Paper Reviews

[Paper Review] Physics-Informed Neural Networks for Turbulence Modeling

Pressure sensors alone rebuild a Re=100 cylinder to under 1% velocity error. That number slips once the physics weight swallows the viscous residual.

2026.03.24

[Paper Review] When the Sound Speed Diverges and the Time Step Survives — Orlando–Bonaventura (2024) AP-IMEX for Non-Ideal Gases

An AP-IMEX-DG scheme that frees the time step from the sound speed across all Mach numbers and any EOS, reproduced in NumPy.

2026.05.03

[Paper Review] Solve with Two Pressures, Merge to One — Saurel (2009) on Multiphase Pressure Relaxation

How a six-equation non-equilibrium model with stiff pressure relaxation routes around the failures of the five-equation diffuse-interface model.

2026.05.09

[Paper Review] When 30 K Breaks Boussinesq — Demou (2018) NOB Natural Convection and the Pressure Split

For water at ΔT=30 K the printed split correction max |1-rho0/rho| is 0.0117, while the pressure Poisson stays constant-coefficient.

2026.05.10

[Paper Review] Split Newton in Two and Free-Surface Becomes Solvable — Casulli–Zanolli (2012)

Day 1 of a 41-cell well has 39 pressurized cells and zero dry cells. By day 10 that is 0 and 12, and the outer Newton count drops from 5 to 1.

2026.05.16

[Paper Review] Why Roe breaks at low Mach — Hope–Collins (2022) and three artificial-diffusion scalings

At Mach 0.01 the convective scaling leaves amplitude 0.018. Acoustic and mixed scalings still hold 0.974 and 0.971 after one acoustic period.

2026.05.17

[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

2026.05.23

[Paper Review] Suspect the Cell After Solving It — A Posteriori MOOD Subcell Limiter for DG

Solve first, doubt later — reproducing the MOOD limiter of Ioriatti, Dumbser, Loubère (2020)

2026.05.24

[Paper Review] Stop letting sound speed swallow your CFL — Peluchon (2017) acoustic-transport IMEX

Liquid at 1500 m/s and flow at 5 m/s force a 0.67 μs explicit step on a 1 mm cell. The acoustic split leaves the outer CFL on flow speed.

2026.05.30

[Paper Review] Two-Phase Flow Without a Poisson Solver — Coupling the General Pressure Equation with MSTACS

Raising artificial sound speed from 5 to 15 cuts the stable step by three. OS-MSTACS lists a volume error E_G of 6.57e-8, four orders under OS-CICSAM.

2026.05.31

[Paper Review] GMRES Ran 1000 Times and Still Wouldn't Stop — Physics-Based Block Preconditioning for an All-Speed Melt Pool

At Mach 1e-3, GMRES spun 1000 times and the residual sat at 1e-2. A velocity–pressure Schur complement returns that count to two or three steps.

2026.06.06

[Paper Review] How a DQN Tamed Airfoil Vortices with a Synthetic Jet — Reinforcement-Learning Flow Control

Over 300 episodes the toy reward moves only from 3.12 to 3.25, and the learned jet stops at 12 m/s, where the waste penalty turns on.

2026.06.07

[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.

2026.06.13

Why a Shout Above Water Never Reaches Below — Acoustics Across a Diffuse Interface

Near an air–water impedance ratio of 3600, about 99.9% of the sound reflects. The 13.4 degree critical angle is checked in a 1D tube.

2026.06.14

[Paper Review] Second-Order Accuracy in a Single Stage — A GRP Solver for the Kapila Multiphase Model

At N=320 a single-stage GRP reports order 2.03 and an L1 error of 1.55e-5, against 2.31e-2 and order 0.97 for Godunov on one sine wave.

2026.06.20

[Paper Review] Not Killing Sound at Low Mach — An AP IMEX Wave Scheme

At ε=0.01 on 64 cells the upwind amplitude falls to 1.980e-7 after 12800 steps, while the implicit AP value stays 1.00. The loss scales as 1/ε.

2026.06.21

[Paper Review] When a Microbubble Burns Like a Star — Keller–Miksis and the Secondary Bjerknes Force

A 5 μm bubble has a Minnaert frequency near 650 kHz. At 0.1 R_E and n=1.4 the polytropic gas pressure is about 20,000 atm.

2026.07.12

Fewer Equations, and It Stopped Blowing Up — The Four-Equation Model and the Interface Equilibrium Condition

A uniform pressure still shakes if Γ is advected conservatively. The four-equation model moves Γ non-conservatively and the error falls to roundoff.

2026.07.18

Why a Droplet at Rest Starts to Flow — Parasitic Currents and Well-Balanced Surface Tension

A 3% curvature error drives the residual to 4.8e5, while exact curvature leaves it at 4.1e-10. That gap is the parasitic current.

2026.07.19

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.

2026.07.25

[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.

2026.08.01

[Paper Review] How to Delete Under-Relaxation — Linearisation in a Coupled Pressure-Based Solver

On the Sod case, M/Co = 2.25 sends the lagged iteration to P = 2.250, while Newton reaches the physical root P = 1 in five iterations.

2026.08.02

[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.

