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1.
有关二维Euler方程的一些估计   总被引:6,自引:0,他引:6  
首先得到Lorentz空间中的一些结果,然后在此基础上得到了有关二维Euler方程解的一些估计。这些估计与该方程当初始旋度ω0∈L^-1∩L^p(p〉1)时解的唯一性有关。  相似文献
2.
简化常数变易法求解二阶欧拉方程   总被引:6,自引:0,他引:6  
胡劲松  郑克龙 《大学数学》2005,21(2):116-119
将“常数变易”法求二阶非齐次欧拉方程特解的过程进行了简化,从而得出了求二阶欧拉方程的通解的一般公式.此方法简单、运算量小.  相似文献
3.
一维高精度离散GDQ方法   总被引:4,自引:0,他引:4       下载免费PDF全文
郑华盛  赵宁  成娟 《计算数学》2004,26(3):293-302
GDQ method is a kind of high order accurate numerical methods developed several years ago, which have been successfully used to simulate the solution of smooth engineering problems such as structure mechanics and incompressible fluid dynamics. In this paper, extending the traditional GDQ method, we develop a new kind of discontinuous GDQ methods to solve compressible flow problems of which solutions may be discontinuous. In order to capture the local features of fluid flows, firstly, the computational domain is divided into many small pieces of subdomains. Then, in each small subdomain, the GDQ method is implementedand some kinds of numerical flux limitation conditions will be required to keep the correct flow direction. At the boundary interface between subdomains, we also use some kind of flux conditions according to the flow direction. The numerical method obtained by the above steps has the advantages of high order accuracy and easy to treat boundary conditions. It can simulate perfectly nonlinear waves such as shock, rarefaction wave and contact discontinuity. Finally, the numerical experiments on one dimensional Burgers equation and Euler equations are given.The numerical results verify the validation of the method.  相似文献
4.
关于不可压、无粘流体的Euler方程初值问题的适定性(Ⅰ)   总被引:3,自引:3,他引:0  
以分层理论为基础,讨论了Euler方程不适定的初值问题以及不适定问题的形式可解性,并给出了某些不适定初值问题存在形式解的条件与计算方法。特别讨论了R^4中的超平面{t=0}上初值问题的适定性并给出了存在不唯一解的例证。  相似文献
5.
高分辨KFVS有限体积方法及其CFD应用   总被引:3,自引:0,他引:3       下载免费PDF全文
汤华中  邬华谟 《计算数学》1999,21(3):375-384
1.引言文中研究三维Euler方程组的数值求解·儿1)中p,(。。,。。,。z),p和E分别表示流体密度,流体速度矢量,压力和总能.方程组(1.1)是不封闭的,除非增加一个额外的方程一状态方程p一pk句,e表示单位质量内能.本文仅限于理想气体,此时状态方程为p一(、-1加e.队2)近H十年来,涌现了许多求解方程组(1.1)的无振荡、高分辨格式,例如TVD格式问,**O格式问等,它们在一定程度上促进了航空航天和造船事业的发展.其中有一类根据双曲方程组(1.l)特征值的符号建立的迎风格式尤为突出,与中心格式相比,迎风格式的耗…  相似文献
6.
Isospectral theory of the Lax pairs of both 3D and 2D Euler equations of inviscid fluids is developed. Eigenfunctions are represented through an ergodic integral. The Koopman group and mean ergodic theorem are utilized. Further harmonic analysis results on the ergodic integral are introduced. The ergodic integral is a limit of the oscillatory integral of the first kind.

  相似文献

7.
Numeric treatment of contact discontinuity with multi-gases   总被引:2,自引:0,他引:2  
In this paper we work with a finite-volume-procedure for the computation of the one-dimensional Euler equations for the treatment of multi-gases and the problem of the correct treatment of the discontinuity was more nearly investigated. A suggested equation was embedded in the finite volumes context and implemented in our code accordingly and regarded as validated.  相似文献
8.
We present a global solution to a Riemann problem for the pressure gradient system of equations.The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values.  相似文献
9.
We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach's experiment for the compressible Euler system, i.e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.  相似文献
10.
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