A fully divergence-free method for generation of inhomogeneous and anisotropic turbulence with large spatial variation

Abstract

A fully divergence-free method is proposed for generation of inhomogeneous/anisotropic turbulence with large spatial variation. The method is based on the method of Smirnov et al., which is known to violate the divergence-free constraint when spatial variation of turbulence is present. In the proposed method a vector potential field is introduced; by taking the vector curl of the potential field one can generate a strictly divergence-free flow field. A novel formulation for scaling the vector potential field, together with a coordinate transformation strategy, is proposed in this work. The result is a six-step procedure for the generation of inhomogeneous turbulence fields. The proposed formulation is proven to reproduce the prescribed velocity correlation with energy spectrum at large Reynolds numbers. Four test cases are considered to evaluate the new method. First, the statistical quantities introduced in the proposed method are verified numerically in a classical homogeneous turbulence case. Then, the performance of the new method is demonstrated in three different inhomogeneous turbulence cases: a confined turbulent flow in a “slip-wall” box, a planar channel flow and an annular flow. It is shown that the unphysical patterns in the fluctuation fields and divergence errors produced with Smirnovʼs method are absent in the results from the new method. The accuracy of the proposed methods is verified by comparing the velocity correlations with the prescribed scaling functions. The proposed method is efficient and simple to implement.