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Every one of the 197 posts, grouped by year. The older work is one click away.
2026197 posts
- Velocity came out one sixth at τ=0.6 — dropping the half-force F/2 from Guo forcing5 min read
- A Small Wobble in Mixture Fraction Drops the Mean Flame Temperature by 964 K — Presumed β-PDF and the Infinity at Z=06 min read
- A Two-Cell Interface Loses 39% of Its Surface Tension — The Anisotropy of the Korteweg Stress6 min read
- [Paper Review] MSTACS with Slope 3 Blew Up After 255 Steps at Co=0.5 — Compressive Differencing and the Courant Limit6 min read
- [Paper Review] Raising β to 2 froze the interface at 14 cells and made a sine worse than first-order upwind — Tallois's compressive limiter3 min read
- Changing only τ changed the density of a gas at rest — the (τ−½)² stress of Shan–Chen velocity-shift forcing6 min read
- Dividing the Reverse Rate by Kp Split 99.6% of AlO at 2500 K — The (p°/RT)^Δn Hidden in the Equilibrium Constant6 min read
- Halving the Grid Spacing Tripled the Error — What an Increment-Based Stopping Rule Hides in Jacobi Iteration6 min read
- Adding a v Term to a v² Term Got Both Ends Right and Missed the Middle by 42% — Prony's Two-Term Drag Law and Re = 607 min read
- Giving Conduction Its Own τ Left Viscous Heating Stuck at Pr = 1 — The Quasi-Equilibrium g* in Two-Population LB7 min read
- [Paper Review] Half Water, Half Air, and Sound Crawls at 24 m/s — The K∇·u Term in the Murrone–Guillard Five-Equation Model8 min read
- [Paper Review] The Tetrahedron That Led With One Sphere Never Broke Apart — A Bluntness Index for Mach 20 Fragment Clusters8 min read
- Shuffling Cell Numbers Made LU-SGS 2.8× Slower — RCM Reordering and the Start Cell That Sets Sweep Direction8 min read
- A 1 μm Aluminum Particle Heated 4.6× Slower Than the Continuum Formula — Sherman Interpolation in the Knudsen Transition Regime8 min read
- Changing One Relaxation Factor Moved the Converged Solution — Where Rhie–Chow Face Velocities Remember Under-Relaxation7 min read
- I Gave Curved Cells Their True Area and ∂x/∂x Stopped Being 1 — Why the Diagonal Cross-Product Area Fits Green–Gauss7 min read
- Upgrading Only the Viscous Term to Second Order Made the Error 1.82x Worse — Why the Semi-Implicit Gear Scheme Extrapolates Convection8 min read
- Water's 1625 m/s Sound Speed Became 18 m/s in the Pressure Subsystem — Where Toro–Vázquez Splitting Moves the Stiffness9 min read
- A Motionless Droplet Melted to Half Its Mass — The Curvature Term Conservative Allen–Cahn Erases8 min read
- Cutting Distance Checks 574x Lost 104 Contacts — One Grain Sets the DEM Sector Size8 min read
- The Same Code Gave 0.79 and 2.00 at Once — What Verification Cases Actually Measure8 min read
- One χ=50, two temperatures: 1759 K and 818 K — where a flamelet library folds8 min read
- Degree six returned 9 where 15 was required — the three Hermite roots that fixed D2Q98 min read
- I Added 64x the Cores and Weak-Scaling Efficiency Fell to 16.3% — The Trap of Measuring It by Refining the Grid9 min read
- I dropped K and the water compressed 1.86x too much — an interface error that refinement does not remove9 min read
- I asked for σ₁₂ = 1.00 and got 0.78 — where an absent phase leaks into the interface in three-component Allen–Cahn8 min read
- Deriving μ and k from One Formula Put Pr Off by 1.98× — the 9/4 Behind a 123.5 K Wall Temperature7 min read
- Filling the Third Moment Honestly Made the Error 2.8x Worse — What a Forcing Term Actually Owes7 min read
- Refining the Grid 8x Never Moved 2.4674 — Two Constants Fourier Left Behind in 18078 min read
- At tau = 0.51 I read the viscosity 51x too high — the half step left behind by the discrete LBE7 min read
- [Paper Review] The Pressure Went Implicit and Δt Still Shrank 100× — the Second 1/M² Hiding in the Relative Velocity8 min read
- [Paper Review] 0.333 in Tension, 0 in Compression — Where SPH Particles Start Pairing Up9 min read
- Moving refine one line below stream cost a 7.2x error — the recursive time cycle of LBM AMR7 min read
