In this paper, we propose a numerical algorithm based on a cell-centered finite volume method to compute a distance from given objects on a three-dimensional computational domain discretized by polyhedral cells. Inspired by the vanishing viscosity method, a Laplacian regularized eikonal equation is solved and the Soner boundary condition is applied to the boundary of the domain to avoid a non-viscosity solution. As the regularization parameter depending on a characteristic length of the discretized domain is reduced, a corresponding numerical solution is calculated. A convergence to the viscosity solution is verified numerically as the characteristic length becomes smaller and the regularization parameter accordingly becomes smaller. From the numerical experiments, the second experimental order of convergence in the $L^1$ norm error is confirmed for a smooth solution. Compared to an algorithm to solve a time-dependent form of eikonal equation, the proposed algorithm has the advantage of reducing computational cost dramatically when a more significant number of cells is used or a region of interest is far away from the given objects. Moreover, the implementation of parallel computing on decomposed domains with $1$-ring face neighborhood structure can be done straightforwardly in a standard cell-centered finite volume code.

翻译：在本文中,我们提出一个基于以单元格为主的有限量计算法的数字算法,以计算与三维计算域上由多角度细胞分离的某一天体的距离。在消失的粘度方法的启发下,解答了拉普拉西亚正规化的eikonal方程式,将索纳边界条件应用于域的边界,以避免非视觉解决办法。随着根据离散域的特征长度而决定的正规化参数缩小,将计算相应的数字解决办法。随着特性长度变小,并相应缩小正规化参数,对粘度溶液的趋同进行了数字核查。从数字实验中,确认了美元为1美元的常规差的第二个实验趋同顺序,以便找到一个平滑的解决方案。与用于解决视时间为主的ekonal等式的算法相比,提议的算法的优点是,在使用数量较大的单元格或感兴趣的区域远离给定对象时,将大幅降低计算成本。此外,在以1美元正值正值的平面结构中,可以在一个不折叠的单元格中直接进行平行计算。