本文選題：油藏?cái)?shù)值模擬 + 多層網(wǎng)格法　； 參考：《昆明理工大學(xué)》2017年博士論文

【摘要】：隨著復(fù)雜類型油藏(低滲、高含水、復(fù)雜巖性油藏等)開發(fā)的日益深入和提高采收率技術(shù)的推廣使用,油藏?cái)?shù)值模擬所依據(jù)的數(shù)學(xué)模型變得越來越復(fù)雜,同時(shí)油藏地質(zhì)模型趨向精細(xì)化、網(wǎng)格復(fù)雜化、井?dāng)?shù)增加以及類型多樣化等,這些因素導(dǎo)致滲流模型數(shù)值離散所形成的雅克比線性代數(shù)方程組的規(guī)模大、性態(tài)壞。在全隱式油藏?cái)?shù)值模擬計(jì)算中,雅克比線性代數(shù)方程組的求解是一個(gè)主要瓶頸,其求解時(shí)間往往占據(jù)整個(gè)模擬計(jì)算時(shí)間的70%～80%,而且隨著問題規(guī)模增大,該比重會(huì)進(jìn)一步提高。設(shè)計(jì)高效的數(shù)值求解算法來提高雅克比線性代數(shù)方程組的求解速度是縮短數(shù)值模擬時(shí)間最有效的途徑之一。另外當(dāng)前計(jì)算機(jī)的硬件架構(gòu)越來越異構(gòu)化,利用眾核處理器(如GPU、MIC)來協(xié)助CPU計(jì)算的解決方案在科學(xué)計(jì)算領(lǐng)域正釋放巨大的能量,并掀起一股新的高性能異構(gòu)并行計(jì)算浪潮。本文針對(duì)經(jīng)典標(biāo)準(zhǔn)黑油模型,為其全隱式離散得到的雅克比線性代數(shù)方程組設(shè)計(jì)高效的串、并行求解算法。首先,針對(duì)黑油模型的強(qiáng)耦合雅克比離散代數(shù)方程組,我們分析幾種常用解耦方法,如交錯(cuò)塊分解解耦、擬隱壓顯飽解耦、隱壓顯飽解耦,并分別考察這幾種方法的解耦效果以及對(duì)壓力方程橢圓性的影響。我們發(fā)現(xiàn):交錯(cuò)塊分解解耦方法能很好地削弱壓力變量和飽和度變量以及飽和度變量和飽和度變量之間的耦合關(guān)系,同時(shí)對(duì)雅克比矩陣的特征值有很好的聚集作用,但該方法破壞了壓力方程的橢圓性,使壓力方程求解難度增加;擬隱壓顯飽解耦和隱壓顯飽解耦方法借助IMPES方法的思想,通過代數(shù)方法得到一個(gè)橢圓性較好的壓力方程,但該解耦方法只削弱了壓力方程中壓力變量與飽和度變量的耦合程度。針對(duì)上述三種解耦方法得到的壓力方程,本文分別比較了經(jīng)典AMG方法、VMB聚集AMG方法以及Pairwise聚集AMG方法的求解速度,并簡(jiǎn)單分析上述三種AMG方法在求解經(jīng)不同解耦方法得到的壓力方程時(shí)收斂速度差異大的原因。經(jīng)上述分析,我們將隱壓顯飽解耦方法與經(jīng)典CPR預(yù)條件子結(jié)合起來形成一類分裂型預(yù)條件子,并用Pairwise聚集AMG方法取代經(jīng)典AMG方法來求解壓力方程,此分裂型預(yù)條件子的求解速度較交錯(cuò)塊分解解耦方法與經(jīng)典CPR預(yù)條件子組成的分裂型預(yù)條件子快了近50%。其次,由于當(dāng)前油藏模擬向精細(xì)化發(fā)展,雅克比矩陣規(guī)模突破千萬量級(jí)且性態(tài)越趨病態(tài),給雅克比線性代數(shù)方程組的求解帶來了極大困難,研發(fā)針對(duì)精細(xì)油藏模擬帶來的超大規(guī)模雅克比線性代數(shù)系統(tǒng)的高效、穩(wěn)健求解算法是十分必要的。本文利用交錯(cuò)塊分解解耦方法具有聚集雅克比矩陣特征值以及削弱物理變量間耦合關(guān)系的性質(zhì),基于輔助空間校正思想,提出了一種穩(wěn)健、高效、節(jié)省內(nèi)存的分裂型預(yù)條件子。該分裂型預(yù)條件子采用交錯(cuò)塊分解解耦方法作為左預(yù)條件子,然后針對(duì)交錯(cuò)塊分解方法解耦后的雅克比矩陣的性質(zhì),設(shè)計(jì)了一種多階段輔助子空間右預(yù)條件子BASP:首先在飽和度子空間用塊高斯賽德爾方法對(duì)飽和度方程進(jìn)行一次近似求解,消除飽和度部分的高頻誤差部分;其次針對(duì)帶強(qiáng)間斷系數(shù)的橢圓型壓力方程,我們采用AMG預(yù)條件Krylov方法來近似求解達(dá)到一定精度,消除由壓力方程控制的低頻誤差;最后在全空間做一次塊高斯賽德爾磨光。通過大量油田實(shí)例測(cè)試,該分裂型預(yù)條件子整體表現(xiàn)得十分高效及穩(wěn)健。基于該預(yù)條件子的模擬器的求解速度比國際主流商業(yè)模擬器快2到3倍,且在臺(tái)式工作站上成功模擬了千萬網(wǎng)格規(guī)模的精細(xì)油藏模型。最后,本文基于CPU-GPU異構(gòu)體系設(shè)計(jì)一種求解雅克比線性代數(shù)方程組的高效并行線性解法器。當(dāng)前超級(jí)計(jì)算機(jī)的計(jì)算能力越來越強(qiáng)大,但體系結(jié)構(gòu)日趨復(fù)雜,大多數(shù)采用多核、眾核處理器、大型高速緩存、高帶寬進(jìn)程間通信結(jié)構(gòu)和高速I/O功能的設(shè)計(jì)模式。如何構(gòu)建現(xiàn)代化高性能應(yīng)用軟件來充分利用計(jì)算機(jī)的異構(gòu)架構(gòu)特點(diǎn)和資源是十分值得探索的。本文針對(duì)油藏模擬中的雅克比矩陣的結(jié)構(gòu)特點(diǎn),提出了一種適合GPU訪存特點(diǎn)的BHYB的稀疏存儲(chǔ)格式,基于該格式的SpMV的加速比最高達(dá)19倍,比世界著名的Nvidia公司研發(fā)的高效CuSparse軟件包最快的HYB格式快30%;其次基于GPU的SIMT編程模擬,本文提出了一種雙密集型并行策略,設(shè)計(jì)了一種并行度高、并行可擴(kuò)展性好的BILU(l)方法,其中BILU(0)分解階段和三角求解階段的平均加速比分別達(dá)到6.27倍和9.46倍;最后結(jié)合計(jì)算機(jī)的異構(gòu)特點(diǎn)以及AMG算法各部分的可并行度,設(shè)計(jì)了一種異構(gòu)并行UA AMG方法,且該并行UA AMG方法沒有損失串行UA AMG方法的收斂速度。通過整合上述并行模塊,我們形成了一種基于CPU-GPU異構(gòu)體系的并行BCPRP預(yù)條件子。數(shù)值試驗(yàn)表明該并行預(yù)條件子十分穩(wěn)健,相比改進(jìn)后的串行BCPRP預(yù)條件算法,該并行BCPRP預(yù)條件子在單GPU卡上的求解速度提高了 3.0倍左右。此外,基于"天河二號(hào)"超級(jí)計(jì)算機(jī),我們研發(fā)了一套分布式并行求解算法,將模擬規(guī)模擴(kuò)展到億量級(jí)網(wǎng)格單元的同時(shí),也極大提高了油藏模擬效率。該分布式并行求解器在千核以內(nèi)都具有良好的可擴(kuò)展性,但擴(kuò)展到10,008個(gè)CPU物理核心后,分布式并行求解器的強(qiáng)可擴(kuò)展性還不夠理想,線性求解器算法還有待進(jìn)一步優(yōu)化。
