Anisotropic mesh adaptation on Lagrangian Coherent Structures

The finite-time Lyapunov exponent (FTLE) is extensively used as a criterion to reveal fluid flow structures, including unsteady separation/attachment surfaces and vortices, in laminar and turbulent flows. However, for large and complex problems, flow structure identification demands computational methodologies that are more accurate and effective. With this objective in mind, we propose a new set of ordinary differential equations to compute the flow map, along with its first (gradient) and second order (Hessian) spatial derivatives. We show empirically that the gradient of the flow map computed in this way improves the pointwise accuracy of the FTLE field. Furthermore, the Hessian allows for simple interpolation error estimation of the flow map, and the construction of a continuous optimal and multiscale LpLp metric. The Lagrangian particles, or nodes, are then iteratively adapted on the flow structures revealed by this metric. Typically, the L1L1 norm provides meshes best suited to capturing small scale structures, while the L∞L∞ norm provides meshes optimized to capture large scale structures. This means that the mesh density near large scale structures will be greater with the L∞L∞ norm than with the L1L1 norm for the same mesh complexity, which is why we chose this technique for this paper. We use it to optimize the mesh in the vicinity of LCS  . It is found that Lagrangian Coherent Structures are best revealed with the minimum number of vertices with the L∞L∞ metric.