def calcFourier(x,y,z,a,alph,freq,mu,c,U,tvec):
soln_u = np.zeros((len(x),len(tvec)),dtype=np.complex128)
soln_v = np.zeros((len(x),len(tvec)),dtype=np.complex128)
soln_w = np.zeros((len(x),len(tvec)),dtype=np.complex128)
for k in range(len(tvec)):
out = lES.sphere3DOscillating(x,y,z,a,alph,freq,mu,c,U,tvec[k])
soln_u[:,k] = out[0]
soln_v[:,k] = out[1]
soln_w[:,k] = out[2]
return soln_u, soln_v, soln_w
def calcFourier(x, y, z, a, alph, freq, mu, c, U, tvec):
soln_u = np.zeros((len(x), len(tvec)), dtype=np.complex128)
soln_v = np.zeros((len(x), len(tvec)), dtype=np.complex128)
soln_w = np.zeros((len(x), len(tvec)), dtype=np.complex128)
for k in range(len(tvec)):
out = lES.sphere3DOscillating(x, y, z, a, alph, freq, mu, c, U,
tvec[k])
soln_u[:, k] = out[0]
soln_v[:, k] = out[1]
soln_w[:, k] = out[2]
return soln_u, soln_v, soln_w
def testOscillatingSphere3D_Drag():
'''
Checks total drag on the sphere (scalar value).
'''
print('Test case: Oscillating sphere in 3D, testing drag (takes a very long time)...')
a = 0.25
freq = 71
t=0
mu = 1.0
nu = 1.1
alph = np.sqrt(1j*2*np.pi*freq/nu)
tN = 400
dtheta = 2*np.pi/tN
theta = np.arange(dtheta/2,2*np.pi,dtheta)
phi = np.arange(dtheta/2,np.pi,dtheta)
xs = np.zeros((tN**2/2,))
ys = np.zeros((tN**2/2,))
zs = np.zeros((tN**2/2,))
for i in range(tN):
th = theta[i]
xs[i*tN/2:(i+1)*tN/2] = a*np.cos(theta[i])*np.sin(phi)
ys[i*tN/2:(i+1)*tN/2] = a*np.sin(theta[i])*np.sin(phi)
zs[i*tN/2:(i+1)*tN/2] = a*np.cos(phi)
spts = np.column_stack([xs,ys,zs])
u,v,w,p,xdrag,ydrag,zdrag = lES.sphere3DOscillating(spts[:,0],spts[:,1],spts[:,2],a,alph,freq,mu)
myfactor = 1.4
elist = [a/(4*(myfactor**k)) for k in range(0,3)]
# elist = [a/(2*(myfactor**k)) for k in range(0,3)]
errdragG = np.zeros((len(elist),3))
errdragE = np.zeros((len(elist),3))
for k in range(len(elist)):
eps = elist[k]
rsd = RS.Brinkman3DGaussianStokesletsAndDipolesSphericalBCs(eps,mu,alph,a)
xdragreg, ydragreg, zdragreg = regOscillatingSphere3D_Drag(rsd,spts,phi,dtheta,a,freq)
errdragG[k,:] = [np.abs(xdrag-xdragreg)/np.abs(xdrag),np.abs(ydrag-ydragreg),np.abs(zdrag-zdragreg)]
if np.all(errdragG < 2.e-4):
print("Gaussian blob, drag passed")
else:
print("Gaussian blob, drag failed")
# print("Drag error should be small:")
# print(errdragG)
myfactor = 1.4
elist = [a/(12*(myfactor**k)) for k in range(2,5)]
# elist = [a/(6*(myfactor**k)) for k in range(2,5)]
for k in range(len(elist)):
eps = elist[k]
rsd = RS.Brinkman3DNegExpStokesletsAndDipolesSphericalBCs(eps,mu,alph,a)
xdragreg, ydragreg, zdragreg = regOscillatingSphere3D_Drag(rsd,spts,phi,dtheta,a,freq)
errdragE[k,:] = [np.abs(xdrag-xdragreg)/np.abs(xdrag),np.abs(ydrag-ydragreg),np.abs(zdrag-zdragreg)]
if np.all(errdragE < 2.e-4):
print("Negative exponential blob, drag passed")
else:
print("Negative exponential blob, drag failed")
def testOscillatingSphere3D_Drag():
'''
Checks total drag on the sphere (scalar value).