[Abstract]:With the increasing development of complex type reservoir (low permeability, high water cut, complex lithologic reservoir, etc.), the mathematical model based on the reservoir numerical simulation becomes more and more complex, and the reservoir geological model tends to be refined, the grid is complicated, the number of wells is increased, and the types are diversified. These factors lead to these factors. The Jacobian linear algebraic equations formed by the numerical dispersion of the percolation model are large and bad. In the numerical simulation of all implicit reservoirs, the solution of the Jacobian linear algebraic equations is a major bottleneck, and the solution time tends to occupy 70% to 80% of the whole simulation time, and with the scale of the problem increasing, the proportion of the equations is increased. It will be further improved. It is one of the most effective ways to improve the speed of solving the Jacobian linear algebraic equations. In addition, the hardware architecture of the current computer is becoming more and more isomerized, using the multiprocessor (such as GPU, MIC) to help the solution of CPU computing in scientific computing collar. The domain is releasing huge energy and set off a new wave of high performance heterogeneous parallel computing. This paper designs an efficient string and parallel algorithm for the Jacobian linear algebraic equations for the classical standard black oil model. First, we analyze the strong coupled Jacobian discrete algebraic equations of the black oil model. Several common decoupling methods, such as staggered block decomposition decoupling, quasi implicit explicit saturation decoupling and implicit pressure explicit saturation decoupling, are used to investigate the decoupling effect of these methods and the influence on the ellipticity of pressure equations respectively. We find that the staggered block decomposition decoupling method can well weaken the pressure variation and saturation variable, saturation variable and saturation. The coupling relationship between variables has a good aggregation effect on the eigenvalues of the Jacobian matrix, but the method destroys the ellipticity of the pressure equation and increases the difficulty of the pressure equation. The method of the pseudo implicit pressure explicit saturation decoupling and implicit pressure saturation decoupling can obtain a better ellipticity by means of the IMPES method. The decoupling method only weakens the coupling degree of pressure variable and saturation variable in the pressure equation. According to the pressure equations obtained by the three decoupling methods mentioned above, this paper compares the solution speed of the classical AMG method, the VMB aggregation AMG method and the Pairwise aggregation AMG method, and simply analyzes the above three AMG methods to solve the problem. After the above analysis, we combine the implicit pressure explicit decoupling method with the classical CPR preconditioners to form a class of split preconditioners, and use the Pairwise aggregation AMG method to replace the classical AMG method to solve the pressure equation, and the solution of the split preconditioner is solved. The decomposition decoupling method compared with the staggered block decomposition is nearly 50%. next to the split preconditioners composed of the classical CPR preconditioners. Due to the development of the current reservoir simulation, the size of the Jacobian matrix breaks through tens of millions of orders and the more morbid state of the state, which brings great difficulties to the solution of the Jacobian linear algebraic equations. The efficient and robust algorithm for the large scale Jacobian linear algebraic system brought by the reservoir simulation is very necessary. This paper uses the interlaced block decomposition decoupling method to gather the eigenvalues of the Jacobian matrix and weaken the coupling relationship between the physical variables. Based on the auxiliary space correction idea, a robust, efficient and economical method is proposed. The