Finite volume method with the Soner boundary condition for computing the signed distance function on polyhedral meshes

A cell-centered finite volume method with the Soner boundary condition is proposed to compute the signed distance function from a given surface in general three-dimensional (3D) computational domains discretized by polyhedral cells. The governing equation is the bidirectional time-relaxed eikonal equation and the proposed numerical method is based on the semi-implicit inflow-implicit and outflow-explicit scheme. Numerical experiments confirm the second order accuracy in L1 and L infinity-norms for chosen examples with smooth solutions. The inclusion of the Soner boundary condition has proven necessary for numerical solutions to reach the viscosity solution of the eikonal equation starting from various initial conditions in general 3D domains.