'''
print(
'Test case: Oscillating sphere in 3D, testing drag (takes a very long time)...'
)
a = 0.25
freq = 71
t = 0
mu = 1.0
nu = 1.1
alph = np.sqrt(1j * 2 * np.pi * freq / nu)
tN = 400
dtheta = 2 * np.pi / tN
theta = np.arange(dtheta / 2, 2 * np.pi, dtheta)
phi = np.arange(dtheta / 2, np.pi, dtheta)
xs = np.zeros((tN**2 / 2, ))
ys = np.zeros((tN**2 / 2, ))
zs = np.zeros((tN**2 / 2, ))
for i in range(tN):
th = theta[i]
xs[i * tN / 2:(i + 1) * tN / 2] = a * np.cos(theta[i]) * np.sin(phi)
ys[i * tN / 2:(i + 1) * tN / 2] = a * np.sin(theta[i]) * np.sin(phi)
zs[i * tN / 2:(i + 1) * tN / 2] = a * np.cos(phi)
spts = np.column_stack([xs, ys, zs])
u, v, w, p, xdrag, ydrag, zdrag = lES.sphere3DOscillating(
spts[:, 0], spts[:, 1], spts[:, 2], a, alph, freq, mu)
myfactor = 1.4
elist = [a / (4 * (myfactor**k)) for k in range(0, 3)]
# elist = [a/(2*(myfactor**k)) for k in range(0,3)]
errdragG = np.zeros((len(elist), 3))
errdragE = np.zeros((len(elist), 3))
for k in range(len(elist)):
eps = elist[k]
rsd = RS.Brinkman3DGaussianStokesletsAndDipolesSphericalBCs(
eps, mu, alph, a)
xdragreg, ydragreg, zdragreg = regOscillatingSphere3D_Drag(
rsd, spts, phi, dtheta, a, freq)
errdragG[k, :] = [
np.abs(xdrag - xdragreg) / np.abs(xdrag),
np.abs(ydrag - ydragreg),
np.abs(zdrag - zdragreg)
]
if np.all(errdragG < 2.e-4):
print("Gaussian blob, drag passed")
else:
print("Gaussian blob, drag failed")
# print("Drag error should be small:")
# print(errdragG)
myfactor = 1.4
elist = [a / (12 * (myfactor**k)) for k in range(2, 5)]
# elist = [a/(6*(myfactor**k)) for k in range(2,5)]
for k in range(len(elist)):
eps = elist[k]
rsd = RS.Brinkman3DNegExpStokesletsAndDipolesSphericalBCs(
eps, mu, alph, a)
xdragreg, ydragreg, zdragreg = regOscillatingSphere3D_Drag(
rsd, spts, phi, dtheta, a, freq)
errdragE[k, :] = [
np.abs(xdrag - xdragreg) / np.abs(xdrag),
np.abs(ydrag - ydragreg),
np.abs(zdrag - zdragreg)
]
if np.all(errdragE < 2.e-4):
print("Negative exponential blob, drag passed")
else:
print("Negative exponential blob, drag failed")
def testOscillatingSphere3D():
'''
Checks velocity outside of a sphere using L2 error;
checks pressure outside of a sphere using L2 error;
checks pointwise surface traction on the sphere using L-infinity error.
'''
print(
'Test case: Oscillating sphere in 3D (be patient, this may take a few minutes)...'
)
a = 0.25
h = a / 5.
