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.
[Paper Review] Two Fragments Flew Together Instead of Pushing Apart — The 144° Equilibrium of a Mach 20 Sphere Pair
At Mach 20 two touching spheres align at one angle and generate lift together instead of repelling. A Newtonian approximation pins that angle down.
Halving the mesh made the blow-up arrive twice as fast — complex eigenvalues in the 6-equation two-fluid model
Slip turns the six-equation two-fluid model complex. The coefficient of interfacial pressure must pass 1.0 to put both slow eigenvalues on the real axis.
[Paper Review] Prying Advection and Pressure Fully Apart — TV Flux Splitting for Baer–Nunziato
Split a Baer–Nunziato flux and sound speed stays in the pressure system. Toro Test 4 beat Rusanov by 1.5×; Noh then sent pressure to −0.12.
Mass Is Conserved Exactly, Yet the Density Is Negative — The Positivity-Preserving Flux Limiter
At CFL 0.45 a limiter-off double rarefaction dies at step 2: density 0.37, pressure -0.163. One θ per face blends LF and the high-order flux.
The Outlet Is Open, Yet the Wave Comes Back — NSCBC and the Price of σ
At σ = 0 a duct reflects 0% and keeps a +0.30 pressure offset; at σ = 0.25 the reflection is 1.9% and the offset drops to 0.0007.
[Paper Review] A Droplet Sends Almost Every Sound Wave Back — Acoustic Impedance and a Sharp-Interface Two-Phase Solver
Air-water reflection returns 99.889% of the acoustic energy. A 1% gas fraction drops Wood's sound speed from 1500 m/s to 120.5 m/s.
The Mach Number Goes to Zero, the Time Step Doesn't Budge — Reproducing an IMEX TVD Scheme
At Mach 10^{-4} the time step stays on the convective CFL. Pure second-order IMEX overshoots by about 0.4 unless theta is held to sqrt(2)-1 or below.
Un-smearing the Interface Every Step — Implementing Anti-Diffusion Sharpening (IST)
After 200 steps a helium bubble edge grows from 6 cells to 20. IST post-processing then locks that smeared thickness to the ratio of ε/a.
Supersonic Flow Can't See Upstream — Characteristics and Sound Waves in the Euler Equations
At 220 m/s in air the speeds are -118.06, 220, and 558.06 m/s. Past Mach 1 the left-going sound wave no longer reaches upstream.
Letting Sound and Matter Flow Separately — Acoustic-Convective Splitting (Lagrange-Projection)
At M=0.02 the acoustic band stays 2c wide while convection crawls. Feeding R back into the upwind step holds the momentum error at 2.2e-16.
[Paper Review] Tired of Differentiating Jacobians by Hand? — Operator-Overloading Automatic Differentiation (ADOO)
Fraysse (2019) seeds dual numbers through an unchanged flux routine and reads a machine-precision Jacobian, with no finite-difference step h to tune.
When Explicit Blows Up, Solve Implicit Without Inverting the Matrix — LU-SGS
Explicit CFL at 0.3 stalls for days. Backward Euler and two LU-SGS sweeps carry a Burgers shock through CFL 5 in 49 steps, with no full-matrix inverse.
Catching Shocks Without Multiplying a Matrix at Every Face — AUSM Flux Splitting
The Shu–Osher left state in the code, density 3.857143 and pressure 10.33333, is the Mach 3 Rankine–Hugoniot state at gamma 1.4.
[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.
Filling an Interface with a Fluid That Isn't There — The Ghost Fluid Method
Copy pressure across a sharp water-air interface, extrapolate density isentropically, and run a single-material solver twice. Stiffness makes it ring.
The Euler Eigensystem in an Arbitrary Direction — Three Waves, Two Repeats, One Singularity
At n_x=0.01 the R-1 left-eigenvector row divides by 100, and at zero it diverges. A 30 degree face keeps R-1; a face along y switches to R-2.
How to Make an Outflow Stop Reflecting Sound — Navier–Stokes Characteristic Boundary Conditions
A six-hour LES drifted 0.3 bar because the outlet reflected sound. NSCBC sets the incoming wave with σ near 0.25 so acoustics leave and the mean holds.
[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