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Remove === section headers from Poiseuille example (CI lint)
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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examples/2D_poiseuille_nn/case.py

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The analytical solution is: u(y) = (G/(2*mu)) * y * (H - y)
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where G = rho * g_x is the effective pressure gradient.
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"""
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import json
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import math
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# === Channel geometry (square domain) ===
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L = 1.0 # Channel length (streamwise, x)
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H = 1.0 # Channel height (wall-normal, y)
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# -- Channel geometry (square domain) --
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L = 1.0 # Channel length (streamwise, x)
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H = 1.0 # Channel height (wall-normal, y)
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# === Grid resolution ===
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Nx = 24 # Cells in x (streamwise, minimal — periodic)
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Ny = 81 # Cells in y (wall-normal)
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# -- Grid resolution --
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Nx = 24 # Cells in x (streamwise, minimal — periodic)
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Ny = 81 # Cells in y (wall-normal)
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# === Fluid properties ===
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rho = 1.0 # Density
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p0 = 1e5 # Reference pressure (high for low Mach)
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gamma = 1.4 # Ratio of specific heats
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# -- Fluid properties --
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rho = 1.0 # Density
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p0 = 1e5 # Reference pressure (high for low Mach)
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gamma = 1.4 # Ratio of specific heats
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# Sound speed and CFL
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c = math.sqrt(gamma * p0 / rho)
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dx = L / (Nx + 1)
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cfl = 0.3
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dt = cfl * dx / c
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# === Body force (pressure gradient substitute) ===
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# -- Body force (pressure gradient substitute) --
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# G = rho * g_x acts as dp/dx driving force
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g_x = 0.5
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# === HB non-Newtonian model parameters ===
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tau0 = 0.0 # Yield stress (set 0 for power-law)
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K = 0.1 # Consistency index
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nn = 2.0 # Flow behavior index (< 1 = shear-thinning)
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hb_m = 1000.0 # Papanastasiou regularization parameter
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mu_min = 1e-4 # Minimum viscosity bound
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mu_max = 10.0 # Maximum viscosity bound
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mu_bulk = 0.0 # Bulk viscosity
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# -- HB non-Newtonian model parameters --
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tau0 = 0.0 # Yield stress (set 0 for power-law)
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K = 0.1 # Consistency index
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nn = 2.0 # Flow behavior index (< 1 = shear-thinning)
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hb_m = 1000.0 # Papanastasiou regularization parameter
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mu_min = 1e-4 # Minimum viscosity bound
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mu_max = 10.0 # Maximum viscosity bound
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mu_bulk = 0.0 # Bulk viscosity
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# Reference Re based on consistency index (used as baseline)
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Re_ref = 1.0 / K # = 100
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Re_ref = 1.0 / K # = 100
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# === Time control ===
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t_end = 10.0 # End time (allow flow to reach steady state)
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t_save = 5.0 # Save interval
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# -- Time control --
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t_end = 10.0 # End time (allow flow to reach steady state)
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t_save = 5.0 # Save interval
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eps = 1e-6
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