Mass Is Conserved Exactly, Yet the Density Is Negative — The Positivity-Preserving Flux Limiter
·8 min read
Bridging a high-order flux and the Lax–Friedrichs flux with a single θ per face
Supersonic Flow Can't See Upstream — Characteristics and Sound Waves in the Euler Equations
·5 min read
Why a small disturbance splits into three characteristic speeds
What You Give Up the Exact Riemann Solution For — the Roe Solver and the Entropy Fix
·6 min read
From the sqrt(rho) average to the entropy glitch, implementing Roe, HLL, and HLLC by hand
Catching Shocks Without Multiplying a Matrix at Every Face — AUSM Flux Splitting
·6 min read
How AUSM splits the Euler flux to capture shocks without Roe — with code
The Euler Eigensystem in an Arbitrary Direction — Three Waves, Two Repeats, One Singularity
·5 min read
Where the left eigenvector breaks when n̂ tilts, and the three conventions that dodge it