The purpose of this paper is to present a numerical methodology for simulating the flow of shock tunnel . the numerical approach uses a maccormack scheme or s - w spiliter for the quasi - one - dimensional euler equation coupled with real gas effect . a simple method is used to track contact discontinuities 采用maccormack格式及s - w分裂方法求解准一维euler方程,考虑高温下分子的振动、气体和壁面间的摩擦和传热,根据高压段的气体质量守恒的方法来跟踪接触间断。
We generated its grid surface on the fuselage or missile body according to the geometry projection relation between aerodynamic components and the bilinear interpolation approach . finally , we successfully developed a new algebra grid generation technique in virtue of the improved four - boundary interpolation . in this thesis , we put emphasis on the researches of aerodynamic inverse design and drag reduction questions for airfoil and wing using euler equations and control theory proposed by jameson ( 2 )进行了应用控制理论和二维欧拉方程的翼型气动反设计,以及有升力约束情形下翼型跨音速减阻问题研究,分别推导了相应的共轭方程及边界条件的数学形式,并给出了相应的梯度求解公式形式,研究发展了共轭方程及梯度的数值求解方法,成功进行了多个翼型的反设计和减阻问题研究。
Numerical experiments with our scheme and other central schemes for the initial value problems of convective equation , burgers equation and euler equations have been implemented . these results demonstrate the desired accuracy and high resolution of our scheme . also our scheme can be easily applied and implemented to a wide variety of problems 本文对所提格式用一维对流方程、 burgers方程、 euler方程的初值问题进行了大量的数值试验,并将结果与其它各阶中心差分格式进行了比较,试验结果表明,本文方法具有分辨率高和准确性好的特点。
The ns solver is developed from euler equation code by adding viscous terms and two - equation turbulence models . in order to get a better result , the improved jameson second and forth artificial dissipation is used , the implicit residual averaging and local time step techniques are employed to accelerate the convergence processing 本文是在欧拉方程求解器的基础上,通过加入粘性(耗散)项,把流场的主控方程由欧拉方程( euler )改为ns方程,然后引入两方程湍流模型,使其封闭。
After domain decomposition utilizing graph domain decompositions methods , the present thesis carries on sub - domain mesh information reorder , and make it spent little time . domain decompositions program and sub - domain mesh information reorder programs may be added to euler equations parallel computing program , so the overall grids information data is only needed to input in the course of euler equations parallel computation 利用图方法对整体网格分区以后,本文对分区后的子网格进行网格信息重排序,使其所花费的时间很少,因此可把分区程序与子网格信息重排程序加入到并行计算程序中,在实际的并行计算过程中只需读入总体网格数据即可。
Because euler equations have disconnected solutions named shock wave in numerical simulation flow field , and to make sure the disconnected solutions not expanding or vanishing among parallel computation sub - domains , there must be certain connections in the numerical value variable among the sub - domains 由于在欧拉方程数值模拟求解流场区域内存在间断解即激波,而计算流体力学并行数值计算是在分区的基础上进行的,为了使流场区域内的间断解不因分区并行计算而膨胀或消失,分区之间的数值变量必然存在着一定的联系。
In this work , we detailedly introduced the whole ideas of rkdg finite element method and the theory of constructing gas - kinetic schemes based on boltzmann equation . and then presented a kind of new computational method for solving id and 2d compressible euler equations , i . e . firstly , we discretize euler equations in the space with discontinuous galerkin finite element method ; secondly , we discretize temporal variable t with runge - kutta formula ; thirdly , for numerical fluxes constructing , we give two kinds of different numerical fluxes - kfvs and bgk numerical fluxes by using gas - kinetic schemes 本文分别对rkdg有限元方法的整个思想和基于boltzmann方程的分子动力学格式的构造思想给予了详细的介绍,并分别结合rkdg有限元方法与kfvs数值通量和bgk数值通量的构造方法,给出了一种求解一维、二维可压缩流体力学方程组新的计算方法,即,我们先用间断有限元方法进行空间离散,然后再对所得到的半离散格式使用runge - kuttatvd方法进行时间离散,得到全离散格式。
In this paper , high - order accurate weighted essentially non - oscillatory ( weno ) schemes are investigated and their applications in hyperbolic conservation laws are discussed . based on this , a new weno difference scheme which based on dispersion - relation - preserving relation is developed , and representative test cases with this scheme for computational aeroacoustics ( caa ) problems has been implemented and compared in order to test capability of wave capturing ; in addition , weno schemes generally do not converge at high order in the presence of contact discontinuity of euler equations , so a conservative front tracking technique coupling weno schemes and level set method to simulate the translating density profile is presented here , and numerical simulation with this technique for representative test case has been implemented and results show the desired accuracy 本文研究了高阶精度加权基本无振荡( weno )格式及其在双曲守恒律方程中的应用,在此基础上作了两个方面的工作:一是针对高频声波问题构造出一种基于保色散关系( drp )的weno有限差分格式,并对计算气动声学( caa )问题的代表性算例进行了大量数值实验,比较了该格式捕捉波数的能力;另外,针对高阶weno格式在处理euler方程的接触间断时精度有所降低的问题,研究了利用界面追踪技术levelset方法和高阶激波捕捉weno格式相结合的一种守恒追踪方法,并且给出有代表性的密度滑移面问题的算例,得到一致高阶精度的数值模拟结果。
The method is also tested by finite volume scheme and partitioning algorithm of euler equation in parallel computing in fluid dynamics . the testing results demonstrate that the suggested method in this method is of practical and scientific significance in parallel computing in fluid dynamics 本文还结合euler方程的有限体积格式和区域分解算法对文中的算法在流体力学并行计算中进行了进一步的验证,从数值计算结果可以看出,本文提出的算法能够很好地应用于计算流体力学并行计算,具有一定的科学应用价值。