An arbitrary order finite difference method for curved boundary domains with Cartesian grid is proposed. The technique handles in a universal manner Dirichlet, Neumann or Robin conditions. We introduce the Reconstruction Off-site Data (ROD) method, that transfers in polynomial functions the information located on the physical boundary to the computational domain. Three major advantages are: (1) a simple description of the physical boundary with Robin condition using a collection of points; (2) no analytical expression (implicit or explicit) is required, particularly the ghost cell centroids projection are not needed; (3) we split up into two independent machineries the boundary treatment and the resolution of the interior problem, coupled by the ghost cell values. Numerical evidences based on the simple 2D convection-diffusion operators are presented to prove the capability of the method to reach at least the 6th-order with arbitrary smooth domains.

提出了一种具有笛卡尔网格的弯曲边界域的任意阶有限差分方法。该技术以通用方式处理Dirichlet，Neumann或Robin条件。我们介绍了重建异地数据（ROD）方法，该方法将多项式函数中的物理边界上的信息传输到计算域。三个主要优点是：（1）使用点集合简单描述具有Robin条件的物理边界；（2）不需要解析表达式（隐式或显式），特别是不需要幻影细胞质心投影；（3）我们将边界处理和内部问题的解决方法分为两个独立的机制，再加上虚像元值。