ANALYSIS OF A ONE-DIMENSIONAL MODEL FOR THE IMMERSED BOUNDARY METHOD
ANALYSIS OF A ONE-DIMENSIONAL MODEL FOR THE IMMERSED BOUNDARY METHOD
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DOI：
10.1137/0729022
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发表时间：
1992-04-01
影响因子：
2.9
通讯作者：
LEVEQUE, RJ
中科院分区：
文献类型：
--
作者：
BEYER, RP;LEVEQUE, RJ
研究了一维带奇异强迫项的热传导方程u（t）= u（xx）+ c（t）delta（x - alpha（t））的数值方法. 用离散近似d（h）（x）代替delta函数delta（x），并在均匀网格上用Crank-Nicolson方法求解所得方程。 分析了该方法在不同d（h）选择下的精度。 的情况下，c（t）是指定的情况下，c是由一个约束的解决方案在α点隐式地确定进行了研究。 这些问题作为Peskin浸入边界法求解不规则区域不可压缩流动问题的模型。 一些洞察力，可以实现的精度和选择适当的离散δ函数的重要性。
Numerical methods are studied for the one-dimensional heat equation with a singular forcing term, u(t) = u(xx) + c(t)delta(x - alpha(t)). The delta function delta(x) is replaced by a discrete approximation d(h)(x) and the resulting equation is solved by a Crank-Nicolson method on a uniform grid. The accuracy of this method is analyzed for various choices of d(h). The case where c(t) is specified and also the case where c is determined implicitly by a constraint on the solution at the point alpha are studied. These problems serve as a model for the immersed boundary method of Peskin for incompressible flow problems in irregular regions. Some insight is gained into the accuracy that can be achieved and the importance of choosing appropriate discrete delta functions.