The Same Code Gave 0.79 and 2.00 at Once — What Verification Cases Actually Measure
Sod's density L1 order is 0.79 on a discontinuous tube. The same MUSCL–HLLC code gives 2.001 on a smooth wave, and minmod pulls that down to 1.491.
The Shock Never Left the Starting Line — Where Conservative and Primitive Forms Split
Flux-form Burgers returns shock speed 0.5006. Writing velocity times a gradient returns 0.0000, and an eightfold grid still settles near 0.639.
[Paper Review] Drawing Shocks with tanh — Implementing TENO-THINC Reconstruction
With beta = 1.8, THINC-BVD holds a top-hat peak of 1.00 and a 30-cell width after five revolutions, while minmod TVD falls to 0.84 and 23 cells.
[Paper Review] One Scheme Can't Handle Every Wave — Chamarthi (2025)
Wave-appropriate reconstruction for compressible multicomponent flows — THINC at contacts, MP5 at shocks, central at viscous tangentials
Where Negative Density Leaks In — A Positivity-Preserving Flux Limiter for Blast Waves
A Le Blanc rarefaction can drive density negative. Per-face θ blends the high-order flux back toward Lax–Friedrichs only as far as the floor requires.
Godunov's Method — One Tiny Shock Tube Inside Every Cell
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.
1950 — When von Neumann Deliberately Smeared the Shock: Artificial Viscosity and Odd-Even Decoupling
The von Neumann term xi^2 (du)^2 kills post-shock sawteeth on a Sod tube. Omit the code's factor 0.25 and the same xi makes Q four times larger.
[Paper Review] When WENO Smears Small Eddies — Fu (2019) Low-Dissipation TENO Finite-Volume Scheme
A 10 percent bump in one smoothness indicator already shifts WENO-JS weights. TENO's 0/1 cutoff does not flip, so the fifth-order linear stencil stays on.