共查询到20条相似文献,搜索用时 187 毫秒
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平面位势流动的速度图方法,对于一些特殊流动,有特别明显的优点。本文利用张量分析工具,对任意流面上的位势流,建立速度图方程,为解决一些特殊流动问题,提供一个分析方法。 相似文献
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该文首先提出了流面和流层的概念,然后推导出了半测地坐标系下流层内的三维NS (Navier-Stokes)方程,以及流面上的二维NS方程.通过引入流面上的流函数,得到了流函数方程的非线性初边值问题,并讨论了方程解的存在性和唯一性.基于以上讨论,提出了求解三维NS方程的维数分裂方法, 并给出了算例. 相似文献
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本文讨论了空气动力学中,不定常位势流同类激波与单波的相互作用在初等波充分弱的假定下,对同类激波与甲波相互作用时单波与激波互相穿透(若入射单波在激波的超音速一侧)或单波被激波反射(若入射单波在激波的亚音速一侧)的情形给出了解的存在性,并对它们相互作用后的(出射)单波的膨涨或压缩性,进行了详细的讨论;从而获得了二维位势流方程同类激波与单波相互作用的完整的结果. 相似文献
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讨论了一类带有组合型非线性项与调和位势的非线性Schr(o)dinger方程.通过构造变分问题,引入位势井方法.给出了位势井的结构和位势井深度函数的性质.得到了问题的相关集合在流之下的不变性.揭示了只要问题的初值属于位势井内或位势井外,则问题在今后所有时间内的解都存在于位势井内或井外.结合凹性方法,给出了解的整体存在性的最佳条件. 相似文献
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在这篇文章中,运用经典的张量分析方法,把流动区域用-个二维流形序列分割成一系列流层之并,推得在流层内半测地坐标之下的Navier-Stokes方程,在流形的法线方向应用向后Euler差分,推导了两维流形上的可压缩Navier-Stokes方程,和流函数满足的方程.在这个基础上,提出了一种维数分裂法的新算法.这种方法不同于区域分解法.对于三维问题,在区域分解法中我们必须在每个子区域上仍解三维问题,但是在这种新方法中,只需要在每个子区域上求解二维问题,不过是几个二维流形上的NS方程.文中还给出了-个透平机械内部流动的数值计算实例. 相似文献
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研究流过密集的具二次变化渗透性的重叠理想聚合体的流体.流体流由达西定律的布林克曼扩展及连续方程来刻画,通过引入流函数,求出上述方程在适当边界条件下的解析解,并将结果与一些已知的结果进行了比较. 相似文献
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A fluid flow in a multiply connected domain generated by an arbitrary number of point vortices is considered. A stream function for this flow is constructed as a limit of a certain functional sequence using the method of images. The convergence of this sequence is discussed, and the speed of convergence is determined explicitly. The presented formulas allow for an easy computation of the values of the stream function with arbitrary precision in the case of well-separated cylinders. The considered problem is important for applications such as eddy flows in oceans. Moreover, since finding the stream function of the flow is essentially identical to finding the modified Green’s function for Laplace’s equation, the presented method can be applied to a more general class of applied problems which involve solving the Dirichlet problem for Laplace’s equation. 相似文献
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How to predict the stability of a small-scale flow subject to perturbations is a significant multiscale problem. It is difficult to directly study the stability by the theoretical analysis for the incompressible flow of a Maxwell fluid because of its analytical complexity. Here, we develop the multiscale analysis method based on the mathematical homogenization theory in the stress–stream function formulation. This method is used to derive the homogenized equation which governs the transport of the large-scale perturbations. The linear stabilities of the large-scale perturbations are analyzed theoretically based on the linearized homogenized equation, while the effect of the nonlinear terms on the linear stability results is discussed numerically based on the nonlinear homogenized equation. The agreements between the multiscale predictions and the direct numerical simulations demonstrate the multiscale analysis method is effective and credible to predict stabilities of flows. 相似文献
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In this paper we will prove existence, uniqueness and regularity of a classical solution to a mixed boundary value problem for Chaplygin's hodograph equation, which is degenerate elliptic on a part of the boundary. This problem is derived from the study of detached bow shock ahead of a straight ramp in uniform supersonic flows in the hodograph plane. The proof depends on Perron's method and some techniques from linear elliptic equations. 相似文献
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Yaning Xie & Wenjun Ying 《高等学校计算数学学报(英文版)》2020,13(3):595-619
