithm is highly robust, thus attenuating the numerical noise during the execution of the steps of the discrete algorithm. The nonlinear discrete equations approximating the inviscid fluid dynamic phenomena are explicitly determined. Furthermore, the wave digital filter circuit realization of the Euler equations is determined. Finally, two alternative MD wave digital filter sets of nonlinear equations, for integrating the Euler equations, are analytically determined.