【摘要】：隨著計(jì)算機(jī)硬件的發(fā)展，多核CPU的應(yīng)用普及和分布式軟件架構(gòu)的成熟，科學(xué)計(jì)算領(lǐng)域也逐漸趨向于問題的并行求解。計(jì)算流體力學(xué)中，不可壓縮管流問題是磁流體應(yīng)用中的重要研究對象，此類問題由于外加磁場和液態(tài)流動(dòng)金屬之間的相互作用以及實(shí)際模擬中對網(wǎng)格要求的嚴(yán)格性，其方程組一般規(guī)模較大，且具有較高的復(fù)雜性，求解過程十分耗時(shí)，因此迫切需要采用并行化求解來提高實(shí)際工程中數(shù)值模擬的效率。當(dāng)前，磁流體應(yīng)用中不可壓縮管流問題數(shù)值模擬方程組一般采用迭代法來進(jìn)行求解，而共軛梯度法作為一種存儲(chǔ)量小，具有步收斂性，穩(wěn)定性高，不需要任何外來參數(shù)的高效求解大型代數(shù)方程組的迭代方法，十分適合此類問題的求解。 本論文針對于磁流體應(yīng)用中不可壓縮管流問題數(shù)值模擬的實(shí)際需求，將科學(xué)計(jì)算中的迭代算法——穩(wěn)定雙共軛梯度算法與計(jì)算機(jī)存儲(chǔ)體系結(jié)構(gòu)進(jìn)行統(tǒng)一研究，結(jié)合數(shù)據(jù)局部性，并行化，性能調(diào)優(yōu)等關(guān)鍵技術(shù)，實(shí)現(xiàn)不可壓縮管流問題數(shù)值模擬的高效求解。本文主要工作總結(jié)如下： （1）查閱并研究大量國內(nèi)外相關(guān)文獻(xiàn)和技術(shù)，總結(jié)了共軛梯度法相關(guān)研究及不足，稀疏矩陣相關(guān)技術(shù)及不足，歸納了計(jì)算流體力學(xué)領(lǐng)域中不可壓縮管流問題求解的相關(guān)技術(shù)及其并行化相關(guān)工作。 （2）針對傳統(tǒng)穩(wěn)定雙共軛梯度算法在數(shù)據(jù)局部性上不足之處，提出了一種基于四叉樹存儲(chǔ)格式的并行穩(wěn)定雙共軛梯度算法（Qtree-BiCGSTAB）。采用這種存儲(chǔ)格式存儲(chǔ)稀疏矩陣，在執(zhí)行矩陣向量乘運(yùn)算時(shí)可以提高緩存命中率，優(yōu)化Cache行為，提高數(shù)據(jù)局部性，進(jìn)而提升穩(wěn)定雙共軛梯度算法的運(yùn)算效率，大大縮短了方程組求解所需要的時(shí)間，，相較于基于傳統(tǒng)CSR存儲(chǔ)格式的穩(wěn)定雙共軛梯度算法有較好的性能提升。同時(shí)通過對基于四叉樹存儲(chǔ)格式的穩(wěn)定雙共軛梯度算法的并行化實(shí)現(xiàn)，提升大規(guī)模方程組求解的執(zhí)行效率。 （3）針對計(jì)算流體力學(xué)中的實(shí)際需求，本文將上述研究成果（Qtree-BiCGSTAB）應(yīng)用到三維穩(wěn)態(tài)不可壓縮管流問題的并行求解過程中，提出了一種基于并行Qtree-BiCGSTAB的SIMPLE算法，以提高有限體積法中離散方程組的求解效率。與傳統(tǒng)的并行SIMPLE方法相比，該算法通過采用步收斂性的穩(wěn)定雙共軛梯度算法來對七對角方程組進(jìn)行求解，加快了求解效率，并在穩(wěn)定雙共軛梯度算法中通過采用基于四叉樹存儲(chǔ)格式的稀疏矩陣，提高了算法的數(shù)據(jù)局部性，同時(shí)通過采用并行化的穩(wěn)定雙共軛梯度算法，提升了大規(guī)模七對角方程組求解的效率，進(jìn)一步有效地提高了三維穩(wěn)態(tài)不可壓縮管流問題數(shù)值模擬的效率。
[Abstract]:With the development of computer hardware, the application of multi-core CPU and the maturity of distributed software architecture, the field of scientific computing tends to solve problems in parallel. In computational fluid dynamics, the incompressible pipe flow problem is an important research object in the application of magnetofluids. This kind of problem is due to the interaction between the external magnetic field and the liquid flowing metal and the strict requirements of the mesh in the actual simulation. Because of its large scale and high complexity, it is very time-consuming to solve the equations, so it is urgent to use parallelization to improve the efficiency of numerical simulation in practical engineering. At present, the numerical simulation equations of incompressible pipe flow in magnetohydrodynamic applications are usually solved by iterative method, while the conjugate gradient method has the advantages of small storage, high step convergence and high stability. The iterative method for solving large algebraic equations without any external parameters is very suitable for solving such problems. In this paper, according to the actual demand of numerical simulation of incompressible pipe flow in magnetohydrodynamic applications, the iterative algorithm of stable double conjugate gradient in scientific calculation and the computer storage architecture are studied, and the data locality is combined. Parallelization, performance optimization and other key techniques are used to efficiently solve the incompressible pipe flow problem. The main work of this paper is summarized as follows: (1) referring to and studying a large number of domestic and foreign related literature and technology, summed up the conjugate gradient method related research and shortcomings, sparse matrix correlation technology and shortcomings, The related techniques and parallelization of the incompressible pipe flow problem in computational fluid dynamics are summarized. (2) aiming at the shortcomings of the traditional stable double conjugate gradient algorithm in data localization, A parallel stable double conjugate gradient algorithm (Qtree-BiCGSTAB) based on quadtree storage scheme is proposed. Using this storage format to store sparse matrix can improve the cache hit ratio, optimize Cache behavior, improve data localization, and improve the efficiency of the stable double conjugate gradient algorithm when performing matrix vector multiplication. The time required to solve the equations is greatly shortened, and the performance of the stable double conjugate gradient algorithm based on the traditional CSR storage scheme is improved. At the same time, by parallelizing the stable double conjugate gradient algorithm based on quadtree storage scheme, the efficiency of solving large scale equations is improved. (3) to meet the practical requirements in computational fluid mechanics, In this paper, we apply the above research results (Qtree-BiCGSTAB) to the parallel solution of three-dimensional steady incompressible pipe flow problem, and propose a parallel Qtree-BiCGSTAB based SIMPLE algorithm to improve the efficiency of solving the discrete equations in the finite volume method. Compared with the traditional parallel SIMPLE method, the algorithm uses a stable double conjugate gradient algorithm with step convergence to solve the seven-diagonal equations. In the stable double conjugate gradient algorithm, the sparse matrix based on the quadtree storage format is used to improve the data localization of the algorithm, and the parallel stable double conjugate gradient algorithm is adopted at the same time. The efficiency of solving large scale seven-diagonal equations is improved, and the efficiency of numerical simulation of three-dimensional steady incompressible pipe flow is further improved.
【學(xué)位授予單位】：杭州電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：O361.3;TP338.6

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本文編號(hào)：2231025