【作者】 李玉冉；

【导师】 李明军；

【作者基本信息】 湘潭大学 ， 计算数学， 2008， 硕士

【摘要】 Rayleigh-Taylor不稳定现象是ICF(InertialConfinementFusion)应用中一个很基础但很重要的问题。它在天体物理、海洋混合层、地质、爆炸等众多领域中都有着重要的作用和意义。近些年来,国内外的许多学者对Rayleigh-Taylor不稳定性现象做了一系列的研究和数值模拟,采用多种数值方法,并取得了许多重要的结果。本文在一些近期文献的基础上对Rayleigh-Taylor不稳定现象做了进一步研究。文中利用一组控制方程组体系描述流场的运动状态,并且考虑固壁边界条件下整个流场形态的变化,发现在壁面附近的界面流体粘滞于初始位置,导致整个界面形状发生很大弯曲;同时,分别利用5rd-WENO,3rd-WENO,3rd-MCeno数值方法对Rayleigh-Taylor不稳定现象数值模拟,通过对数值结果的比较发现修正系数格式具有很大的计算优势。第一章介绍计算流体力学的发展状况,对本文主要研究工作的背景及其发展进行简要的介绍。第二章以描述高雷诺数流动为目的,将流场分为三个区域。通过对Navier-Stokes(NS)方程组的简化,得到一组描述流场的控制方程组体系。第三章描述Rayleigh-Taylor不稳定现象的数值方法很多,本文对5rd-WENO,3rd-WENO,3rd-MCeno这三种数值格式进行介绍,最后通过数值例子来说明3rd-MCeno方法的有效性和优越性。第四章在已有理论的基础上,首先利用高阶精度的5rd-WENO格式数值模拟滑移边界条件下的RT不稳定现象,让其与固壁边界条件下的数值结果比较,从而发现流场形态的巨大变化;其后通过利用3rd-MCeno和高阶数值格式5rd-WENO方法分别模拟此现象,通过比较图像结果发现3rd-MCeno格式的优势,其捕捉界面的能力接近于高阶精度格式,并且节约了相当多的CPU时间。更多还原

【Abstract】 The problem of Rayleigh-Taylor instability plays a crucial role in ICF(InertialConfinementFusion). In many fields, such as astrophysics, ocean mixed layer,geology, explosion, this problem has important application and significance. Inrecent years, many scholars adopt various computational methods to simulatethis phenomenon, and receive series of numerical results.In this paper, based on some recent methods, we present further research us-ing a system of control equations to describe the state of ?ow field; by consideringrigid boundary condition, we also find the interface nearby the well located to theinitial position, which leads to the whole interface shape changing largely. Onthe other hand, we compare three numerical methods―5rd-WENO, 3rd-WENO,3rd-MCeno, and obtain the advantageous of 3rd-MCeno, which has less runningtime than the other two.In chapter one, we introduce the development of computational ?uid dynam-ics, and some background knowledge.In chapter two, in order to describe high Reynolds number ?ows precisely,the ?ow field has been divided into three sections: inviscid region, viscid-inviscidregion, boundary region. By simplifying Naiver-Stokes equations, get a systemof equations.In chapter three, by comparing with numerical methods 5rd-WENO,3rd-WENO, 3rd-MCenohas showed the validity and advantages with simulating theRT instability.In chapter four, firstly, we compare the results of RT instability on thecondition of slip boundary condition with it on the condition of rigid boundarycondition, which show di?erent ?ow state. Then, numerical example shows thatthe 3rd-MCeno scheme has ability to capture interface and uses less runningtime.更多还原