Shuffling Cell Numbers Made LU-SGS 2.8× Slower — RCM Reordering and the Start Cell That Sets Sweep Direction
·8 min read
Shuffling cell numbers on a 576-cell grid pushed LU-SGS from 9 iterations to 25. RCM cuts bandwidth to 24, but the start corner still splits 9 from 21.
CFL = 1 takes ten thousand steps, CFL = 100 explodes — Switched Evolution Relaxation
·6 min read
Fixed CFL of 3 needs 588 iterations on steady Burgers. SER with p=1 finishes in 34, then the step is Newton only while a finite CFL cap is still in place.
Why Droplet Simulations Get Trapped by Δt — Solving Surface Tension Implicitly
·6 min read
From N=64 to N=256, dt_sigma falls by 8. omega*dt_sigma stays 2.221 on every mesh, and explicit integration breaks past about 0.9 dt_sigma.
When Explicit Blows Up, Solve Implicit Without Inverting the Matrix — LU-SGS
·6 min read
Explicit CFL at 0.3 stalls for days. Backward Euler and two LU-SGS sweeps carry a Burgers shock through CFL 5 in 49 steps, with no full-matrix inverse.
Implicit Diffusion and the Thomas Algorithm — Buying Stability with One Tridiagonal Solve
·6 min read
At r=0.6 explicit diffusion reaches 1e12 in 60 steps. One Thomas sweep keeps the implicit update finite at that same r, and still finite at r=2.