Optimal evaluation of time step size in numerical simulation for two-dimensional flow sensing

Abstract

This paper proposes an optimal evaluation of time step size for numerical computations based on the 180 numerical simulations of the two-dimensional unsteady flow at low Reynolds number around a circular cylinder. A proper time step size is very important to obtain the right magnitude and frequency for the numerical computation to simulating the real flow. The optimal evaluation is found out after analyzing the influences of the time step sizes on the Strouhal numbers, vortex-shedding periods, lift and drag coefficients. The time step size is found out to be a function of the dividend of vortex-shedding period, the velocity, the feature size and the Strouhal number. The optimal dividend point of the vortex-shedding periods for the optimal time step size is in the interval $$\left[ {50,90} \right) $$ , and the average partition counts of the interval is an optimum approximation. So, the proposed optimal evaluation of time step size is calculated by $$D/\left( {14U} \right) $$ , of which D is the feature size and U is the velocity. The calculation to decide time step size is efficient and consequently the numerical simulations are more stable. Numerical results based on the provided time step size also bring on better agreements of the model parameters to reflect the real flow theoretically.