【作者】 万钊；

【导师】 邓小刚； 毛枚良；

【作者基本信息】 中国空气动力研究与发展中心 ， 力学、流体力学， 2010， 硕士

【摘要】 研究表明,邓小刚等提出的微可压缩模型(SCM)求解低速流动很有效。然而由于采用了与完整Navier-Stokes方程相同的连续方程和动量方程,其特征系统在来流马赫数很低的时候表现出较强的刚性,难以求解极低马赫数的流动。针对这一问题发展的预处理形式微可压模型(SCM-P)本质上也存在着方程不相容的缺陷,在定常领域内取得较大成功的同时,却在非定常流场和临界状态计算中很可能由于误差的积累而得到非物理解。针对这些问题,本文发展了一种新的代数预处理形式微可压模型(SCM-AP),通过一系列典型算例的模拟,验证了代数预处理后的微可压模型算法,取得了良好的效果。本文共分为六章,各章内容如下:第一章为引言,简要介绍了数值模拟低马赫数流动研究背景和目前比较流行的算法,简述了微可压缩模型(SCM)和预处理形式的微可压模型(SCM-P)在低马赫数和极低马赫数流动计算中的模拟特性以及面临的问题。最后介绍了本文的工作。第二章简要介绍了微可压模型(SCM)及其在极低马赫数条件下采用特征分裂方法时的刚性问题,并通过代数预处理方法提出了四种解决方案,确保了离散方程左端隐式矩阵主对角占优。第三章对第二章提出的四种方案进行了稳定性分析,选择了两种满足稳定性要求的方案作进一步的发展,并分析了两种方案实施过程中所作的近似处理对稳定性的影响。第四章考察了本文发展的两种新算法:SCM-AP1、SCM-AP2,把它们应用于模拟方腔流、定常/非定常粘性圆柱绕流、定常/非定常翼型绕流等二维算例,并与SCM和SCM-P在计算精度和效率上进行了比较,发现SCM-AP2有良好的计算精度和收敛速度。第五章将SCM-AP2应用到三角翼流场、椭球流场的模拟中,展示了SCM-AP2对大攻角下尖前缘外形分离涡流场的良好模拟能力和计算精度。第六章为结束语,对本文工作进行了概括总结,指出了仍需进一步研究的一些工作。最后是致谢及本文的参考文献。更多还原

【Abstract】 The Slightly Compressible ModeI(SCM)efficient for lOW Mach number flow calculationderived by Deng Xiaogang is veryBut the eigenvalue system ofthe SCM equations shows strong stiffness when the freesteam Mach number is very low,because the same governing equations with the Navier-Stokes equations are introducedin SCM．A preconditioned method proposed for SCM(SCM-P)is not very effective in solving the unsteady flow calculations and critical state，since the continuity equationis only satisfied in the steady state．In this thesis based on SCM．a new preconditioned method has been proposed．This thesis iS composed of six chapters：The first chapter is the preface of this thesis．The background of the simulation forlOW Mach number flows iS introduced jn brief SO as to the popular arithmetic．The characteristic and problems confronted in using SCM and SCM．P to calculate the low and very low Mach number flows are included in the next part．The last part is theresearch work ofthis thesis．In the second chapter,the stiffneSS of SCM iS introduced．Four schemes areproposed based on algebraic preconditioned methods．the results indicate an importantimprovement．In the third chapter，the stability and the convergence characteristics of methodsproposed in chapter 2 are investigated．SCM-APl and SCM-AP2 which exhibitfeasible results are further developed in this thesis．The effects of the approximationsintroduced in the implementations on the stability are analysed．In the fourth chapter,some two．dimensionaJ results calculated by SCM．APl andSCM-AP2 are presented and compared with the results calculated by SCM and SCM-PIn the present work，SCM·AP2 is more excellent in the precision and convergence．In the fifth chapter，flow fields around a delta wing and an ellipsoid are simulatedby the SCM-AP2．Results show that SCM．AP2 is effective in simulating unsteadyseparation flows at high angle of attack．The concluding remarks are given in the sixth chapter,where the summary ofcurrent study work is presented and the job tO be carried on in future is pointed out asweIlIn the end，the references and acknowledgements are presented．更多还原