On the computation of instabilities and symmetry-breaking in fluid mechanics

A review on the implementation of modern computational fluid dynamics (CFD) methods for simulating low- and high-speed flows featuring turbulent mixing, instabilities and symmetry-breaking is presented. Results are reviewed for several complex flows including turbulent mixing associated with Richtmyer-Meshkov and Rayleigh-Taylor instabilities, incompressible flows in suddenly expanded geometries, shock-induced instabilities, free-shear instabilities and complex vortex dynamics. Many of the results presented in this review have been obtained by large eddy simulation (LES), monotone integrated LES (MILES) in particular. The computational challenges associated with complex flow physics and nonlinear behaviour of the numerics are discussed.