[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.
[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.
[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.
[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.
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.
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.
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.
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.
[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.
[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.
[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.
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.
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.
[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.
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.
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.
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] 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.
[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.
[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.
[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.
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.
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.
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.
[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.
[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.
[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.
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.
[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] 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.
[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.
[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.
[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.
[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)
[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
[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.
[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.
[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.
[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.
[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.
[Paper Review] Pick the Reconstruction with Smaller Jumps — Deng (2018) MUSCL-THINC-BVD
Deng (2018) builds MUSCL and THINC in every cell, then keeps the one with the smaller jump on the two faces. The rule is called BVD.
[Paper Review] Beating the Storm Clock — Casulli–Walters (2000) Semi-Implicit Shallow Water on Unstructured Orthogonal Grids
At 28 m depth the explicit limit is 0.2 s. Keeping only the free-surface gradient implicit is what lets a five-minute step survive the estuary.
[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.
[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.