Raising the time step 5x ran 1.9x faster; 10x ran no faster at all — the window implicit surface tension opens
Breaching the capillary time-step constraint leaves other ceilings standing. Janodet et al. (2025) measured the stability limit and the speed-up optimum at a density ratio of 1000.
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
The single-pressure six-equation two-fluid model turns complex the moment the phases slip past each other. Raising the interfacial-pressure coefficient past exactly 1.0 puts the eigenvalues back 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 colour function caps the time step at CFL 0.05.
[Paper Review] Prying Advection and Pressure Fully Apart — TV Flux Splitting for Baer–Nunziato
Split the BN flux in two and the sound speed ends up entirely in the pressure system
[Paper Review] How to Delete Under-Relaxation — Linearisation in a Coupled Pressure-Based Solver
Why fixed-coefficient vs Newton linearisation decides all-Mach convergence
[Paper Review] A Droplet Sends Almost Every Sound Wave Back — Acoustic Impedance and a Sharp-Interface Two-Phase Solver
Why a liquid-gas interface reflects 99.9% of an acoustic wave, and the fake sound speed a smeared interface invents
Un-smearing the Interface Every Step — Implementing Anti-Diffusion Sharpening (IST)
A post-processing technique that pins a numerically smeared interface to a constant thickness
Why a Droplet at Rest Starts to Flow — Parasitic Currents and Well-Balanced Surface Tension
The parasitic currents born from curvature error, and the well-balanced method that eliminates them
Deleting an Equation Made It More Robust — The Four-Equation Model and the Interface Equilibrium Condition
How the four-equation multiphase model kills interface pressure oscillations
[Paper Review] When a Microbubble Burns Like a Star — Keller–Miksis and the Secondary Bjerknes Force
Directly integrating bubble radial oscillation, collapse, and bubble-pair coupling in ultrasound
[Paper Review] Not Killing Sound at Low Mach — An AP IMEX Wave Scheme
Why upwind viscosity erases the solution at low Mach, and the AP-IMEX cure
[Paper Review] Second-Order Accuracy in a Single Stage — A GRP Solver for the Kapila Multiphase Model
How a GRP solver buys second-order time accuracy and tames the stiff volume-fraction source at once
Why a Shout Above Water Never Reaches Below — Acoustics Across a Diffuse Interface
How an impedance jump reflects and refracts sound, reproduced with a weak-compressibility model
[Paper Review] Drawing Shocks with tanh — Implementing TENO-THINC Reconstruction
How THINC keeps a sub-cell jump alive when polynomials smear the contact
[Paper Review] How a DQN Tamed Airfoil Vortices with a Synthetic Jet — Reinforcement-Learning Flow Control
DQN and Dueling DQN drive a synthetic jet to raise lift and cut drag
[Paper Review] GMRES Ran 1000 Times and Still Wouldn't Stop — Physics-Based Block Preconditioning for an All-Speed Melt Pool
A velocity–pressure Schur complement preconditioner keeps the iteration count flat as the Mach number goes to zero
[Paper Review] Two-Phase Flow Without a Poisson Solver — Coupling the General Pressure Equation with MSTACS
Swap the elliptic Poisson step for a hyperbolic GPE and run two-phase flow fully explicitly
[Paper Review] Stop letting sound speed swallow your CFL — Peluchon (2017) acoustic-transport IMEX
Splitting acoustic from transport gives a 1/M time-step gain on the five-equation model
[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
How a standard Roe flux collapses at M=0.01, and the three scalings the asymptotics prescribe.
[Paper Review] Split Newton in Two and Free-Surface Becomes Solvable — Casulli–Zanolli (2012)
How wet and dry cells live in one system with monotone convergence.
[Paper Review] When 30 K Breaks Boussinesq — Demou (2018) NOB Natural Convection and the Pressure Split
Keeping a constant-coefficient Poisson at large ΔT without giving up variable properties
[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
Choosing between two candidate reconstructions by minimizing total boundary variation
[Paper Review] Beating the Storm Clock — Casulli–Walters (2000) Semi-Implicit Shallow Water on Unstructured Orthogonal Grids
A shallow-water algorithm that stays stable at large time steps
[Paper Review] When WENO Smears Small Eddies — Fu (2019) Low-Dissipation TENO Finite-Volume Scheme
Why 5th-order WENO-JS still smears smooth scales, and how TENO's sharp cutoff fixes it
[Paper Review] Physics-Informed Neural Networks for Turbulence Modeling
A novel approach to reconstructing flow fields from sparse data using neural networks with physical laws embedded directly in the loss function.