$ cd ..
ls -lt posts/// 145
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Every one of the 145 posts, grouped by year. The older work is one click away.
2026145 posts
- Raising the time step 5x ran 1.9x faster; 10x ran no faster at all — the window implicit surface tension opens8 min read
- At acoustic CFL 10 the preconditioner multiplied the error by 100 every sweep — the one arrow a block preconditioner throws away8 min read
- Pushing the cell Péclet number to 2 drove the solution to -0.33 — where the energy to minimize disappeared7 min read
- The Coriolis Force Did Zero Work, Yet the Impeller Added 1800 J/kg — Energy in a Rotating Frame7 min read
- I Dropped the −1/2 and the Viscosity Came Back Six Times Too Large — the Δt/2 Left Behind by LBM's Discretisation6 min read
- The Kinked String Was Fine, the Cut String Overshot by 9% — How the 1747 Wave-Equation Fight Ended Numerically5 min read
- Three at a wall, five at a corner — counting the populations an LBM boundary node loses7 min read
- Halving the mesh made the blow-up arrive twice as fast — complex eigenvalues in the 6-equation two-fluid model7 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 budget7 min read
- One Fewer Quadrature Point and the Solution Blew Up — DG's Integration Floor and the Taylor Basis8 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 Transformation7 min read
- [Paper Review] The Capillary Shackle Came Off and CFL 0.05 Was Still There — The Real Ceiling on VOF Interface Advection8 min read
- Raise the Velocity, Lose 27% of Your Diffusion — The Extra Flux in LBM Convection-Diffusion6 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 Fix7 min read
- Viscosity Is Not What Kills a Vortex — Newton's 1/r and the Lamb–Oseen Core7 min read
- Same Answer From 18% of the Cells — AMR Tagging Criteria and Coarse-Fine Refluxing8 min read
- [Paper Review] Prying Advection and Pressure Fully Apart — TV Flux Splitting for Baer–Nunziato8 min read
- Four Shocks Beat One — The Oblique Shock Train in a Supersonic Inlet7 min read
- Mass Is Conserved Exactly, Yet the Density Is Negative — The Positivity-Preserving Flux Limiter8 min read
- The Outlet Is Open, Yet the Wave Comes Back — NSCBC and the Price of σ8 min read
- A Wall the Grid Never Sees — IBM Delta Kernels and Multi-Direct Forcing8 min read
- [Paper Review] How to Delete Under-Relaxation — Linearisation in a Coupled Pressure-Based Solver9 min read
- [Paper Review] A Droplet Sends Almost Every Sound Wave Back — Acoustic Impedance and a Sharp-Interface Two-Phase Solver8 min read
- Where Jacobi Dies on a Boundary-Layer Mesh — the Linelet Line-Implicit Preconditioner7 min read
- Why Laundry Dries at 5 °C — Diffusion-Limited Evaporation vs. Heat-Driven Boiling7 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 Bending9 min read
- Where Half the Force Goes in LBM — Four Forcing Schemes and 1−1/(2τ)9 min read
- The Mach Number Goes to Zero, the Time Step Doesn't Budge — Reproducing an IMEX TVD Scheme10 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 Equations5 min read
- How Far Must Water Flow Before It Becomes a Parabola — Entrance Length and Hagen–Poiseuille4 min read
- When Pressure Rings in a Checkerboard — SIMPLE and Rhie-Chow Coupling5 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 Boundaries5 min read
- Why a Droplet at Rest Starts to Flow — Parasitic Currents and Well-Balanced Surface Tension6 min read
- Deleting an Equation Made It More Robust — The Four-Equation Model and the Interface Equilibrium Condition5 min read
- When Gradients Go Wrong on Skewed Meshes — Green–Gauss vs. Weighted Least-Squares Reconstruction5 min read
- Why a Spinning Ball Curves — the Magnus Effect and Circulation5 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 Fix6 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)5 min read
- Why Does the Bridge Sag Like That? The Direct Stiffness Method for Trusses4 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 Front7 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 Limiters6 min read
- [Paper Review] Tired of Differentiating Jacobians by Hand? — Operator-Overloading Automatic Differentiation (ADOO)6 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 Step5 min read
- The Shock Wave in Your Kitchen Sink — Froude Number and the Hydraulic Jump6 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 Relaxation5 min read
- Why Droplet Simulations Get Trapped by Δt — Solving Surface Tension Implicitly5 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 Diesel6 min read
- Solving Without Inverting the Matrix — GMRES and the Arnoldi Subspace6 min read
- Measure the Drag, Get the Heat Transfer — The Reynolds Analogy5 min read
- When Explicit Blows Up, Solve Implicit Without Inverting the Matrix — LU-SGS5 min read
- [Paper Review] Not Killing Sound at Low Mach — An AP IMEX Wave Scheme5 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 Metrics5 min read
- Why Droplets Are Round and Water Climbs the Glass — Surface Tension and Contact Angle5 min read
- Advecting Without Splitting Directions — The Bell-Colella-Glaz Unsplit Upwind Scheme6 min read
- Why a Shout Above Water Never Reaches Below — Acoustics Across a Diffuse Interface5 min read
- [Paper Review] Drawing Shocks with tanh — Implementing TENO-THINC Reconstruction6 min read
