Inflow-Based Gradient Finite Volume Method for a Propagation in a Normal Direction in a Polyhedron Mesh

An inflow-based gradient is proposed to solve a propagation in a normal direction with a cell-centered finite volume method. The proposed discretization of the magnitude of gradient is an extension of Rouy–Tourin scheme (SIAM J Numer Anal 29:867–884, 1992 ) and Osher–Sethian scheme (J Comput Phys 79:12–49, 1988 ) in two cases; the first is that the proposed scheme can be applied in a polyhedron mesh in three dimensions and the second is that its corresponding form on a regular structured cube mesh uses the second order upwind difference. Considering a practical application in three dimensional mesh, we use the simplest decomposed domains for a parallel computation. Moreover, the implementation is straightforwardly and easily combined with a conventional finite volume code. A higher order of convergence and a recovery of signed distance function from a sparse data are illustrated in numerical examples on hexahedron or polyhedron meshes.