A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
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DOI：
10.1006/jcph.1998.5965
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发表时间：
1998-11-20
影响因子：
4.1
通讯作者：
Colella, P
中科院分区：
文献类型：
--
作者：
Johansen, H;Colella, P
我们提出了一种在二维区域上求解具有可变系数和狄利克雷边界条件的泊松方程的数值方法。该方法使用有限体积离散化，将域嵌入到常规笛卡尔网格中。我们将解视为以细胞为中心的量，即使这些中心位于域之外。包含部分域边界的单元在每个单元体积上使用二阶精确通量的保守差分。边界通量的计算确保基质的调节相对不受小细胞体积的影响。这使我们能够使用带有简单点松弛策略的多重网格迭代。我们将其与自适应网格细化（AMR）程序结合起来。我们提供的证据表明该算法在各种精确解上都是二阶准确的，并比较了自适应和非自适应计算。 (C) 1998 年学术出版社。
We present a numerical method for solving Poisson's equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. We treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservative differencing of second-order accurate fluxes on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows us to use multigrid iterations with a simple point relaxation strategy. We have combined this with an adaptive mesh refinement (AMR) procedure. We provide evidence that the algorithm is second-order accurate on various exact solutions and compare the adaptive and nonadaptive calculations. (C) 1998 Academic Press.