- Four times the speed, still 19.47 degrees — where water depth blows the Kelvin wedge open to 908 min read
- Giving every species its own tau threw the total mass off by 16.8% — correction velocity in multicomponent LBM8 min read
- 202x More Scalar Dissipation, 13% Less Temperature — Where a Laminar Flamelet Quenches7 min read
- One node pushed the error from 0.21% to 76% — local relaxation time in power-law LBM8 min read
- [Paper Review] The Same Point Read 0.544 Apart Along Two Paths — Curl Involutions on a Staggered Grid8 min read
- The bill for a 1001x larger time step — why a semi-implicit pressure scheme is not L∞ stable8 min read
- Mobility Up 10×, Interface Width Unchanged — The Anti-Diffusion Term in Conservative Allen–Cahn8 min read
- 2.0000 in laminar flow, 1.0322 in turbulent — the coefficient in front of the velocity head7 min read
- Pushing the Frame to 0.2 Cut the Viscosity by 5.97% — The Missing Third Moment in LBM Equilibria7 min read
- 49.9% of the Dynamic Coefficients Came Out Negative — the Germano Identity and the Averaging Operator8 min read
- One Integral Read as 0.1406 and 56.91 — Torsion Stress Function and Duct Laminar Flow9 min read
- A 9% Smaller Drag Coefficient Left the Droplet 35% Slower — Where the Distortion and Vaporization Corrections Attach7 min read
- 27 of 1,681 Voxels Flipped Inside Out — Ray Parity and Link Cutting in STL Voxelization11 min read
- Pressure Jumped 21% in a Problem Where Nothing Should Happen — The Abgrall Criterion and the Nonconservative Term9 min read
- [Paper Review] Two Fragments Flew Together Instead of Pushing Apart — The 144° Equilibrium of a Mach 20 Sphere Pair9 min read
- Doubling τ Left Pr at 1.0000 — The Two Constants Locked Inside Thermal LBM9 min read
- Where Total Pressure Dropped 1,080 Pa, Dissipation Was Zero — When the Bernoulli Constant Crosses Streamlines8 min read
- ρ and u Agree to the Last Digit While the Strain Rate Swells 45% — Nonequilibrium Rescaling at an LBM Refinement Interface8 min read
- A 1% Error in Diameter Is a 4% Error in Flow Rate — Half a Cell of Wall and Poiseuille's Constant8 min read
- A 30° rigid rotation read -13% strain — conjugate stress-strain pairs in large-strain shells8 min read
- Raising the time step 5x ran 1.9x faster; 10x ran no faster at all — the window implicit surface tension opens9 min read
- At acoustic CFL 10 the preconditioner multiplied the error by 100 every sweep — the one arrow a block preconditioner throws away10 min read
- Pushing the cell Péclet number to 2 drove the solution to -0.33 — where the energy to minimize disappeared8 min read
- The Coriolis Force Did Zero Work, Yet the Impeller Added 1800 J/kg — Energy in a Rotating Frame8 min read
- I Dropped the −1/2 and the Viscosity Came Back Six Times Too Large — the Δt/2 Left Behind by LBM's Discretisation7 min read
- The Kinked String Was Fine, the Cut String Overshot by 9% — How the 1747 Wave-Equation Fight Ended Numerically6 min read
- Three at a wall, five at a corner — counting the populations an LBM boundary node loses8 min read
- Halving the mesh made the blow-up arrive twice as fast — complex eigenvalues in the 6-equation two-fluid model8 min read
- I Plugged in Pressure Directly and a Still Interface Started to Shiver — Two Forms of Nonideal LBM Forcing6 min read
- Sending the smoke down 1 m cost 7 Pa of draft — Franklin's stove and the buoyancy budget8 min read
- One Fewer Quadrature Point and the Solution Blew Up — DG's Integration Floor and the Taylor Basis9 min read
- The Shock Never Left the Starting Line — Where Conservative and Primitive Forms Split8 min read
- Skew the Element 45° and the Stiffness Grows 2.5x — Metric Tensors and Constitutive Tensor Transformation8 min read
- [Paper Review] The Capillary Shackle Came Off and CFL 0.05 Was Still There — The Real Ceiling on VOF Interface Advection9 min read
- Raise the Velocity, Lose 27% of Your Diffusion — The Extra Flux in LBM Convection-Diffusion7 min read
- The Weight Sits on Top and She Still Rights Herself — Metacentric Height and the Free Surface Effect8 min read