2026.08.09

[Paper Review] The Capillary Shackle Came Off and CFL 0.05 Was Still There — The Real Ceiling on VOF Interface Advection

Implicit surface tension breaks the capillary time-step limit, yet the compressive scheme carrying the color function caps the time step at CFL 0.05.

2026.08.16

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.

2026.08.23

At acoustic CFL 10 the preconditioner multiplied the error by 100 every sweep — the one arrow a block preconditioner throws away

Block Gauss-Seidel discards a pressure-velocity feedback whose gain is exactly the acoustic CFL squared. A 1D acoustic model measures the cost.

2026.08.29

Raising the time step 5x ran 1.9x faster; 10x ran no faster at all — the window implicit surface tension opens

At density ratio 1000, raising the capillary step 5x ran 1.9x faster. Pushing to 10x did not. Janodet et al. (2025) measured both walls.

2026.08.30

[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.

2026.09.05

Pressure Jumped 21% in a Problem Where Nothing Should Happen — The Abgrall Criterion and the Nonconservative Term

Uniform pressure and velocity stop staying uniform because of the nonconservative term, not the flux. I remeasured Re-Abgrall's H_u operator on one grid.

2026.09.06

The bill for a 1001x larger time step — why a semi-implicit pressure scheme is not L∞ stable

A semi-implicit pressure scheme drops sound speed from the CFL limit and gains a 1001x step at M = 0.001. The discontinuity oscillation does not decay.

2026.09.19

[Paper Review] The Same Point Read 0.544 Apart Along Two Paths — Curl Involutions on a Staggered Grid

A staggered grid holds interface curl near 1e-12 for 400 steps. The collocated Rusanov run on the same shear opens a path gap of 0.544.

2026.09.20

[Paper Review] 0.333 in Tension, 0 in Compression — Where SPH Particles Start Pairing Up

The same SPH code holds under compression and pairs in tension. At h/dx = 1.2 the rate is 0.333; freezing the kernel on the initial lattice drives it to 0.

2026.09.26

[Paper Review] The Pressure Went Implicit and Δt Still Shrank 100× — the Second 1/M² Hiding in the Relative Velocity

In an isentropic two-phase all-Mach split, the enthalpy jump hides a second 1/M². The CFL stays tied to Mach until that term is integrated implicitly too.

2026.09.27

I dropped K and the water compressed 1.86x too much — an interface error that refinement does not remove

Deriving the compressibility factor K of compressible VOF straight from the isobaric closure, then measuring how much liquid volume a zeroed or sign-flipped K shaves off in a 1D compression test.

2026.10.03

I Added 64x the Cores and Weak-Scaling Efficiency Fell to 16.3% — The Trap of Measuring It by Refining the Grid

Why Krylov iterations grew 6.1x in a weak-scaling study that refined the grid, and how adding one multigrid level put the efficiency curve back to flat.

2026.10.04

Cutting Distance Checks 574x Lost 104 Contacts — One Grain Sets the DEM Sector Size

Sector pruning in DEM neighbor search is only safe when shell·s exceeds d_max, and 2400 agglomerating grains show exactly what a shorter reach costs.

2026.10.08

Water's 1625 m/s Sound Speed Became 18 m/s in the Pressure Subsystem — Where Toro–Vázquez Splitting Moves the Stiffness

At 1 bar, water's split wave speed A is 18.44 m/s, not the 1624.9 m/s sound speed. A/c is 0.011, so the stiffness now sits between the two IMEX steps.

2026.10.10

[Paper Review] The Tetrahedron That Led With One Sphere Never Broke Apart — A Bluntness Index for Mach 20 Fragment Clusters

Four spheres at Mach 20 separate by tetrahedron attitude. Bluntness B and asymmetry A on 40,000 orientations show which number sets the split.

2026.10.17

[Paper Review] Half Water, Half Air, and Sound Crawls at 24 m/s — The K∇·u Term in the Murrone–Guillard Five-Equation Model

A 50% air–water mix carries sound at 23.6 m/s, slower than either phase. Dropping K∇·u from the five-equation model makes the same pulse run at 745 m/s.

2026.10.18

[Paper Review] Raising β to 2 froze the interface at 14 cells and made a sine worse than first-order upwind — Tallois's compressive limiter

With a β=2 compressive limiter on the volume fraction, a slab interface stays 14 cells wide after five periods. The same limiter gives a sine wave a larger L1 error than first-order upwind.

2026.10.24

[Paper Review] MSTACS with Slope 3 Blew Up After 255 Steps at Co=0.5 — Compressive Differencing and the Courant Limit

We ran the compressive scheme of MSTACS eq. (18) on a 1D slab. Without redistribution it diverges above Co=0.44. The culprit is the product of the NVD slope k and the Courant number.

2026.10.25

[Paper Review] A water-air interface in uniform flow produced an 8×10⁸ Pa pressure spike — the non-disturbance condition in a pressure-based BN model

Reproducing the non-disturbance condition from Re and Abgrall's 2022 pressure-based Baer–Nunziato model: if volume fraction and phase mass don't share one flux, interface pressure jumps by hundreds of MPa.

2026.10.31