Adaptive remeshing for compressible flow computations
Journal of Computational Physics
Long and thin triangles can be good for linear interpolation
SIAM Journal on Numerical Analysis
Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications
IEEE Transactions on Visualization and Computer Graphics
Adaptive boundary layer meshing for viscous flow simulations
Engineering with Computers - Special Issue: 5th Symposium on Trends in Unstructured Mesh Generation in 2006. Guest Editor: Steven J. Owen
Continuous metrics and mesh adaptation
Applied Numerical Mathematics
Size gradation control of anisotropic meshes
Finite Elements in Analysis and Design
An Eulerian approach for computing the finite time Lyapunov exponent
Journal of Computational Physics
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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 L^p metric. The Lagrangian particles, or nodes, are then iteratively adapted on the flow structures revealed by this metric. Typically, the L^1 norm provides meshes best suited to capturing small scale structures, while the 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^~ norm than with the L^1 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^~ metric.