X = np.mgrid[-2 * a + h / 2:2 * a:h, -2 * a + h / 2:2 * a:h,
-2 * a:2 * a + h / 2:h]
M = X.shape[-1]
N = np.floor(M / 2.0)
zlev = X[2, 0, 0, N]
xg = X[0, :, :, N]
yg = X[1, :, :, N]
x = X[0, :, :, :].flatten()
y = X[1, :, :, :].flatten()
z = X[2, :, :, :].flatten()
obspts = np.column_stack([x, y, z])
freq = 71
t = 0
mu = 1.0
nu = 1.1
alph = np.sqrt(1j * 2 * np.pi * freq / nu)
# spts = a*np.loadtxt(os.path.join(os.path.split(__file__)[0], 'voronoivertices0300.dat'))
tN = 50
dtheta = 2 * np.pi / tN
theta = np.arange(dtheta / 2, 2 * np.pi, dtheta)
phi = np.arange(dtheta / 2, np.pi, dtheta)
xs = np.zeros((tN**2 / 2, ))
ys = np.zeros((tN**2 / 2, ))
zs = np.zeros((tN**2 / 2, ))
for i in range(tN):
th = theta[i]
xs[i * tN / 2:(i + 1) * tN / 2] = a * np.cos(theta[i]) * np.sin(phi)
ys[i * tN / 2:(i + 1) * tN / 2] = a * np.sin(theta[i]) * np.sin(phi)
zs[i * tN / 2:(i + 1) * tN / 2] = a * np.cos(phi)
spts = np.column_stack([xs, ys, zs])
u, v, w, p, xdrag, ydrag, zdrag = lES.sphere3DOscillating(
x, y, z, a, alph, freq, mu)
t1, t2, t3 = lES.sphere3DOscillatingSurfaceTraction(
spts[:, 0], spts[:, 1], spts[:, 2], a, alph, freq, mu)
# umlevs=vRS.contourCircle(xg,yg,a,np.abs(u.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestuabs.pdf' ),None, "|u| for sphere at z=%f" % zlev)
# vmlevs=vRS.contourCircle(xg,yg,a,np.abs(v.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvabs.pdf'),None, "|v| for sphere at z=%f" % zlev)
# ualevs=vRS.contourCircle(xg,yg,a,np.angle(u.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestuang.pdf'),None,"angle(u) for sphere at z=%f" % zlev)
# valevs=vRS.contourCircle(xg,yg,a,np.angle(v.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvang.pdf'),None,"angle(v) for sphere at z=%f" % zlev)
# pmlevs=vRS.contourCircle(xg,yg,a,np.abs(p.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpabs.pdf'),None, "|p| for sphere at z=%f" % zlev)
# palevs=vRS.contourCircle(xg,yg,a,np.angle(p.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpang.pdf'),None,"angle(p) for sphere at z=%f" % zlev)
# print("exact soln")
# print(xdrag,ydrag,zdrag)
myfactor = 1.4
elist = [a / (4 * (myfactor**k)) for k in range(0, 3)]
# elist = [a/(2*(myfactor**k)) for k in range(0,3)]
errmagG = np.zeros((len(elist), ))
errangG = np.zeros((len(elist), ))
errmagE = np.zeros((len(elist), ))
errangE = np.zeros((len(elist), ))
errpmagG = np.zeros((len(elist), ))
errpangG = np.zeros((len(elist), ))
errpmagE = np.zeros((len(elist), ))
errpangE = np.zeros((len(elist), ))
errtmagG = np.zeros((len(elist), 3))
errtangG = np.zeros((len(elist), 3))
errtmagE = np.zeros((len(elist), 3))
errtangE = np.zeros((len(elist), 3))
for k in range(len(elist)):
eps = elist[k]
rsd = RS.Brinkman3DGaussianStokesletsAndDipolesSphericalBCs(
eps, mu, alph, a)
ureg, vreg, wreg, preg, t1reg, t2reg, t3reg = regOscillatingSphere3D(
rsd, obspts, spts, a, freq)
# vRS.contourCircle(xg,yg,a,np.abs(ureg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittesturegabs%02d.pdf' % k ),umlevs, "Reg |u| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.abs(vreg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvregabs%02d.pdf' % k),vmlevs, "Reg |v| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(ureg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittesturegang%02d.pdf' % k),ualevs,"Reg angle(u) for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(vreg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvregang%02d.pdf' % k),valevs,"Reg angle(v) for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.abs(preg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpregabs%02d.pdf' % k),pmlevs, "Reg |p| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(preg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpregang%02d.pdf' % k),palevs,"Reg angle(p) for sphere at z=%f" % zlev)
# print("Gaussian approx -- drag")
# print(xdragreg,ydragreg,zdragreg)
ind = np.nonzero(x**2 + y**2 + z**2 > a**2)