- Solving an Impeller by Holding It Still — Rotating Frames and MRF6 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 Boltzmann5 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 Bisection7 min read
- [Paper Review] How a DQN Tamed Airfoil Vortices with a Synthetic Jet — Reinforcement-Learning Flow Control5 min read
- [Paper Review] GMRES Ran 1000 Times and Still Wouldn't Stop — Physics-Based Block Preconditioning for an All-Speed Melt Pool6 min read
- Filling an Interface with a Fluid That Isn't There — The Ghost Fluid Method6 min read
- Fluid That Warms Up While Standing Still — Natural Convection and Rayleigh 17085 min read
- The Euler Eigensystem in an Arbitrary Direction — Three Waves, Two Repeats, One Singularity5 min read
- Turbulence Runs Three Rulers at Once — The Kolmogorov Cascade and the -5/3 Law5 min read
- Saving Gradients on Unstructured Grids — Moving Least-Squares Approximation5 min read
- [Paper Review] Two-Phase Flow Without a Poisson Solver — Coupling the General Pressure Equation with MSTACS7 min read
- [Paper Review] Stop letting sound speed swallow your CFL — Peluchon (2017) acoustic-transport IMEX6 min read
- How to Make an Outflow Stop Reflecting Sound — Navier–Stokes Characteristic Boundary Conditions5 min read
- Three Portraits of a Flow — Why Streamlines, Pathlines, and Streaklines Diverge5 min read
- Delaunay Triangulation — the Empty-Circumcircle Rule and Bowyer–Watson Insertion6 min read
- Why Smokestack Plumes Curl Up Instead of Lying Flat — The Jet in Crossflow and Its Counter-Rotating Vortex Pair6 min read
- Nine Arrows of Maxwell–Boltzmann — Why LBM's Equilibrium Is a Polynomial5 min read
- [Paper Review] Suspect the Cell After Solving It — A Posteriori MOOD Subcell Limiter for DG6 min read
- [Paper Review] One Scheme Can't Handle Every Wave — Chamarthi (2025)7 min read
- The Star That Started Moving — Well-Balanced FVM and Angular Momentum in Polar Coordinates5 min read
- Two Functions Added, and a Cylinder Appeared — Complex Potential and d'Alembert's Paradox6 min read
- Where Negative Density Leaks In — A Positivity-Preserving Flux Limiter for Blast Waves5 min read
- Three Faces of Porous Flow — Darcy, Forchheimer, and Brinkman5 min read
- Godunov's Method — One Tiny Shock Tube Inside Every Cell4 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)5 min read
- A Heart Valve Without a Body-Fitted Mesh — Peskin's Immersed Boundary Method and the Discrete Delta5 min read
- The Paramecium Swims Through Honey — Where Viscosity Comes From and Why Fourier and Fick Wrote the Same Line5 min read
- 1950 — When von Neumann Deliberately Smeared the Shock: Artificial Viscosity and Odd-Even Decoupling5 min read
- Above Mach 1, You Must Widen to Speed Up — The Laval Nozzle Paradox5 min read
- Skewed Cells Bend Gradients — Green–Gauss vs Least-Squares Reconstruction5 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 Relaxation5 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 Theorem5 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 Boundary7 min read
- Implicit Diffusion and the Thomas Algorithm — Buying Stability with One Tridiagonal Solve4 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-BVD6 min read
- When Characteristics Collide, a Shock Is Born — Burgers and the (x,t) Plane5 min read
- Water Boils at 20°C Too — The Physics of Cavitation5 min read
- SPH Without Tears — Solving Fluids with Particles, from Kernel to Artificial Viscosity5 min read
- Two Faces of a Whirl — Free Vortex, Forced Vortex, and Helmholtz5 min read
- Quadtree AMR — Letting the Mesh Grow Where It Needs To6 min read
- [Paper Review] Beating the Storm Clock — Casulli–Walters (2000) Semi-Implicit Shallow Water on Unstructured Orthogonal Grids5 min read
- [Paper Review] When WENO Smears Small Eddies — Fu (2019) Low-Dissipation TENO Finite-Volume Scheme5 min read
- When Lax–Wendroff Shook at a Step — Building a 2nd-Order TVD Advection Scheme with Flux Limiters5 min read
- Why Water Streams Break into Droplets — Plateau–Rayleigh Instability and Breakup Regimes5 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 Marching6 min read
- Bugs Swim in Honey — The World of Flow Changed by Reynolds Number5 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 Tensors3 min read
- Dean Flow: Analytical Solution and CFD Validation for Helical Pipe Flow4 min read
- Poiseuille Flow: Analytical Solution Derivation and Finite Difference Validation4 min read
- [CFD Q&A] When simpleFoam Pressure Residual Fails to Converge3 min read
- [OpenFOAM Tutorial] Backward Facing Step Flow Analysis — Capturing Recirculation Zones with simpleFoam2 min read
- Reynolds Number and Flow Transition, Through Visualization3 min read
- [Paper Review] Physics-Informed Neural Networks for Turbulence Modeling3 min read
- Mach Architect: Learn Compressible Flow by Designing Nozzles2 min read
- Rhie-Chow Interpolation for Compressible Multiphase Flows11 min read
- FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques6 min read
- Numerical Dungeon: Learn Numerical Methods Through a Game2 min read
- 5-Equation Model Implementation Guide: Building a Multiphase Flow Solver in Python2 min read
- Interface Capturing Methods: VOF vs Level Set vs Diffuse Interface4 min read
- From the Riemann Problem to Godunov's Scheme - The Essence of Numerical Flux3 min read
- Compressible Multiphase Flow CFD: Why It's Hard, Why It Matters3 min read
- Starting a Blog with Contentlayer & LaTeX1 min read