Application of fast parallel and sequential tree codes to computing three-dimensional flows with the vortex element and boundary element methods
Application of fast parallel and sequential tree codes to computing three-dimensional flows with the vortex element and boundary element methods
复制标题
快速并行和顺序树代码在涡元和边界元方法计算三维流中的应用
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
B. Jodoin
中科院分区：
文献类型：
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作者：
G. Winckelmans;J. Salmon;Michael S. Warren;A. Leonard;B. Jodoin
最初为三维 N 体引力模拟开发的快速并行八叉树代码被修改为 (1) 使用正则化涡粒子法 (VEM) 进行粘性和无粘性涡流计算的快速 N 涡流代码，以及 (2) 使用边界元法 (BEM) 求解势流空气动力学中的边界积分方程的快速 N 面板代码。快速树代码的核心在不同的应用代码之间基本保持不变：引力、VEM、BEM 等。只有实际编码物理模型的模块发生了变化。特别注意控制由于使用多极展开来表示由元素组产生的场而引入的误差，即树代码误差。特别是，使用任何多极展开近似的可接受误差界限是一个运行时参数。程序输出包括所有元素位置现场评估误差的统计数据。涉及 N 在 10 4 到超过 10 6 范围内的 VEM 和 BEM 问题是在并行超级计算机上计算的。 N 在 10 3 到 10 5 范围内的问题在工作站上计算。给出了性能结果以及示例计算结果。对于 VEM 方法，高阶粒子重新分布方案已以有效的方式合并到并行树代码中。如有必要，可应用它来确保在长时间计算中仍然满足核心重叠条件。此外，还纳入了两种不同的放松方案并进行了部分测试。如有必要，应用此类方案以确保涡量场的粒子表示在长时间计算中保持真实无散度涡量场的良好表示。
A fast parallel oct-tree code originally developed for three-dimensional N-body gravitational simulations was modified into (1) a fast N-vortex code for viscous and inviscid vortex flow computations using the regularized vortex particle method (VEM), and (2) a fast N-panel code for solving boundary integral equations in potential flow aerodynamics using the boundary element method (BEM). The core of the fast tree code remains essentially unchanged between the different application codes: gravitation, VEM, BEM, etc. Only the modules that actually encode the physical model are changed. Particular attention is given to controlling the error introduced by the use of multipole expansions to represent the field produced by groups of elements, i.e., the tree code error. In particular, the acceptable error bound for use of any multipole expansion approximation is a run-time parameter. Program outputs include statistics on the errors for the field evaluation at all element locations. Problems in VEM and BEM involving N in the range 10 4 to over 10 6 are computed on parallel supercomputers. Problems with N in the range 10 3 to 10 5 are computed on workstations. Performance results are presented, together with sample computational results. For the VEM method, a high order particle redistribution scheme has been incorporated, in an efficient way, into the parallel tree code. It is applied, if necessary, to ensure that the core overlapping condition remains satisfied in long time computations. In addition, two different relaxation schemes have also been incorporated and partially tested. Such schemes are applied, if necessary, to ensure that the particle representation of the vorticity field remains a good representation of the true divergence free vorticity field in long time computations.