L2errmag = h**(1.5) * np.sqrt(
((np.abs(u[ind]) - np.abs(ureg[ind]))**2).sum() +
((np.abs(v[ind]) - np.abs(vreg[ind]))**2).sum() +
((np.abs(w[ind]) - np.abs(wreg[ind]))**2).sum())
L2errang = h**(1.5) * np.sqrt(
((np.angle(u[ind]) - np.angle(ureg[ind]))**2).sum() +
((np.angle(v[ind]) - np.angle(vreg[ind]))**2).sum() +
((np.angle(w[ind]) - np.angle(wreg[ind]))**2).sum())
errmagG[k] = L2errmag
errangG[k] = L2errang
L2errpmag = h**(1.5) * np.sqrt(
((np.abs(p[ind]) - np.abs(preg[ind]))**2).sum())
L2errpang = h**(1.5) * np.sqrt(
((np.angle(p[ind]) - np.angle(preg[ind]))**2).sum())
errpmagG[k] = L2errpmag
errpangG[k] = L2errpang
L2errtmag = [
np.max(np.abs((np.abs(t1) - np.abs(t1reg))) / np.abs(t1)),
np.max(np.abs((np.abs(t2) - np.abs(t2reg))) / np.abs(t2)),
np.max(np.abs((np.abs(t3) - np.abs(t3reg))) / np.abs(t3))
]
L2errtang = [
np.max(np.abs((np.angle(t1) - np.angle(t1reg)) / np.angle(t1))),
np.max(np.abs((np.angle(t2) - np.angle(t2reg)) / np.angle(t2))),
np.max(np.abs((np.angle(t3) - np.angle(t3reg)) / np.angle(t3)))
]
errtmagG[k, :] = L2errtmag
errtangG[k, :] = L2errtang
convmagG = np.zeros((len(elist) - 1, ))
convangG = np.zeros((len(elist) - 1, ))
convpmagG = np.zeros((len(elist) - 1, ))
convpangG = np.zeros((len(elist) - 1, ))
for k in range(len(elist) - 1):
convmagG[k] = np.log(errmagG[k] / errmagG[k + 1]) / np.log(myfactor)
convangG[k] = np.log(errangG[k] / errangG[k + 1]) / np.log(myfactor)
convpmagG[k] = np.log(errpmagG[k] / errpmagG[k + 1]) / np.log(myfactor)
convpangG[k] = np.log(errpangG[k] / errpangG[k + 1]) / np.log(myfactor)
if np.all(errmagG < 2.e-4) and np.all(errangG < 2.e-4):
print("Gaussian blob, velocity passed")
else:
print("Gaussian blob, velocity failed")
if np.all(errpmagG < 2.e-4) and np.all(errpangG < 2.e-4):
print("Gaussian blob, pressure passed")
else:
print("Gaussian blob, pressure failed")
if np.all(errtmagG < 2.e-4) and np.all(errtangG < 2.e-4):
print("Gaussian blob, surface traction passed")
else:
print("Gaussian blob, surface traction failed")
print("Surface traction error should be small:")
print(errtmagG)
print(errtangG)
print("Vel L2 error should be small:")
print(errmagG)
print(errangG)
print("Vel convergence rates should be high: ")
print(convmagG)
print(convangG)
print("Pressure L2 error should be small:")
print(errpmagG)
print(errpangG)
print("Pressure convergence rates should be high: ")
print(convpmagG)
print(convpangG)
myfactor = 1.4
elist = [a / (12 * (myfactor**k)) for k in range(2, 5)]
# elist = [a/(6*(myfactor**k)) for k in range(2,5)]
for k in range(len(elist)):
eps = elist[k]
rsd = RS.Brinkman3DNegExpStokesletsAndDipolesSphericalBCs(
eps, mu, alph, a)
ureg, vreg, wreg, preg, t1reg, t2reg, t3reg = regOscillatingSphere3D(
rsd, obspts, spts, a, freq)
