def uavgGrad(n_chunk,chunk_bounds,T,uavg,zeta,profile=True):
'''
returns the time averaged sensitivity of the mean x-velocity profile
to the mass averaged velocity. Inputs are the number of time chunks, the
starting and ending step index of each chunk (chunk_bounds),
total simulation time T, the time averaged mean x-velocity profile
uavg, and time dilation terms zeta (length n_chunk vector)
if profile = 1, sensitivity of the entire profile is compute, otherwise
only the sesitivity of the centerline velocity is computed
'''
if profile:
grad = np.zeros(c_channel.c_qpts())
else:
grad = 0.0
y, w = quad()
for i in range(n_chunk):
start_step = chunk_bounds[i]
end_step = chunk_bounds[i+1]
vavg = IvelAvg(start_step,end_step,T,profile)
uEnd = (vel(end_step).mean(2)).mean(0)
if not(profile): uEnd = uEnd[c_channel.c_qpts()/2 + 1]
grad = grad + vavg + (1./T) * zeta[i]*(uEnd-uavg)
return grad
def velAvg(start_step,end_step,T,profile=True):
'''
returns the time averaged velocity profile
'''
if profile:
uavg = np.zeros(c_channel.c_qpts())
else:
uavg = 0.0
y, w = quad()
assert 0 <= start_step <= end_step <= c_channel.c_nsteps()
for i in range(start_step,end_step):
u = vel(i)
u = (u.mean(2)).mean(0)
if not(profile): u = u[c_channel.c_qpts()/2 + 1]
uavg = uavg + (dt/T) * u
return uavg
def IvelAvg(start_step,end_step,T,profile=True):
'''
returns the time averaged mean velocity sensitivity profile
'''
if profile:
vavg = np.zeros(c_channel.c_qpts())
else:
vavg = 0.0
y, w = quad()
assert 0 <= start_step <= end_step <= c_channel.c_nsteps()
for i in range(start_step,end_step):
v = Ivel(i,project = False)
v = (v.mean(2)).mean(0)
if not(profile): v = v[c_channel.c_qpts()/2 + 1]
vavg = vavg + (dt/T) * v
return vavg
def spec2phys(solution):
if isinstance(solution, str):
solution = read_solution(solution)
if isinstance(solution, int):
solution = get_solution(solution, copy=False)
assert solution.dtype == complex
assert solution.shape == (c_channel.c_Nz(), 2, c_channel.c_dimR(),
c_channel.c_Nx() / 2)
flow = np.zeros([3, int(c_channel.c_Nx() * 3 / 2), c_channel.c_qpts(),
int(c_channel.c_Nz() * 3 / 2)], np.float64)
c_channel.c_spec2phys(solution, flow)
return flow
