  In this article, we propose a divergence-free method for the generation of
inhomogeneous and anisotropic turbulence. Based on the idea of correlation
reconstruction, the method uses the Cholesky decomposition matrix to
re-establish the turbulence correlation functions, which avoids the
time-consuming procedure that solves eigenvalues and eigenvectors in every
location needed by the coordinate transformation in the conventional method and
thus reduces the computational complexity and improves the efficiency of
generating synthetic turbulence. Through adjusting the generation strategy of
specific random vectors, the proposed method, which is based on the classical
spectrum-based method widely used to generate uniform isotropic turbulence, can
obtain inhomogeneous and anisotropic turbulence with a relatively low
divergence level in practice with almost no additional computational burden.
There are two versions of this new method: the shifter version and the inverter
version. Both versions of the method are highly efficient, easy to implement,
and compatible with high-performance computing. Suitable for providing
high-quality initial or boundary conditions for scale-resolving turbulence
simulations with large grid numbers (such as direct numerical simulation or
large eddy simulation), this method can be quickly implemented either based on
various open-source CFD codes or common commercial CFD software.