# vRS.contourCircle(xg,yg,a,np.abs(ureg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittesturegabs%02d.pdf' % k ),umlevs, "Reg |u| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.abs(vreg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvregabs%02d.pdf' % k),vmlevs, "Reg |v| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(ureg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittesturegang%02d.pdf' % k),ualevs,"Reg angle(u) for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(vreg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvregang%02d.pdf' % k),valevs,"Reg angle(v) for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.abs(preg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpregabs%02d.pdf' % k),pmlevs, "Reg |p| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(preg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpregang%02d.pdf' % k),palevs,"Reg angle(p) for sphere at z=%f" % zlev)
# print("Neg exp approx")
# print(xdragreg,ydragreg,zdragreg)
ind = np.nonzero(x**2 + y**2 + z**2 > a**2)
L2errmag = h**(1.5) * np.sqrt(
((np.abs(u[ind]) - np.abs(ureg[ind]))**2).sum() +
((np.abs(v[ind]) - np.abs(vreg[ind]))**2).sum() +
((np.abs(w[ind]) - np.abs(wreg[ind]))**2).sum())
L2errang = h**(1.5) * np.sqrt(
((np.angle(u[ind]) - np.angle(ureg[ind]))**2).sum() +
((np.angle(v[ind]) - np.angle(vreg[ind]))**2).sum() +
((np.angle(w[ind]) - np.angle(wreg[ind]))**2).sum())
errmagE[k] = L2errmag
errangE[k] = L2errang
L2errpmag = h**(1.5) * np.sqrt(
((np.abs(p[ind]) - np.abs(preg[ind]))**2).sum())
L2errpang = h**(1.5) * np.sqrt(
((np.angle(p[ind]) - np.angle(preg[ind]))**2).sum())
errpmagE[k] = L2errpmag
errpangE[k] = L2errpang
L2errtmag = [
np.max(np.abs((np.abs(t1) - np.abs(t1reg))) / np.abs(t1)),
np.max(np.abs((np.abs(t2) - np.abs(t2reg))) / np.abs(t2)),
np.max(np.abs((np.abs(t3) - np.abs(t3reg))) / np.abs(t3))
]
L2errtang = [
np.max(np.abs((np.angle(t1) - np.angle(t1reg)) / np.angle(t1))),
np.max(np.abs((np.angle(t2) - np.angle(t2reg)) / np.angle(t2))),
np.max(np.abs((np.angle(t3) - np.angle(t3reg)) / np.angle(t3)))
]
errtmagE[k, :] = L2errtmag
errtangE[k, :] = L2errtang
convmagE = np.zeros((len(elist) - 1, ))
convangE = np.zeros((len(elist) - 1, ))
convpmagE = np.zeros((len(elist) - 1, ))
convpangE = np.zeros((len(elist) - 1, ))
for k in range(len(elist) - 1):
convmagE[k] = np.log(errmagE[k] / errmagE[k + 1]) / np.log(myfactor)
convangE[k] = np.log(errangE[k] / errangE[k + 1]) / np.log(myfactor)
convpmagE[k] = np.log(errpmagE[k] / errpmagE[k + 1]) / np.log(myfactor)
convpangE[k] = np.log(errpangE[k] / errpangE[k + 1]) / np.log(myfactor)
if np.all(errmagE < 2.e-4) and np.all(errangE < 2.e-4):
print("Negative exponential blob, velocity passed")
else:
print("Negative exponential blob, velocity failed")
if np.all(errpmagE < 2.e-4) and np.all(errpangE < 2.e-4):
print("Negative exponential blob, pressure passed")
else:
print("Negative exponential blob, pressure failed")
if np.all(errtmagE < 2.e-4) and np.all(errtangE < 2.e-4):
print("Negative exponential blob, surface traction passed")
else:
print("Negative exponential blob, surface traction failed")
print("Surface traction error should be small:")
print(errtmagE)
print(errtangE)
print("Vel L2 error should be small:")
print(errmagE)
print(errangE)
print("Vel convergence rates should be high: ")
print(convmagE)
print(convangE)
print("Pressure L2 error should be small:")
print(errpmagE)
print(errpangE)
print("Pressure convergence rates should be high: ")
print(convpmagE)
print(convpangE)
def testOscillatingSphere3D():
'''
Checks velocity outside of a sphere using L2 error;
checks pressure outside of a sphere using L2 error;
checks pointwise surface traction on the sphere using L-infinity error.
'''
print('Test case: Oscillating sphere in 3D (be patient, this may take a few minutes)...')
a = 0.25
h = a/5.
