A Method to Solve Hamilton–Jacobi Type Equation on Unstructured Meshes

A new method is developed to approximate a first-order Hamilton-Jacobi equation in the context of an interface moving along its normal vector field. The interface is tracked with the help of a "Level-Set" function approximated through a finite-volume Godunov-type scheme. Contrarily to most computational approaches that consider smooth Level-Set functions, the present one considers sharp "Level-Set", the numerical diffusion being controlled with the help of the Overbee limiter (Chiapolino et al., 2017). The method requires gradient computation that is addressed through the least squares approximation. Multidimensional results on unstructured meshes are provided and checked against analytical solutions. Geometrical properties such as interfacial area and volume computation are addressed as well. Results show excellent agreement with the exact solutions.