Mathematical and Numerical Analyses of Dynamical Structure of Numerical Solutions of Two-Dimensional Fluid Equations

Abstract

In the present paper the structure of dynamical systems which were produced by discretizing the two-dimensional Burgers' equation is analyzed. An analytical approach and several numerical nonlinear dynamics approaches such as bifurcation diagram and so on are applied in order to discuss the structure of asymptotic numerical solutions. In particular, the dependence of the nonlinear structure of the numerical solutions on the temporal discretization parameter (Δ t ) are considered. Furtheremore, these numerical approaches are applied to the analyses of the results of more practical two-dimensional CFD (Computational Fluid Dynamics) calculations. The subsonic flow around a circular cylinder is selected as a model and the dependence of the structure of dynamical systems which are given from the computed time series of the drag coefficient on the temporal discretization parameter is discussed.