Abstract: The unsteady two-dimensional impulsive flow of a
viscous incompressible fluid about a stationary circular cylinder of an infinite
length is considered. The governing equations of motion are formulated in terms
of the vorticity and stream functions. A new implicit special finite-difference
method is used to approximate the vorticity-transport equation. An energy
function is formulated using this new implicit finite-difference formula.
Poisson’s equation is discretized using the standard central-difference
approximation and a corresponding energy function is formulated. A Hopfield
Neural Network is then designed to minimize the two energy functions
simultaneously. The results are compared to numerical solutions obtained by the
successive over relaxation (SOR) iterative method for the range of the Reynolds number on different
grid sizes.
Keywords and phrases: circular cylinder, implicit special finite-difference method, Hopfield neural nets, energy function.
