Pro Tier Module
Blasius / Falkner-Skan Boundary Layer
Shoot the Falkner-Skan ODE for wall shear and check it against the published Hartree table.
This tool runs inside GDBS Pro. What it computes and the authorities it applies are below.
The problem
Laminar wedge-flow boundary-layer parameters are tabulated in classic references, but recomputing and verifying them usually means a one-off ODE shoot in a separate tool.
The local-first solution
This plugin drives the real wasm engine to shoot the third-order Falkner-Skan ODE in the browser, returning the wall shear f''(0) and boundary-layer thicknesses, with the headline checked against the published Hartree table and the Blasius value.
What it does
Shooting solution of f''' + f f'' + beta(1 - f'^2) = 0 to convergence
Wall shear f''(0) for wedge angles from stagnation to incipient separation
99% thickness plus displacement and momentum thicknesses
Validation against the Hartree wedge table and Blasius f''(0) = 0.4696
True residual of the shot solution mapped to the trust verdict
Honest scope
This is the exact 1D similarity reduction of the 2D boundary-layer equations, valid only for the power-law external flow it assumes; real geometries with pressure-gradient history or separation past beta = -0.1988 are outside its validity. A verification harness and bridge to full Navier-Stokes HPC, not a replacement, and EXACT is never claimed for a shot ODE solution.
Authorities cited
- Blasius, H. (1908). Grenzschichten in Fluessigkeiten mit kleiner Reibung. Z. Math. Phys. 56, 1-37. Flat-plate wall shear f''(0) = 0.4696.
- Hartree, D. R. (1937). On an equation occurring in Falkner and Skan's approximate treatment of the equations of the boundary layer. Proc. Camb. Phil. Soc. 33(2), 223-239. doi:10.1017/S0305004100019575. Tabulated f''(0) for wedge angles beta.
- Falkner, V. M. & Skan, S. W. (1931). Solutions of the boundary-layer equations. Phil. Mag. (Ser. 7) 12(80), 865-896. doi:10.1080/14786443109461870.
- White, F. M. (2010). Viscous Fluid Flow, 3rd ed., McGraw-Hill, Section 4.3 - Blasius flat plate f''(0) = 0.4696, delta_99 ~ 5.0 x / sqrt(Re_x).
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Compute the wall shear
Run the similarity solve in the browser and save the validated result to Sandbox, attach it to a Worklog case, or route it into a Gate client portal. Nothing leaves your machine to anyone's cloud.