Created
November 7, 2010 15:56
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ah but it doesnt work ffffuuuuu...
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| #! /usr/bin/python2 | |
| """This is a module that returns the analytical velocity. | |
| Once u_i(y) and cos(l_i*z) are known. The variables might be renamed | |
| this is just a guide. | |
| m&b refers to text. | |
| """ | |
| from math import fabs, cos, sin, cosh, sinh, hypot, pi | |
| TOL = 1e-6 | |
| def velocity(ha, asp, y_co, z_co): | |
| """Return final velocity at some point in domain. | |
| From the fourier modes of y and z contributions. | |
| 1.0<= ha <= 100 | |
| 0.01<=asp<1.0 | |
| 0.0<=y_co<=asp*z_co | |
| 0.0<=z_co<=1 | |
| """ | |
| i = 1 | |
| u = 0.0 | |
| uiy = u_y(ha, asp, i, y_co) | |
| uiz = u_z(asp, z_co, i) | |
| while 1: | |
| uiy = u_y(ha, asp, y_co, i) | |
| uiz = u_z(asp, z_co, i) | |
| if fabs(uiy*uiz) <= TOL: | |
| break | |
| u += uiy*uiz | |
| i += 2 | |
| return u | |
| def u_z(a, z, i): | |
| """The z contribution to velocity from formulae in m&b | |
| """ | |
| return cos(0.5*i*pi*a*z) | |
| def f(y, p1, p2): | |
| """intermediary function for u_y computation | |
| """ | |
| return sinh(p1)*cosh(p2*y)-sinh(p2)*cosh(p1*y) | |
| def u_y(h, a, y, i): | |
| """The y contribution of velocity, from formula. | |
| """ | |
| l = 0.5*i*pi*a | |
| k = -2*a*sin(l/a)/l | |
| pi1 = 0.5*(h - hypot(h, 2*l)) | |
| pi2 = 0.5*(h + hypot(h, 2*l)) | |
| return (k/l**2)*(1-(f(y, pi1, pi2)/f(1.0, pi1, pi2)) |
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