X = np.mgrid[-2*a+h/2:2*a:h,-2*a+h/2:2*a:h,-2*a:2*a+h/2:h]
M = X.shape[-1]
N = np.floor(M/2.0)
zlev = X[2,0,0,N]
xg = X[0,:,:,N]
yg = X[1,:,:,N]
x = X[0,:,:,:].flatten()
y = X[1,:,:,:].flatten()
z = X[2,:,:,:].flatten()
obspts = np.column_stack([x,y,z])
freq = 71
t=0
mu = 1.0
nu = 1.1
alph = np.sqrt(1j*2*np.pi*freq/nu)
# spts = a*np.loadtxt(os.path.join(os.path.split(__file__)[0], 'voronoivertices0300.dat'))
tN = 50
dtheta = 2*np.pi/tN
theta = np.arange(dtheta/2,2*np.pi,dtheta)
phi = np.arange(dtheta/2,np.pi,dtheta)
xs = np.zeros((tN**2/2,))
ys = np.zeros((tN**2/2,))
zs = np.zeros((tN**2/2,))
for i in range(tN):
th = theta[i]
xs[i*tN/2:(i+1)*tN/2] = a*np.cos(theta[i])*np.sin(phi)
ys[i*tN/2:(i+1)*tN/2] = a*np.sin(theta[i])*np.sin(phi)
zs[i*tN/2:(i+1)*tN/2] = a*np.cos(phi)
spts = np.column_stack([xs,ys,zs])
u,v,w,p,xdrag,ydrag,zdrag = lES.sphere3DOscillating(x,y,z,a,alph,freq,mu)
t1,t2,t3 = lES.sphere3DOscillatingSurfaceTraction(spts[:,0],spts[:,1],spts[:,2],a,alph,freq,mu)
# umlevs=vRS.contourCircle(xg,yg,a,np.abs(u.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestuabs.pdf' ),None, "|u| for sphere at z=%f" % zlev)
# vmlevs=vRS.contourCircle(xg,yg,a,np.abs(v.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvabs.pdf'),None, "|v| for sphere at z=%f" % zlev)
# ualevs=vRS.contourCircle(xg,yg,a,np.angle(u.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestuang.pdf'),None,"angle(u) for sphere at z=%f" % zlev)
# valevs=vRS.contourCircle(xg,yg,a,np.angle(v.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvang.pdf'),None,"angle(v) for sphere at z=%f" % zlev)
# pmlevs=vRS.contourCircle(xg,yg,a,np.abs(p.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpabs.pdf'),None, "|p| for sphere at z=%f" % zlev)
# palevs=vRS.contourCircle(xg,yg,a,np.angle(p.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpang.pdf'),None,"angle(p) for sphere at z=%f" % zlev)
# print("exact soln")
# print(xdrag,ydrag,zdrag)
myfactor = 1.4
elist = [a/(4*(myfactor**k)) for k in range(0,3)]
# elist = [a/(2*(myfactor**k)) for k in range(0,3)]
errmagG = np.zeros((len(elist),))
errangG = np.zeros((len(elist),))
errmagE = np.zeros((len(elist),))
errangE = np.zeros((len(elist),))
errpmagG = np.zeros((len(elist),))
errpangG = np.zeros((len(elist),))
errpmagE = np.zeros((len(elist),))
errpangE = np.zeros((len(elist),))
errtmagG = np.zeros((len(elist),3))
errtangG = np.zeros((len(elist),3))
errtmagE = np.zeros((len(elist),3))
errtangE = np.zeros((len(elist),3))
for k in range(len(elist)):
eps = elist[k]
rsd = RS.Brinkman3DGaussianStokesletsAndDipolesSphericalBCs(eps,mu,alph,a)
ureg, vreg, wreg, preg,t1reg,t2reg,t3reg = regOscillatingSphere3D(rsd,obspts,spts,a,freq)
# vRS.contourCircle(xg,yg,a,np.abs(ureg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittesturegabs%02d.pdf' % k ),umlevs, "Reg |u| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.abs(vreg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvregabs%02d.pdf' % k),vmlevs, "Reg |v| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(ureg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittesturegang%02d.pdf' % k),ualevs,"Reg angle(u) for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(vreg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvregang%02d.pdf' % k),valevs,"Reg angle(v) for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.abs(preg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpregabs%02d.pdf' % k),pmlevs, "Reg |p| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(preg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpregang%02d.pdf' % k),palevs,"Reg angle(p) for sphere at z=%f" % zlev)
# print("Gaussian approx -- drag")
# print(xdragreg,ydragreg,zdragreg)
ind = np.nonzero(x**2+y**2+z**2 > a**2)
