Numerical integration of fluid dynamics problems by discrete dynamical systems

A discrete time algorithm for the numerical solution of the Navier–Stokes equations, namely the set of nonlinear partial differential equations (PDEs) characterizing the flow of viscous and compressible fluids is presented. The good performance of the algorithm is guaranteed by preserving the passivity property of both the continuous time and discrete multidimensional dynamical descriptions of the Navier–Stokes equations. The present results are applied to compute the steady flows between parallel plates (Couette shear flows).