三维非定常等熵流中的Chaplygin方程——Dirac-Pauli表象的复变函数理论及其在流体力学中的应用(Ⅲ)
Chaplygin Equation in Three-Dimensional Non-Constant Isentropic Flow——The Theory of Functions of a Complex Variable under Dirac-Pauli Represen tation and Its Application in Fluid Dynamics(Ⅲ)
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摘要: 本文是文[1]的继续。在本文中,我们将等熵气体动力学方程组分成两类问题来处理:其一为三维非定常无旋流(因而也是等熵流),其二为三维非定常等熵无散流(即不可压缩等熵流)。我们应用Dirac-Pauli表象的复变函数理论并采用Legendre变换,将此两类问题的方程组变换到速度空间,从而得到了两种推广的Chaplygin方程。推广的Chaplygin方程是一个线性偏微分方程,它的通解至多由超几何函数表示。由此,我们求得了气体动力学三维非定常等熵流的一般问题的通解。Abstract: This work is the continuation of the discussion of ref, [1], In this paper we resolve the equations of isentropic gas dynamics into two problems: the three-dimensional non-constant irrotational flow (thus the isentropic flow, too), and the three-dimensional non-constant indivergent flow(i.e, the incompressible isentropic flow).We apply the theory of functions of a complez variable under Dirac-Pauli representation and the Legendre transformation,transform these equations of two problems from physical space into velocity space,and obtain two general Chaplygin equations in this paper, The general Chaplygin equation is a linear difference equation,and its general solution can be expressed at most by the hypergeometric functions, Thus we can obtain the general solution of general problems for the three-dimensional non-constant isentropic flow of gas dynamics.
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