This paper presents a fourth-order kernel-free boundary integral method for the time-dependent, incompressible Stokes and Navier-Stokes equations defined on irregular bounded domains. By the stream function-vorticity formulation, the incompressible flow equations are interpreted as vorticity evolution equations. Time discretization methods for the evolution equations lead to a modified Helmholtz equation for the vorticity, or alternatively, a modified biharmonic equation for the stream function with two clamped boundary conditions. The resulting fourth-order elliptic boundary value problem is solved by a fourth-order kernel-free boundary integral method, with which integrals in the reformulated boundary integral equation are evaluated by solving corresponding equivalent interface problems, regardless of the exact expression of the involved Green's function. To solve the unsteady Stokes equations, a four-stage composite backward differential formula of the same order accuracy is employed for time integration. For the Navier-Stokes equations, a three-stage third-order semi-implicit Runge-Kutta method is utilized to guarantee the global numerical solution has at least third-order convergence rate. Numerical results for the unsteady Stokes equations and the Navier-Stokes equations are presented to validate efficiency and accuracy of the proposed method. 相似文献
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Jakob J. Keller 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(6):821-836
Introducing a vector potential, that is based on a pair of stream functions, and a velocity potential, antisymmetric equations for the stream functions are derived with the help of a variational principle. It is found that the equations are in a suitable form to investigate flows with helical symmetry, and, for example, to connect upstream axisymmetric flows with downstream helical flows. The special case of a transition from an upstream solid-body vortex to a downstream helical flow is investigated in detail. Furthermore, the stream-function equations are particularly useful to investigate general small-amplitude inertia waves on vortex flows. Time-dependent helical flows that are time-independent in a suitably rotating frame of reference can also be discussed with the proposed method. 相似文献
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S. Chen 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,289(1):387-409
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含开边界二维Stokes问题的Galerkin边界元解法 总被引:1,自引:1,他引:0
本文推导了含有开边界的二维有限域上Stokes问题的边界积分方程, 得出基于单层位势的第一类间接边界积分方程.对与之等价的边界变分方程用Galerkin边界元求解以得出单层位势的向量密度. 对于含有开边界端点的边界单元,采用特别的插值函数, 以模拟其固有的奇异性.论文用若干数值算例模拟了含有开边界的有限区域上不可压缩粘性流体的绕流.
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Shuxing Chen 《Journal of Differential Equations》2003,189(1):292-317
This paper concerns the multi-dimensional piston problem, which is a special initial boundary value problem of multi-dimensional unsteady potential flow equation. The problem is defined in a domain bounded by two conical surfaces, one of them is shock, whose location is also to be determined. By introducing self-similar coordinates, the problem can be reduced to a free boundary value problem of an elliptic equation. The existence of the problem is proved by using partial hodograph transformation and nonlinear alternating iteration. The result also shows the stability of the structure of shock front in symmetric case under small perturbation. 相似文献
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在本文中,一类新的矩阵型修正Korteweg-de Vries(简记为mmKdV)方程被首次通过RiemannHilbert方法研究,而且,这一方程可通过选取特殊的势矩阵来降阶为我们熟知的耦合型修正Kortewegde Vries方程.从方程对应的Lax对的谱分析入手,作者成功地建立了方程对应的Riemann-Hilbert问题.在无反射势的特殊条件下,mmKdV方程的精确解可由Riemann-Hilbert问题的解给出.而且,基于特殊势矩阵所对应的特殊对称性,作者可以对原有的孤子解进行分类,从而得到一些有趣的解的现象,比如呼吸孤子、钟形孤子等. 相似文献