Advecting Without Splitting Directions — The Bell-Colella-Glaz Unsplit Upwind Scheme
·7 min read
Directional splitting twists a diagonal scalar. Bell-Colella-Glaz keeps the rotating disk's peak with a (1-CFL) slope weight plus a transverse correction.
Godunov's Method — One Tiny Shock Tube Inside Every Cell
·5 min read
The Lax tube returns star pressure 3.40948 and star velocity 0.62556. Left state 3.528 makes the left wave a rarefaction and the right a shock.
From the Riemann Problem to Godunov's Scheme - The Essence of Numerical Flux
·4 min read
Godunov flux comes from p* in a two-constant Riemann problem. Shock branches use a square-root f_K; rarefactions use an isentropic power.