论文标题
关于任意几何形状的非常高级的笛卡尔栅格有限差异方法
Very high-order Cartesian-grid finite difference method on arbitrary geometries
论文作者
论文摘要
提出了带有笛卡尔网格的曲线边界域的任意订单有限差方法。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，该方法在多项式函数中传输了位于物理边界上的信息。三个主要优点是：（1）使用点的集合对物理边界的简单描述； （2）不需要分析表达（隐式或显式），尤其是不需要幽灵细胞中心的投影； （3）我们将边界处理和内部问题的分辨率分为两个独立的机械，并由幽灵细胞值结合。提出了基于简单的2D对流扩散算子的数值证据，以证明该方法至少可以使用任意平滑域的6阶达到6阶的能力。
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 condition. We introduce the Reconstruction Off-site Data (ROD) method, that transfers in polynomial functions the information located on the physical boundary. 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 the ghost cell values. Numerical evidences based on the simple 2D convection-diffusion operators are presented to prove the ability of the method to reach at least the 6th-order with arbitrary smooth domains.
