def ddx_exactVeen(x):
_, u = exactVeen(x)
Qg = ug * Hg
tmp = Qg + Mg * (x - xg)
Cs = (rho * g * omega / (4.0 * Bg))**n
dudx = Cs * tmp**n / u**n
dHdx = (Mg * u - tmp * dudx) / u**2
return dHdx, dudx
def getsides(x):
if x <= xg:
H, u, _ = exactBod(x)
T, B = exactBodBueler(x)
dH, du = ddx_exactBod(x)
LL = np.array([[(2.0/n)*B*H*du**q, 0, 0],
[H, u, 0],
[0, -rg*H, 1]])
RR = np.array([[0, -2.0*B*du**(1.0/n), 1],
[-dH, -du, 0],
[-k*rg*H, -k*rg*u+rg*dH, 0]])
else:
H, u = exactVeen(x)
dH, du = ddx_exactVeen(x)
LL = np.array([[(2.0/n)*Bg*H*du**q, 0, 0],
[H, u, 0],
[0, -omega*rg*H, 1]])
RR = np.array([[0, -2.0*Bg*du**(1.0/n), 1],
[-dH, -du, 0],
[0, omega*rg*dH, 0]])
return LL, RR
ax2fig3.set_ylim(0.0,2.0)
bbeta[x > exactsolns.xg] = 0.0
ax1fig3.plot((x-exactsolns.xa)/1000.0,bbeta/1.0e10,'k:',lw=1.5)
imagename = nameroot + '-beta-T.pdf'
plt.savefig(imagename)
print ' image file %s saved' % imagename
#plt.show()
# thickness error and velocity error in figure 5
Hexact = np.zeros(np.shape(H))
uexact = np.zeros(np.shape(u))
for j in range(len(x)):
if x[j] < exactsolns.xg:
Hexact[j], uexact[j], _ = exactsolns.exactBod(x[j])
else:
Hexact[j], uexact[j] = exactsolns.exactVeen(x[j])
fig = plt.figure(figsize=(6,5))
plt.subplot(2,1,1)
plt.semilogy((x-exactsolns.xa)/1000.0,abs(H-Hexact),'k',lw=2.0)
plt.semilogy((x-exactsolns.xa)/1000.0,abs(Hmid-Hexact),'k--',lw=3.0)
ax1 = plt.gca()
ax1.set_xlim([0.0,(xoceanend-exactsolns.xa)/1000.0])
plt.grid(True)
plt.ylabel("H error (m)", fontsize=14)
plt.subplot(2,1,2)
plt.semilogy((x-exactsolns.xa)/1000.0,abs(u-uexact) * exactsolns.secpera,'k',lw=2.0)
plt.semilogy((x-exactsolns.xa)/1000.0,abs(umid-uexact) * exactsolns.secpera,'k--',lw=3.0)
ax2 = plt.gca()
ax2.set_xlim([0.0,(xoceanend-exactsolns.xa)/1000.0])
ax2.set_yticks([1.0e-14,1.0e-12,1.0e-10,1.0e-8,1.0e-6,1.0e-4,1.0e-2])
plt.grid(True)