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Viewing changes to tests/sw_fsphere/Williamson_RHwave.py

merge with branch including remap_surface_to_field but then removed this change and approached it a different way which seems to work

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tests/sw_fsphere/Williamson_RHwave.py
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from math import pi, cos, sin
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from fluidity.spheretools import cart2polar
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a=6.37122e6
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K=7.848e-6
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R=4
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omega=7.292e-5
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w=K
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h0=8e3
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g=9.80616
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def initial_velocity():
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    def sol(X,t):
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        theta=2*pi*X[0]/360.0
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        phi=2*pi*X[1]/360.0
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        u=a*w*cos(phi)+a*K*cos(phi)**(R-1)*(R*sin(phi)**2-cos(phi)**2)*cos(R*phi)
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        v=-a*K*R*cos(phi)**(R-1)*sin(phi)*sin(R*phi)
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        return ([u,v])
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    return sol
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def initial_height():
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    def sol(X,t):
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        ([theta,phi])=cart2polar(X)
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        A=0.5*w*(2*omega+w)*cos(phi)**2+0.25*K**2*cos(phi)**(2*R)*((R+1)*cos(phi)**2+(2*R**2-R-2)-2*R**2*cos(phi)**-2)
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        B=((2*(omega+w)*K)/((R+1)*(R+2)))*cos(phi)**R*((R**2+2*R+2)-(R+1)**2*cos(phi)**2)
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        C=0.25*K**2*cos(phi)**(2*R)*((R+1)*cos(phi)**2-(R+2))
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        return h0+(a**2/g)*(A+B*cos(R*phi)+C*cos(2*R*phi))
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    return sol