Semi-implicit Level Set Method with Inflow-Based Gradient in a Polyhedron Mesh

In this paper, a semi-implicit method is proposed to solve a propagation in a normal direction with a cell-centered finite volume method. An inflow-based gradient is used to discretize the magnitude of the gradient and it brings the second order upwind difference in an evenly spaced one dimensional domain. In three dimensional domain, we numerically verify that the proposed scheme is second order. The implementation is straightforwardly combined with a conventional finite volume code and 1-ring face neighborhood for parallel computation. An experimental order of convergence and a comparison of wall clock time between semi-implicit and explicit method are illustrated by numerical examples.