COMPUTATION OF FORWARD-TIME FINITE-TIME LYAPUNOV EXPONENTS USING DISCONTINUOUS-GALERKIN SPECTRAL ELEMENT METHODS

We present an algorithm for computing forward-time finite-time Lyapunov exponents (FTLEs) using discontinuous-Galerkin (DG) operators. Passive fluid tracers are initialized at Gauss-Lobatto quadrature nodes and advected concurrently with direct numerical simulation (DNS) using DG spectral element methods. The flow map is approximated by a high-order polynomial and the deformation gradient tensor is then determined by the spectral derivative. Since DG operators are used to compute the deformation gradient, the algorithm is high-order accurate and is consistent with the DG methods used to compute the fluid solution. The method is validated with a benchmark of a periodic gyre, a vortex advected in uniform flow and the flow around a square cylinder. An exact equation for the FTLE of the advected vortex is derived.