A Steady-State Preconditioner Inside a Dual-Time Loop Took 19× More Inner Iterations — A Low-Mach Acoustic Pulse Test
Put a Weiss–Smith preconditioner into physical time and the acoustic pulse freezes in place. Put it inside dual time and the answer returns, but inner iterations jump from 16 to 305.
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