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Subject: Mechanics ; Computer Science (provided by Thomson Reuters)
Title:
二维各向同性湍流直接数值模拟的六边形谱方法及GPU实现和优化
Alternative Title: hexagonal spectral methods for direct numerical simulation of two-dimensional homogeneous isotropic turbulence and their gpu implementation and optimization
Author: 乔海军 ; 李会元
Keyword: GPU ; CUDA ; 六边形傅里叶谱方法 ; 二维各向同性湍流 ; 直接数值模拟
Source: 数值计算与计算机应用
Issued Date: 2013
Volume: 34, Issue:2, Pages:147-160
Indexed Type: CNKI ; WANFANG ; CSCD
Department: 中国科学院软件研究所;中国科学院研究生院;
Sponsorship: 国家自然科学基金项目(No.91130014)资助|广东省计算科学重点实验室和广东省引进创新科研团队计算科学科研团队支持
Abstract: 本文在六边形傅里叶分析及六边形快速傅里叶变换的基础上,提出了二维各向同性湍流直接数值模拟的对偶六边形傅里叶谱方法和六边形傅里叶谱方法,基于二维Navier-Stokes方程的涡度-速度形式,构造了两种六边形傅里叶谱方法的离散格式,设计了其快速求解算法,并且在GPU高性能平台上研制并优化了相应的数值模拟程序.根据方程的具体形式和六边形傅里叶谱方法的特点,从算法层面对方程的求解过程,尤其是非线性Jacobian项快速计算进行优化,经过优化之后,方程求解算法的计算复杂度减少了约30%;根据GPU的体系结构和数值模拟程序的功能要求,将计算模块全部设计为在GPU上运行的kernel函数,尽量避免内存与显存之间的数据拷贝,并在软件工程层面上对代码进行性能优化.优化后的GPU程序获得了高达50倍的加速比.在此基础上,我们对二维各向同性湍流进行了初步的数值模拟,并考察了在不同初始雷诺数条件下,能量和拟涡能随着时间的演变曲线.计算结果表明六边形傅里叶谱方法与传统的傅里叶谱方法一样高效精确.
English Abstract: In this paper, a hexagonal spectral method and a dual hexagonal spectral method are proposed for the direct numerical simulation (DNS) of the tow-dimensional homogeneous isotropic turbulences on the basis of Fourier analysis and fast Fourier transform (FFT) on hexagons. Taking advantage of the vorticity-velocity form of the two-dimensional Navier-Stokes equations, we develop a discrete scheme of the two hexagonal spectral methods, and design their fast implementation algorithm on the GPU platform. A collection of optimizations are then made in the algorithm level for seeking the numerical solution, in particular, for evaluation the nonlinear Jacobian term. These efforts yield a reduction of 30 percent for the total computational complexity. On the other hand, a number of optimization efforts are made in the software engineering level to improve performance of our programs, such as avoiding data copy between host memory and GPU memory, increasing the parallel granularity, optimizing the storage hierarchy, merging the kernel functions. These steps finally obtain a 50-times speedup or our GPU programs in comparison to the CPU programs. With the help of our high performance GPU programs, a series of experiments are carried out for the DNS of two-dimensional homogeneous isotropic turbulences. The evolution of energy and enstrophy of turbulences with different initial Reynolds numbers are studied. Our experimental results show that the DNS results of both the hexagonal and the dual hexagonal Fourier spectral methods possess the same accuracy and efficiency as the classical rectangular Fourier spectral method.
Language: 中文
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Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/15605
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
乔海军,李会元. 二维各向同性湍流直接数值模拟的六边形谱方法及GPU实现和优化[J]. 数值计算与计算机应用,2013-01-01,34(2):147-160.
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