On the Derivation of the Nonlinear Discrete Equations Numerically Integrating the Euler PDEs

Abstract

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 multidimensional passive (MD-passive) dynamic system, using principles ofMD 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 WDF circuit rehlization of the Euler equations is determined. Finally, two alternative MD WDF set of nonlinear equations, integrating the Euler equations are analytically determined.