Nonlinear Evolution Of R-T Instability And SPH Simulation

This dissertation is focused on two issues. Firstly,Rayleigh-Taylor (R-T) is studied. For initial rectangular and hexagonal disturbances on the interface,nonlinear fluid mechanics governing equations are solved respectively with the perturbation method,and 2nd-order approximate solutions are obtained. Then effects of nonlinearity on R-T instability are discussed,and its significance is manifested. After analyzing and comparing nonlinear evolution of R-T instability in two dimension with that in three dimension,it is the conclusions given that three-dimensional (3D) disturbance grows rapider than two-dimensional (2D) one,its timely evolution factor being 1.41 to 1.26 time as large as 2D's,in R-T instability linearly developing regime,and with time increasing,three-dimensional wave shape gradually deviates from 2D's. Even if 2nd-order modification being taken into account,difference between them is quite obvious. And therefore,there are some disparities when 3D interface instability is studied by using 2D technique whether quantitively or qualitatively.Secondly,the author independently develops a SPH code. Sod shock tube and strong shock are calculated as examples to test the code,and as well 2D R-T instability is simulated. SPH is a fullyLagrange gridless numeric technique. In chapter two,SPH is comment ed synoptically,its fundamentals is reviewed,and SPH formulae of Euler Equations are derived. In chapter five,several fundamental problems occurring in SPH implementation are discussed detailedly,e.g. the choice of kernel,the definition of smoothing length,the approach of searching the nearest neighbors,how to dispose boundary,and how to initialize the particles etc.The current researches pave a way for us to continue investigating R-T instability and extend science and engineering applications of SPH technique. Conclusions are presented in chapter six,and also the problems to be settled in future are indicated.