Pushing the cell Péclet number to 2 drove the solution to -0.33 — where the energy to minimize disappeared
Advection breaks the symmetry of the stiffness matrix, and the minimum total potential energy principle goes with it. Here is the real cause of Galerkin oscillations and what stabilization buys instead.
I Dropped the −1/2 and the Viscosity Came Back Six Times Too Large — the Δt/2 Left Behind by LBM's Discretisation
One trapezoidal integration and one change of variables leave a Δt/2 in three separate places: the viscosity, the velocity, and the stress. A scalar ODE and a D2Q9 lattice measure all three.
What Jacobi Cannot Kill in 10,000 Sweeps, a V-Cycle Kills in 10 — The Real Secret of Multigrid
Swap the grid, swap the frequency: how a hierarchy converts stubborn low modes into easy ones
Implicit Diffusion and the Thomas Algorithm — Buying Stability with One Tridiagonal Solve
Past the explicit blow-up wall, the cost of unconditional stability is one O(N) sweep
When Characteristics Collide, a Shock Is Born — Burgers and the (x,t) Plane
How nonlinear self-advection breaks a smooth curve into a shock.
Quadtree AMR — Letting the Mesh Grow Where It Needs To
Forty years of adaptive mesh data structures and refinement criteria, since Berger–Oliger
When Lax–Wendroff Shook at a Step — Building a 2nd-Order TVD Advection Scheme with Flux Limiters
Sidestep Godunov's theorem to build a monotone 2nd-order advection scheme
Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB
Comparing the characteristics and convergence speeds of the four major Krylov subspace solvers with code and simulation.