Sports Stream Function Equations Of Two-dimensional Laminar Flow Direct Method

Sudden expansion flow is an usual flow. However, there are some nonlinear phenomena that are paying much attention to by researchers.At present, for this problem the researchers concentrate on these aspects as follow: the length that is needed when the flow develop enough after passing the sudden expansion cross; the length of circulating region and intensity of circulating; the influence which some parameters of cross before suddenly expanding have on the movement factors after suddenly expanding. But, there are no theories on the phenomena existing in sudden expansion flow indeed. Besides, the influence which the symmetry of the cross before the sudden expanding have on the flow after sudden expanding have not been mentioned .Moreover, as for as the sudden expansion flow of open channel, the confirming of the maximum length, which the main flow after suddenly expanding departure the symmetric axis, and the location of the relevant cross, are as important as the calculation of the length of circulating region and the intensity of circulating.Before, the original equation chosen in calculating of sudden expansion flow are mainly N-S equation and vortex-stream function equation, which refer to many unknown quantities and having too many courses before getting the results, even bring on the difficulty in dealing with the boundary condition.This paper, derives from the basic equation of fluid flow ,N-S equation, considering of the definition of vortex and stream function, educes the vorticity stream function equations, and then ,at this basic, founds the stream function equation:In the equation, all of the movement factors are expressed by stream functions ,the thought are distinct, the number of unknown quantities becomes less and the boundary condition simplifies. Thus, the equationcan solve the problem of vortex on wall existing in the former vorticity stream function equation.Because of the higher non-linearity of the stream function equation, it doesn't fit the traditional mathematical physics equation . This paper tries to circulate accurate numerical solutions. And then , at the basic of analysis of the usual numerical solutions, this paper chooses finite differential method to disperse the stream function...