Discrete Dynamics in Nature and Society
Volume 2 (1998), Issue 1, Pages 41-51

On the derivation of the nonlinear discrete equations numerically integrating the Euler PDEs

F. N. Koumboulis,1 M. G. Skarpetis,2 and B. G. Mertzios3

1University of Thessaly, School of Technological Sciences, Department of Mechanical & Industrial Engineering, Volos, Greece
2National Technical University of Athens, Department of Electrical and Computer Engineering, Division of Electroscience, Greece
3Democritus University of Thrace, Department of Electrical and Computer Engineering, Xanthi 67100, Greece

Received 27 September 1997

Copyright © 1998 F. N. Koumboulis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 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 WDF circuit realization of the Euler equations is determined. Finally, two alternative MD WDF set of nonlinear equations, integrating the Euler equations are analytically determined.