- Thinner Means Stiffer — Shear Locking in Shell Elements and the MITC Tying Fix8 min read
- Viscosity Is Not What Kills a Vortex — Newton's 1/r and the Lamb–Oseen Core8 min read
- Same Answer From 18% of the Cells — AMR Tagging Criteria and Coarse-Fine Refluxing9 min read
- [Paper Review] Prying Advection and Pressure Fully Apart — TV Flux Splitting for Baer–Nunziato10 min read
- Four Shocks Beat One — The Oblique Shock Train in a Supersonic Inlet6 min read
- Mass Is Conserved Exactly, Yet the Density Is Negative — The Positivity-Preserving Flux Limiter9 min read
- The Outlet Is Open, Yet the Wave Comes Back — NSCBC and the Price of σ9 min read
- A Wall the Grid Never Sees — IBM Delta Kernels and Multi-Direct Forcing9 min read
- [Paper Review] How to Delete Under-Relaxation — Linearisation in a Coupled Pressure-Based Solver10 min read
- [Paper Review] A Droplet Sends Almost Every Sound Wave Back — Acoustic Impedance and a Sharp-Interface Two-Phase Solver7 min read
- Where Jacobi Dies on a Boundary-Layer Mesh — the Linelet Line-Implicit Preconditioner8 min read
- Why Laundry Dries at 5 °C — Diffusion-Limited Evaporation vs. Heat-Driven Boiling8 min read
- The Mesher That Dies Defending Your Boundary — Constrained Delaunay and Steiner Points9 min read
- Where Turbulence Stops Speeding Up a Flame — Damköhler's Wrinkling Hypothesis and Bending10 min read
- Where Half the Force Goes in LBM — Four Forcing Schemes and 1−1/(2τ)10 min read
- The Mach Number Goes to Zero, the Time Step Doesn't Budge — Reproducing an IMEX TVD Scheme11 min read
- Un-smearing the Interface Every Step — Implementing Anti-Diffusion Sharpening (IST)7 min read
- Supersonic Flow Can't See Upstream — Characteristics and Sound Waves in the Euler Equations6 min read
- How Far Must Water Flow Before It Becomes a Parabola — Entrance Length and Hagen–Poiseuille5 min read
- When Pressure Rings in a Checkerboard — SIMPLE and Rhie-Chow Coupling6 min read
- A Single Ripple Outruns Its Own Group — Wave Dispersion and Group Velocity5 min read
- In Lattice Boltzmann, the Wall Isn't on the Node — Bounce-Back and Zou-He Boundaries6 min read
- Why a Droplet at Rest Starts to Flow — Parasitic Currents and Well-Balanced Surface Tension6 min read
- Fewer Equations, and It Stopped Blowing Up — The Four-Equation Model and the Interface Equilibrium Condition6 min read
- When Gradients Go Wrong on Skewed Meshes — Green–Gauss vs. Weighted Least-Squares Reconstruction6 min read
- Why a Spinning Ball Curves — the Magnus Effect and Circulation6 min read
- Waves Hanging in the Sky — The Kelvin-Helmholtz Instability7 min read
- What You Give Up the Exact Riemann Solution For — the Roe Solver and the Entropy Fix7 min read
- [Paper Review] When a Microbubble Burns Like a Star — Keller–Miksis and the Secondary Bjerknes Force6 min read
- Letting Sound and Matter Flow Separately — Acoustic-Convective Splitting (Lagrange-Projection)7 min read
- Why Does the Bridge Sag Like That? The Direct Stiffness Method for Trusses5 min read
- Chaos That Begins at the Bottom of a Pot — Rayleigh–Bénard Convection and the Lorenz Equations5 min read
- Two Philosophies for Triangulating a Point Cloud — Bowyer–Watson and Advancing Front8 min read
- Why a Raindrop Is Not Tear-Shaped — The Weber Number and TAB Breakup6 min read
- The Fake Extrema a Second-Order Reconstruction Invents on Unstructured Grids — Barth–Jespersen and Venkatakrishnan Limiters7 min read
- [Paper Review] Tired of Differentiating Jacobians by Hand? — Operator-Overloading Automatic Differentiation (ADOO)7 min read
- [Paper Review] Fooling a Nonlinear Flux Into Behaving Linearly — Jin–Xin & Suliciu Relaxation7 min read
- The Man Who Erased Pressure — Chorin's Projection Method and Fractional Step6 min read
- The Shock Wave in Your Kitchen Sink — Froude Number and the Hydraulic Jump7 min read
- When the Mesh Skews, the Laplacian Leaks — Non-Orthogonal Diffusion Correction5 min read
- Where the Ideal Gas Starts to Lie — Compressibility Factor Z and the van der Waals Equation6 min read
- CFL = 1 takes ten thousand steps, CFL = 100 explodes — Switched Evolution Relaxation6 min read
