On dependence of dynamical structure of numerical solutions of fluid simulations on forcibly added randomness

In the present paper, the dependencies of the numerical results of fluid simulations on forcibly added randomness are discussed. The incompressible Navier–Stokes equations and the continuity equation are solved numerically by using the MAC (Maker-And-Cell) method and implicit temporal scheme. The model adopted in the present study is a flow around a two-dimensional circular cylinder and the Reynolds number is 1500. The randomness which is given by using the pseudo-random number is forcibly added in the time marching step of the discretized Navier–Stokes equations. Dependencies of the averaged structure of asymptotic numerical solutions on the randomness are discussed. Furthermore, the dependence of the qualitative structure of the asymptotic solution of each sample calculation on the amplitude of randomness is also studied. It is clarified that forcibly added random errors may cover the nonlinear errors which make the system unstable.