Studying turbulent flows with DNS : from faster pseudo-spectral algorithms to anisotropic Kolmogorov laws
This talk presents two complementary advances in the numerical study of turbulent flows.
First, while truncation and phase-shifting methods are widely used in pseudos-pectral DNS to eliminate aliasing errors arising from nonlinear products in the incompressible Navier-Stokes equations, they remain poorly documented. We present a comprehensive numerical study of these methods applied to Taylor-Green vortices and homogeneous isotropic turbulence. Our results demonstrate that combining phase-shifting with minimal truncation achieves computational speedups by a factor of 3 compared to classical approaches, while preserving accuracy to within 3%.
Second, we investigate theoretical predictions (public link) that extend Kolmogorov’s exact relations to anisotropic and axisymmetric configurations. This work predicts that the third-order flux vector $\mathbfJ$ follows a generalized law characterized by a single anisotropy exponent $n$. By computing vectorial and anisotropic structure functions, we examine whether $n$ approaches a universal value in the strongly stratified regime, as theory suggests, or depends on specific flow parameters.
Both developments are implemented in the open-source framework Fluidsim.
Contact Pierre Augier for more information or to schedule a discussion with the seminar speaker.