Where Jacobi Dies on a Boundary-Layer Mesh — the Linelet Line-Implicit Preconditioner
·8 min read
On a 64 by 48 mesh, Jacobi climbs from 18 sweeps at aspect ratio 1 to 5471 at 1000, while a wall-normal linelet finishes in 2.
How Far Must Water Flow Before It Becomes a Parabola — Entrance Length and Hagen–Poiseuille
·5 min read
In laminar pipe flow a flat inlet needs about 0.05 Re diameters to become a parabola, and 64/Re is not valid until that station.
Measure the Drag, Get the Heat Transfer — The Reynolds Analogy
·6 min read
At Re_x = 1e5 on a flat plate, Cf/2 stays at 1.050e-3, and St times Pr to the 2/3 matches that value at Pr = 0.7, 1, and 7.
Why a Rougher Ball Flies Farther — The Drag Crisis and Boundary-Layer Separation
·5 min read
At 70 m/s and Re = 1.99e5 the same ball gives 2.049 N smooth and 0.488 N dimpled. Separation at 82 degrees versus 120 opens that gap.
When the Stream Breaks — Reynolds' Critical Number and the Layered Turbulent Boundary
·8 min read
Pipe transition is usually quoted near Re 2300, yet a quiet pipe can stay laminar to 50,000. The wall then splits into sublayer, buffer, and log layer.