Modeling almost incompressible fluid flow with CNN

Abstract

A novel method for transferring the Navier-Stokes equations for two-dimensional almost incompressible, viscous flow to cellular neural network (CNN) is discussed. The problem has been treated previously by Kozek et al. (1994, 1995), where the CNN layer that represents the pressure had to perform on a much faster time-scale than the layers representing the velocity components. This is a drawback, especially when hardware realizations are considered. The method presented in this contribution avoids the use of a double time-scale CNN and requires fewer connections between the cells. The treatment of boundary conditions is discussed and the accuracy of the results is determined for two known analytical solutions.