- Why Droplet Simulations Get Trapped by Δt — Solving Surface Tension Implicitly6 min read
- Giving Each Phase Its Own Equations — The Baer–Nunziato Seven-Equation Model6 min read
- Surviving the Low-Viscosity Regime Where BGK Blows Up — MRT Lattice Boltzmann Collision5 min read
- Why Gasoline Engines Stop at a Compression Ratio of 12 — Otto vs Diesel7 min read
- Solving Without Inverting the Matrix — GMRES and the Arnoldi Subspace7 min read
- Measure the Drag, Get the Heat Transfer — The Reynolds Analogy6 min read
- When Explicit Blows Up, Solve Implicit Without Inverting the Matrix — LU-SGS6 min read
- [Paper Review] Not Killing Sound at Low Mach — An AP IMEX Wave Scheme6 min read
- [Paper Review] Second-Order Accuracy in a Single Stage — A GRP Solver for the Kapila Multiphase Model6 min read
- Catching Shocks Without Multiplying a Matrix at Every Face — AUSM Flux Splitting6 min read
- To Go Supersonic, Widen the Pipe — The De Laval Nozzle and Choking6 min read
- Wrapping a Rectangular Grid Around a Wing — Curvilinear Coordinate Transforms and Grid Metrics6 min read
- Why Droplets Are Round and Water Climbs the Glass — Surface Tension and Contact Angle6 min read
- Advecting Without Splitting Directions — The Bell-Colella-Glaz Unsplit Upwind Scheme7 min read
- Why a Shout Above Water Never Reaches Below — Acoustics Across a Diffuse Interface6 min read
- [Paper Review] Drawing Shocks with tanh — Implementing TENO-THINC Reconstruction7 min read
- Solving an Impeller by Holding It Still — Rotating Frames and MRF7 min read
- Heating It Hotter Made It Cooler — The Boiling Curve and Critical Heat Flux6 min read
- Entropy Stops the Blow-Up — Karlin's Entropic Lattice Boltzmann6 min read
- Why a Rougher Ball Flies Farther — The Drag Crisis and Boundary-Layer Separation5 min read
- When a Bullet Passes Straight Through a Wall — Continuous Collision Detection by Inclusion Bisection8 min read
- [Paper Review] How a DQN Tamed Airfoil Vortices with a Synthetic Jet — Reinforcement-Learning Flow Control6 min read
- [Paper Review] GMRES Ran 1000 Times and Still Wouldn't Stop — Physics-Based Block Preconditioning for an All-Speed Melt Pool7 min read
- Filling an Interface with a Fluid That Isn't There — The Ghost Fluid Method7 min read
- Fluid That Warms Up While Standing Still — Natural Convection and Rayleigh 17086 min read
- The Euler Eigensystem in an Arbitrary Direction — Three Waves, Two Repeats, One Singularity6 min read
- Turbulence Runs Three Rulers at Once — The Kolmogorov Cascade and the -5/3 Law6 min read
- Saving Gradients on Unstructured Grids — Moving Least-Squares Approximation6 min read
- [Paper Review] Two-Phase Flow Without a Poisson Solver — Coupling the General Pressure Equation with MSTACS8 min read
- [Paper Review] Stop letting sound speed swallow your CFL — Peluchon (2017) acoustic-transport IMEX7 min read
- How to Make an Outflow Stop Reflecting Sound — Navier–Stokes Characteristic Boundary Conditions6 min read
- Three Portraits of a Flow — Why Streamlines, Pathlines, and Streaklines Diverge6 min read
- Delaunay Triangulation — the Empty-Circumcircle Rule and Bowyer–Watson Insertion7 min read
- Why Smokestack Plumes Curl Up Instead of Lying Flat — The Jet in Crossflow and Its Counter-Rotating Vortex Pair8 min read
- Nine Arrows of Maxwell–Boltzmann — Why LBM's Equilibrium Is a Polynomial7 min read
- [Paper Review] Suspect the Cell After Solving It — A Posteriori MOOD Subcell Limiter for DG7 min read
- [Paper Review] One Scheme Can't Handle Every Wave — Chamarthi (2025)8 min read
- The Star That Started Moving — Well-Balanced FVM and Angular Momentum in Polar Coordinates6 min read
- Two Functions Added, and a Cylinder Appeared — Complex Potential and d'Alembert's Paradox7 min read
- Where Negative Density Leaks In — A Positivity-Preserving Flux Limiter for Blast Waves6 min read
- Three Faces of Porous Flow — Darcy, Forchheimer, and Brinkman6 min read
- Godunov's Method — One Tiny Shock Tube Inside Every Cell5 min read
- [Paper Review] Why Roe breaks at low Mach — Hope–Collins (2022) and three artificial-diffusion scalings6 min read