split preconditioners are used as left preconditioners using the staggered block decomposition decoupling method, and then a multi-stage auxiliary subspace right preconditioners BASP: is designed to saturate the saturation subspace by the block Gauss Seidel method. The degree equation is an approximate solution to eliminate the high frequency error part of the saturation part; secondly, for the elliptic pressure equation with the strong interbreak coefficient, we use the AMG preconditioned Krylov method to approximate a certain precision and eliminate the low frequency error controlled by the pressure equation; finally, we do a block Gauss Seidel polishing in the whole space. Through a large number of oil field examples, the split preconditioners are highly efficient and robust. The speed of the simulator based on the preconditioners is 2 to 3 times faster than the international mainstream commercial simulator, and the fine oil reservoir model of tens of millions of grids is successfully simulated on the desktop workstation. Finally, this paper is based on the CPU-GPU isomeric system. An efficient parallel linear solution for solving the Jacobian linear algebraic equations is designed. The computing power of the supercomputer is becoming more and more powerful, but the architecture is becoming more and more complex. Most of them are multi core, many core processors, large cache, high bandwidth inter process communication structure and high speed I/O function design mode. Using high performance applications to make full use of the features and resources of the computer's isomeric architecture is worth exploring. In this paper, a sparse storage format for BHYB, which is suitable for GPU storage characteristics, is proposed for the structure characteristics of the Jacobian matrix in reservoir simulation. The acceleration ratio of SpMV based on this format is 19 times higher than that of the world famous Nvi The fastest HYB format of high efficiency CuSparse software package developed by dia company is fast 30%. Secondly, based on SIMT programming simulation based on GPU, a double dense parallel strategy is proposed in this paper. A BILU (L) method with high parallelism and good parallel scalability is designed, in which the average acceleration ratio of the BILU (0) decomposition stage and the triangle solution phase is 6.27 times respectively. 9.46 times; finally, a heterogeneous parallel UA AMG method is designed based on the heterogeneity of the computer and the parallelism of each part of the AMG algorithm. And the parallel UA AMG method does not lose the convergence speed of the serial UA AMG method. By integrating the parallel modules, we form a parallel BCPRP preconditioners based on the CPU-GPU isomer system. The numerical experiment shows that the parallel preconditioners are very robust. Compared with the improved serial BCPRP precondition algorithm, the parallel BCPRP preconditioners can improve the solution speed of the single GPU card by 3 times. In addition, based on the "Tianhe two" supercomputer, we developed a set of distributed parallel algorithm to expand the simulation scale to 100 million. At the same time, the efficiency of reservoir simulation is greatly improved. The distributed parallel solver has good scalability within thousands of cores, but after extending to 10008 CPU physical cores, the strong scalability of the distributed parallel solver is not ideal, and the linear solver algorithm still needs to be further optimized.
【學(xué)位授予單位】：昆明理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：TE319

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