Entropy Stops the Blow-Up — Karlin's Entropic Lattice Boltzmann
Stabilizing LBM with an H-theorem-enforcing entropic collision
The Euler Eigensystem in an Arbitrary Direction — Three Waves, Two Repeats, One Singularity
Where the left eigenvector breaks when n̂ tilts, and the three conventions that dodge it
Nine Arrows of Maxwell–Boltzmann — Why LBM's Equilibrium Is a Polynomial
A second-order Hermite truncation builds D2Q9, and the same truncation chains LBM to low-Mach flows
The Star That Started Moving — Well-Balanced FVM and Angular Momentum in Polar Coordinates
Mis-discretize 2P/r and a quiet star will leak gas out of its center.
Where Negative Density Leaks In — A Positivity-Preserving Flux Limiter for Blast Waves
The one-line θ-blend that keeps ρ above zero in a Le Blanc shock tube.
Godunov's Method — One Tiny Shock Tube Inside Every Cell
The Riemann fan, the exact Lax solution, and the wall that bounds Godunov to first order.
A Heart Valve Without a Body-Fitted Mesh — Peskin's Immersed Boundary Method and the Discrete Delta
How to put a moving body into a fluid without ever remeshing — one regularized delta function does the work
1950 — When von Neumann Deliberately Smeared the Shock: Artificial Viscosity and Odd-Even Decoupling
The ξ²(Δu)² trick that killed post-shock wiggles, and the new problem it left behind.
When FTCS Trembles, Upwind Goes Numb — First-Order Advection, Artificial Viscosity, and the CFL Trade
Why centered differencing explodes, why upwind survives, and what it pays for it
Mach Architect: Learn Compressible Flow by Designing Nozzles
An interactive simulator for experiencing isentropic flow, choking, and normal shocks by directly tuning the geometry and back pressure of a converging-diverging nozzle.
FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques
A comparison of the mathematical origins, pros and cons, and best application areas for the Finite Difference Method (FDM), Finite Element Method (FEM), and Finite Volume Method (FVM).
Numerical Dungeon: Learn Numerical Methods Through a Game
Master core numerical methods concepts—from CFL conditions to compressible multiphase flow—by clearing five dungeon stages.
Compressible Multiphase Flow CFD: Why It's Hard, Why It Matters
Why compressible multiphase numerics differ fundamentally from single-phase flow, and why this remains an active research field.