Symmetry Reduction and Numerical Solution of Von K a ´ rm a ´ n Swirling Viscous Flow

Abstract

Abstract:In this paper, the numerical solutions of von Kármán swirling viscous flow are obtained based on the effective combination of the symmetry method and the Runge-Kutta method. Firstly, the multi-parameter symmetry of von Kármán swirling viscous flow is determined based on the differential characteristic set algorithm. Secondly, we used the symmetry to reduce von Kármán swirling viscous flow to an initial value problem of the original differential equations. Finally, we numerically solve the initial value problem of the original differential equations by using the Runge-Kutta method.