L2errmag = h**(1.5)*np.sqrt( ((np.abs(u[ind])-np.abs(ureg[ind]))**2).sum() + ((np.abs(v[ind])-np.abs(vreg[ind]))**2).sum() + ((np.abs(w[ind])-np.abs(wreg[ind]))**2).sum() )
L2errang = h**(1.5)*np.sqrt( ((np.angle(u[ind])-np.angle(ureg[ind]))**2).sum() + ((np.angle(v[ind])-np.angle(vreg[ind]))**2).sum() + ((np.angle(w[ind])-np.angle(wreg[ind]))**2).sum() )
errmagG[k] = L2errmag
errangG[k] = L2errang
L2errpmag = h**(1.5)*np.sqrt( ((np.abs(p[ind])-np.abs(preg[ind]))**2).sum() )
L2errpang = h**(1.5)*np.sqrt( ((np.angle(p[ind])-np.angle(preg[ind]))**2).sum() )
errpmagG[k] = L2errpmag
errpangG[k] = L2errpang
L2errtmag = [np.max(np.abs((np.abs(t1)-np.abs(t1reg)))/np.abs(t1)),np.max(np.abs((np.abs(t2)-np.abs(t2reg)))/np.abs(t2)),np.max(np.abs((np.abs(t3)-np.abs(t3reg)))/np.abs(t3))]
L2errtang = [np.max(np.abs((np.angle(t1)-np.angle(t1reg))/np.angle(t1))),np.max(np.abs((np.angle(t2)-np.angle(t2reg))/np.angle(t2))),np.max(np.abs((np.angle(t3)-np.angle(t3reg))/np.angle(t3)))]
errtmagG[k,:] = L2errtmag
errtangG[k,:] = L2errtang
convmagG = np.zeros((len(elist)-1,))
convangG = np.zeros((len(elist)-1,))
convpmagG = np.zeros((len(elist)-1,))
convpangG = np.zeros((len(elist)-1,))
for k in range(len(elist)-1):
convmagG[k]=np.log(errmagG[k]/errmagG[k+1])/np.log(myfactor)
convangG[k]=np.log(errangG[k]/errangG[k+1])/np.log(myfactor)
convpmagG[k]=np.log(errpmagG[k]/errpmagG[k+1])/np.log(myfactor)
convpangG[k]=np.log(errpangG[k]/errpangG[k+1])/np.log(myfactor)
if np.all(errmagG < 2.e-4) and np.all(errangG < 2.e-4):
print("Gaussian blob, velocity passed")
else:
print("Gaussian blob, velocity failed")
if np.all(errpmagG < 2.e-4) and np.all(errpangG < 2.e-4):
print("Gaussian blob, pressure passed")
else:
print("Gaussian blob, pressure failed")
if np.all(errtmagG < 2.e-4) and np.all(errtangG < 2.e-4):
print("Gaussian blob, surface traction passed")
else:
print("Gaussian blob, surface traction failed")
print("Surface traction error should be small:")
print(errtmagG)
print(errtangG)
print("Vel L2 error should be small:")
print(errmagG)
print(errangG)
print("Vel convergence rates should be high: ")
print(convmagG)
print(convangG)
print("Pressure L2 error should be small:")
print(errpmagG)
print(errpangG)
print("Pressure convergence rates should be high: ")
print(convpmagG)
print(convpangG)
myfactor = 1.4
elist = [a/(12*(myfactor**k)) for k in range(2,5)]
# elist = [a/(6*(myfactor**k)) for k in range(2,5)]
for k in range(len(elist)):
eps = elist[k]
rsd = RS.Brinkman3DNegExpStokesletsAndDipolesSphericalBCs(eps,mu,alph,a)
ureg, vreg, wreg, preg,t1reg,t2reg,t3reg = regOscillatingSphere3D(rsd,obspts,spts,a,freq)