- [Paper Review] Split Newton in Two and Free-Surface Becomes Solvable — Casulli–Zanolli (2012)7 min read
- A Heart Valve Without a Body-Fitted Mesh — Peskin's Immersed Boundary Method and the Discrete Delta6 min read
- The Paramecium Swims Through Honey — Where Viscosity Comes From and Why Fourier and Fick Wrote the Same Line7 min read
- 1950 — When von Neumann Deliberately Smeared the Shock: Artificial Viscosity and Odd-Even Decoupling6 min read
- Above Mach 1, You Must Widen to Speed Up — The Laval Nozzle Paradox7 min read
- Skewed Cells Bend Gradients — Green–Gauss vs Least-Squares Reconstruction7 min read
- [Paper Review] When 30 K Breaks Boussinesq — Demou (2018) NOB Natural Convection and the Pressure Split5 min read
- [Paper Review] Solve with Two Pressures, Merge to One — Saurel (2009) on Multiphase Pressure Relaxation6 min read
- When FTCS Trembles, Upwind Goes Numb — First-Order Advection, Artificial Viscosity, and the CFL Trade4 min read
- Why a Spinning Ball Curves — Circulation, Magnus, and the Kutta–Joukowski Theorem6 min read
- What Jacobi Cannot Kill in 10,000 Sweeps, a V-Cycle Kills in 10 — The Real Secret of Multigrid6 min read
- When the Stream Breaks — Reynolds' Critical Number and the Layered Turbulent Boundary8 min read
- Implicit Diffusion and the Thomas Algorithm — Buying Stability with One Tridiagonal Solve6 min read
- [Paper Review] When the Sound Speed Diverges and the Time Step Survives — Orlando–Bonaventura (2024) AP-IMEX for Non-Ideal Gases6 min read
- [Paper Review] Pick the Reconstruction with Smaller Jumps — Deng (2018) MUSCL-THINC-BVD7 min read
- When Characteristics Collide, a Shock Is Born — Burgers and the (x,t) Plane6 min read
- Water Boils at 20°C Too — The Physics of Cavitation6 min read
- SPH Without Tears — Solving Fluids with Particles, from Kernel to Artificial Viscosity7 min read
- Two Faces of a Whirl — Free Vortex, Forced Vortex, and Helmholtz5 min read
- Quadtree AMR — Letting the Mesh Grow Where It Needs To7 min read
- [Paper Review] Beating the Storm Clock — Casulli–Walters (2000) Semi-Implicit Shallow Water on Unstructured Orthogonal Grids7 min read
- [Paper Review] When WENO Smears Small Eddies — Fu (2019) Low-Dissipation TENO Finite-Volume Scheme6 min read
- When Lax–Wendroff Shook at a Step — Building a 2nd-Order TVD Advection Scheme with Flux Limiters6 min read
- Why Water Streams Break into Droplets — Plateau–Rayleigh Instability and Breakup Regimes6 min read
- Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB5 min read
- Solving Wall Distance in O(N log N): Eikonal Equation and Fast Marching7 min read
- Bugs Swim in Honey — The World of Flow Changed by Reynolds Number6 min read
- Discontinuous Galerkin Method (DGM): High-Precision Discretization for Unstructured Grid Compressible Flow Analysis4 min read
- FEM for Rigid Body Dynamics: Quaternion-based Rotation Handling and Inertia Tensors4 min read
- Dean Flow: Analytical Solution and CFD Validation for Helical Pipe Flow5 min read
- Poiseuille Flow: Analytical Solution Derivation and Finite Difference Validation5 min read
- [CFD Q&A] When simpleFoam Pressure Residual Fails to Converge4 min read
- [OpenFOAM Tutorial] Backward Facing Step Flow Analysis — Capturing Recirculation Zones with simpleFoam4 min read
- Reynolds Number and Flow Transition, Through Visualization4 min read
- [Paper Review] Physics-Informed Neural Networks for Turbulence Modeling5 min read
- Mach Architect: Learn Compressible Flow by Designing Nozzles4 min read
- Rhie-Chow Interpolation for Compressible Multiphase Flows11 min read
- FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques8 min read
- Numerical Dungeon: Learn Numerical Methods Through a Game4 min read
- 5-Equation Model Implementation Guide: Building a Multiphase Flow Solver in Python5 min read
- Interface Capturing Methods: VOF vs Level Set vs Diffuse Interface5 min read
- From the Riemann Problem to Godunov's Scheme - The Essence of Numerical Flux4 min read
- Compressible Multiphase Flow CFD: Why It's Hard, Why It Matters5 min read