def Compute_AllH(t, x, n, turbhandler):
# Define the contributions to the H coefficients for the Shestakov Problem
H1 = np.ones_like(x)
H7 = shestakov_nonlinear_diffusion.H7contrib_Source(x)
(H2, H3, data) = turbhandler.Hcontrib_turbulent_flux(n)
H4 = None
H6 = None
return (H1, H2, H3, H4, H6, H7)
def __call__(self, t, x, n):
# Define the contributions to the H coefficients for the Shestakov Problem
H1 = np.ones_like(x)
H7 = shestakov_nonlinear_diffusion.H7contrib_Source(x)
(H2, H3, extradata) = self.turbhandler.Hcontrib_turbulent_flux(n)
H4 = None
H6 = None
return (H1, H2, H3, H4, H6, H7, extradata)
def __call__(self, t, x, profiles, HCoeffsTurb):
# Define the contributions to the H coefficients for the Shestakov Problem
H1 = np.ones_like(x)
H7 = shestakov_nonlinear_diffusion.H7contrib_Source(x)
HCoeffs = tango.multifield.HCoefficients(H1=H1, H7=H7)
HCoeffs = HCoeffs + HCoeffsTurb
return HCoeffs
def test_lodestro_shestakovproblem():
# test the LoDestro Method on the analytic shestakov problem
# setup
L = 1 # size of domain
N = 500 # number of spatial grid points
dx = L / (N-1) # spatial grid size
x = np.arange(N)*dx # location corresponding to grid points j=0, ..., N-1
nL = 1e-2 # right boundary condition
lmax = 2000 # max number of iterations
dt = 1e4 # timestep
thetaParams = {'Dmin': 1e-5,
'Dmax': 1e13,
'dpdxThreshold': 10}
lmParams = {'EWMAParamTurbFlux': 0.30,
'EWMAParamProfile': 0.30,
'thetaParams': thetaParams}
FluxModel = shestakov_nonlinear_diffusion.shestakov_analytic_fluxmodel(dx)
turbhandler = lodestro_method.TurbulenceHandler(dx, x, lmParams, FluxModel)
# initial condition
n = 1 - 0.5*x
tol = 1e-11 # tol for convergence
t = np.array([0, 1e6])
# initialize "m minus 1" variables for the first timestep
n_mminus1 = n
for m in range(1, len(t)):
# Implicit time advance: iterate to solve the nonlinear equation!
dt = t[m] - t[m-1] # use this if using non-constant timesteps
converged = False
l = 1
while not converged:
# compute H's from current iterate n
H1 = np.ones_like(x)
H7 = shestakov_nonlinear_diffusion.H7contrib_Source(x)
# this needs to be packaged... give n, get out H2, H3.
(H2, H3, data) = turbhandler.Hcontrib_turbulent_flux(n)
# compute matrix system (A, B, C, f)
(A, B, C, f) = HToMatrixFD.H_to_matrix(dt, dx, nL, n_mminus1, H1, H2=H2, H3=H3, H7=H7)
# check convergence
# convergence check: is || ( M[n^l] n^l - f[n^l] ) / max(abs(f)) || < tol
# could add more convergence checks here
resid = A*np.concatenate((n[1:], np.zeros(1))) + B*n + C*np.concatenate((np.zeros(1), n[:-1])) - f
resid = resid / np.max(np.abs(f)) # normalize residuals
rms_error = np.sqrt( 1/len(resid) * np.sum(resid**2))
if rms_error < tol:
converged = True
# compute new iterate n
n = HToMatrixFD.solve(A, B, C, f)
# Check for NaNs or infs
if np.all(np.isfinite(n)) == False:
raise RuntimeError('NaN or Inf detected at l=%d. Exiting...' % (l))
# about to loop to next iteration l
l += 1
if l >= lmax:
raise RuntimeError('Too many iterations on timestep %d. Error is %f.' % (m, rms_error))
# end of while loop for iteration convergence
# Converged. Before advancing to next timestep m, save some stuff
n_mminus1 = n
nss_analytic = shestakov_nonlinear_diffusion.GetSteadyStateSolution(x, nL)
solution_residual = (n - nss_analytic) / np.max(np.abs(nss_analytic))
solution_rms_error = np.sqrt( 1/len(n) * np.sum(solution_residual**2))
obs = solution_rms_error
exp = 0
testtol = 1e-3
assert abs(obs - exp) < testtol