# vRS.contourCircle(xg,yg,a,np.abs(ureg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittesturegabs%02d.pdf' % k ),umlevs, "Reg |u| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.abs(vreg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvregabs%02d.pdf' % k),vmlevs, "Reg |v| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(ureg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittesturegang%02d.pdf' % k),ualevs,"Reg angle(u) for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(vreg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestvregang%02d.pdf' % k),valevs,"Reg angle(v) for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.abs(preg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpregabs%02d.pdf' % k),pmlevs, "Reg |p| for sphere at z=%f" % zlev)
# vRS.contourCircle(xg,yg,a,np.angle(preg.reshape((M-1,M-1,M))[:,:,N]),os.path.expanduser('~/scratch/unittestpregang%02d.pdf' % k),palevs,"Reg angle(p) for sphere at z=%f" % zlev)
# print("Neg exp approx")
# print(xdragreg,ydragreg,zdragreg)
ind = np.nonzero(x**2+y**2+z**2 > a**2)
L2errmag = h**(1.5)*np.sqrt( ((np.abs(u[ind])-np.abs(ureg[ind]))**2).sum() + ((np.abs(v[ind])-np.abs(vreg[ind]))**2).sum() + ((np.abs(w[ind])-np.abs(wreg[ind]))**2).sum() )
L2errang = h**(1.5)*np.sqrt( ((np.angle(u[ind])-np.angle(ureg[ind]))**2).sum() + ((np.angle(v[ind])-np.angle(vreg[ind]))**2).sum() + ((np.angle(w[ind])-np.angle(wreg[ind]))**2).sum() )
errmagE[k] = L2errmag
errangE[k] = L2errang
L2errpmag = h**(1.5)*np.sqrt( ((np.abs(p[ind])-np.abs(preg[ind]))**2).sum() )
L2errpang = h**(1.5)*np.sqrt( ((np.angle(p[ind])-np.angle(preg[ind]))**2).sum() )
errpmagE[k] = L2errpmag
errpangE[k] = L2errpang
L2errtmag = [np.max(np.abs((np.abs(t1)-np.abs(t1reg)))/np.abs(t1)),np.max(np.abs((np.abs(t2)-np.abs(t2reg)))/np.abs(t2)),np.max(np.abs((np.abs(t3)-np.abs(t3reg)))/np.abs(t3))]
L2errtang = [np.max(np.abs((np.angle(t1)-np.angle(t1reg))/np.angle(t1))),np.max(np.abs((np.angle(t2)-np.angle(t2reg))/np.angle(t2))),np.max(np.abs((np.angle(t3)-np.angle(t3reg))/np.angle(t3)))]
errtmagE[k,:] = L2errtmag
errtangE[k,:] = L2errtang
convmagE = np.zeros((len(elist)-1,))
convangE = np.zeros((len(elist)-1,))
convpmagE = np.zeros((len(elist)-1,))
convpangE = np.zeros((len(elist)-1,))
for k in range(len(elist)-1):
convmagE[k]=np.log(errmagE[k]/errmagE[k+1])/np.log(myfactor)
convangE[k]=np.log(errangE[k]/errangE[k+1])/np.log(myfactor)
convpmagE[k]=np.log(errpmagE[k]/errpmagE[k+1])/np.log(myfactor)
convpangE[k]=np.log(errpangE[k]/errpangE[k+1])/np.log(myfactor)
if np.all(errmagE < 2.e-4) and np.all(errangE < 2.e-4):
print("Negative exponential blob, velocity passed")
else:
print("Negative exponential blob, velocity failed")
if np.all(errpmagE < 2.e-4) and np.all(errpangE < 2.e-4):
print("Negative exponential blob, pressure passed")
else:
print("Negative exponential blob, pressure failed")
if np.all(errtmagE < 2.e-4) and np.all(errtangE < 2.e-4):
print("Negative exponential blob, surface traction passed")
else:
print("Negative exponential blob, surface traction failed")
print("Surface traction error should be small:")
print(errtmagE)
print(errtangE)
print("Vel L2 error should be small:")
print(errmagE)
print(errangE)
print("Vel convergence rates should be high: ")
print(convmagE)
print(convangE)
print("Pressure L2 error should be small:")
print(errpmagE)
print(errpangE)
print("Pressure convergence rates should be high: ")
print(convpmagE)
print(convpangE)
