A method to solve Hamilton-Jacobi type equation on unstructured meshes
A Level-Set type method is developed to approximate a first-order Hamilton-Jacobi equation on fixed unstructured meshes in the context of the constant motion of an interface in the normal direction. The interface is captured with the help of a Level-Set function approximated using a finite-volume Godunov-type scheme. Unlike, most computational approaches that consider a signed-distance function, the present Level-Set function is sharp. The method requires gradient computation that is addressed thanks to the least squares approximation. A second-order MUSCL-type scheme is used and gradients are reconstructed at face centers. Some numerical tests are presented to show the efficiency of the proposed method.
scientific article; zbMATH DE number 7359312
scientific article