面向高阶精度CFD的JFNK算法及其并行计算

发布时间：2018-05-25 14:19

本文选题：高阶精度格式 + JFNK算法　；参考：《计算机科学与探索》2017年01期

【摘要】：目前计算效率低是限制计算流体力学(computational fluid dynamics,CFD)高阶精度格式方法的重要因素之一。由于高阶精度格式计算模板相对复杂,很难精确计算其Jacobian矩阵,从而影响传统LU-SGS(lowerupper symmetric Gauss-Seidel)等算法的收敛效率。JFNK(Jacobian-free Newton-Krylov)算法是Krylov子空间方法与非精确牛顿方法的结合,拥有较好的迭代收敛效率,采用无矩阵思想,只计算Jacobian矩阵与矢量的乘积,从而有效避免Jacobian矩阵的计算和存储。在真实高精度结构网格CFD应用程序中,设计并实现了JFNK时间求解算法。在有粘低速圆柱绕流的算例测试中,和传统LU-SGS算法相比,JFNK算法拥有更好的计算稳定性,同时可使迭代收敛效率提高2倍以上。以天河2号超级计算机为并行计算平台,对JFNK算法和传统的LU-SGS算法的并行强可扩展性进行了测试,二者均表现出良好的并行效率。
[Abstract]:At present, low computational efficiency is one of the most important factors that limit the high order accuracy of computational fluid dynamics (CFD). It is difficult to calculate the Jacobian matrix precisely because of the complexity of the calculation template of high-order precision scheme, which affects the convergence efficiency of the traditional LU-SGS(lowerupper symmetric Gauss-Seidel.JFNKN Jacobian-free Newton-Krylov-algorithm is a combination of Krylov subspace method and imprecise Newton method. In order to avoid the computation and storage of Jacobian matrix, it has better iterative convergence efficiency, and only calculates the product of Jacobian matrix and vector by using the idea of no matrix. In the real high precision grid CFD application, the JFNK time solving algorithm is designed and implemented. Compared with the traditional LU-SGS algorithm, the LU-SGS algorithm has better computational stability and can increase the convergence efficiency by more than 2 times. Using Tianhe-2 supercomputer as the parallel computing platform, the parallel strong scalability of JFNK algorithm and traditional LU-SGS algorithm are tested. Both of them show good parallel efficiency.
【作者单位】：国防科学技术大学计算机学院;中国空气动力研究与发展中心空气动力学国家重点实验室;国防科学技术大学;
【基金】：国家自然科学基金国防科技大学科研计划重大应用基础研究项目空气动力学国家重点实验室开放课题~~
【分类号】：O35

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