Iterative inflow-implicit outflow-explicit finite volume scheme for level-set equations on polyhedron meshes

Abstract

In this paper, we propose a cell-centered finite volume method for advective and normal flows on polyhedron meshes which is second-order accurate in space and time for smooth solutions. In order to overcome a time restriction caused by CFL condition, an implicit time discretization of inflow fluxes and an explicit time discretization of outflow fluxes are used in an iterative procedure. For an efficient computation, an 1-ring face neighborhood structure is introduced. Since it is limited to access unknown variables in an 1-ring face neighborhood structure, an iterative procedure is proposed to resolve the limitation of assembled linear system. Two types of gradient approximations, an inflow-based gradient and an average-based gradient, are studied and compared from the point of numerical accuracy. Numerical schemes are tested for an advective and a normal flow of level-set functions illustrating a behavior of the proposed method for an implicit tracking of a smooth and a piecewise smooth interface.