| Summary: | In this paper, the numerical solutions of von K a ´ rm a ´ n 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 K a ´ rm a ´ n swirling viscous flow is determined based on the differential characteristic set algorithm. Secondly, we used the symmetry to reduce von K a ´ rm a ´ n 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.
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