Study on Direct Numerical Simulation of Two-dimensional Turbulence

Abstract

Turbulence is one of the unsolved problems in fluid mechanics. The study of 3D turbulence is very complex and difficult to achieve; while 2D turbulence is similar to 3D turbulence in many properties, and the related study is easier to carry out. Therefore, the study of 2D turbulence is significant to understand the characteristics of 3D turbulence. In this paper, the vorticity-stream function method is applied to the direct numerical simulation of 2D turbulence without any turbulence model. The third order Runge Kutta-Crank Nicholson method is used as the time integration method, and finite difference method of second order accuracy is for space discretization with central difference scheme and staggered grid. Turbulence conditions are used as boundary conditions and initial conditions. The vorticity distribution under different Reynolds number and different grid resolutions are obtained by numerical simulation. When the Reynolds number is low, the numerical discretization method with low order accuracy can resolve all vortex structures in space with higher grid resolution. But as the Reynolds number increases, the higher accuracy of the numerical discretization method is the best choice compared with the grid resolution enhancement.