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| 基于自适应笛卡尔网格平衡排序的隐式LU-SGS算法 |
| Research on implicit LU-SGS algorithm based on adaptive Cartesian grid bal-anced ordering |
| 投稿时间：2024-10-20 修订日期：2024-11-22 |
| DOI： |
| 中文关键词: 自适应笛卡尔网格 LU-SGS算法 隐式重排序 |
| 英文关键词:Adaptive Cartesian Grid LU-SGS Algorithm Implicit Reordering |
| 基金项目:无基金资助项目. |
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| 摘要点击次数: 37 |
| 全文下载次数: 0 |
| 中文摘要: |
| 自适应笛卡尔网格通常采用叉树数据结构,其在网格拓扑、邻居关系以及数据访问上有别于传统的结构/非结构网格。因此,原有的LU-SGS隐式算法需要在自适应笛卡尔网格中进行扩展。本文发展了一种自适应笛卡尔网格框架下的LU-SGS算法,通过采用递归Z曲线方式对计算网格进行重排序,实现网格的平衡编号。针对悬挂网格附近邻居关系复杂的情况,采用分类选取合适的插值方式来获取邻居信息。典型算例测试结果表明,对于定常问题,推进收敛效率较改进前提升了一个量级。三维无粘算例气动力快速评估中,残差下降了10个数量级,气动力系数在370步时达到收敛,较Runge-Kutta格式的1280步和Euler格式的4070步提升显著。 |
| 英文摘要: |
| Adaptive Cartesian grids typically employ an octree data structure, which differs from traditional structured/unstructured grids in terms of grid topology, neighbor relationships, and data access. Therefore, the conventional LU-SGS implicit algorithm needs to be extended for adaptive Cartesian grids. This paper develops an LU-SGS algorithm within the framework of adaptive Cartesian grids. By employing a recursive Z-curve method to reorder the computational grid, balanced grid numbering is achieved. For the complex neighbor relationships near hanging nodes, appropriate interpolation methods are selected categorically to obtain neighbor information. Results from typical test cases indicate that, for steady-state problems, the convergence efficiency has improved by an order of magnitude compared to the previous approach. In the rapid aerodynamic evaluation of three-dimensional inviscid cases, the residual decreased by 10 orders of magnitude, and the aerodynamic coefficients converged in 370 iterations, which is a significant im-provement over the 1280 iterations required by the Runge-Kutta format and the 4070 iterations required by the Euler format. |
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