$ man cfd-glossary
Glossary
74 CFD terms · 73 linked to published posts
74 / 74
- AMG13 hitswiki ↗
- Algebraic Multigrid. Multilevel preconditioner built from the matrix graph, no geometric grid needed.
- AMR28 hitswiki ↗
- Adaptive Mesh Refinement — refines the grid only where the solution varies sharply.
- AUSM27 hits
- Advection Upstream Splitting Method — pressure/advection split flux family.
- BiCGSTAB13 hitswiki ↗
- Bi-Conjugate Gradient Stabilized. Krylov solver for non-symmetric matrices.
- Boundary Layer79 hits
- Thin near-wall region where viscous effects concentrate velocity gradients.
- Burgers15 hitswiki ↗
- u_t + u u_x = ν u_xx. Canonical 1D nonlinear PDE modeling shocks and viscosity.
- Casulli13 hits
- Casulli–Walters semi-implicit algorithm for the unstructured shallow-water equations.
- CFL260 hitswiki ↗
- Courant–Friedrichs–Lewy condition. Stability bound for explicit time integration.
- CG29 hitswiki ↗
- Conjugate Gradient. Optimal Krylov solver for symmetric positive-definite systems; O(n^(1/2)) convergence.
- Checkerboard Pressure5 hits
- Nonphysical alternating pressure mode caused by weak pressure-velocity coupling.
- Collocated Grid7 hits
- Grid arrangement storing pressure, velocity, and other variables at the same cell center.
- Dean Vortex3 hits
- Pair of secondary-flow vortices generated by centrifugal effects in curved pipes.
- DG37 hits
- Discontinuous Galerkin method; a high-order Galerkin family allowing inter-element jumps.
- Diffuse Interface25 hits
- Model that represents an interface as a finite-thickness transition layer instead of a sharp discontinuity.
- DNS24 hits
- Direct Numerical Simulation. Resolves all turbulence scales directly.
- Eikonal8 hitswiki ↗
- Stationary PDE ‖∇φ‖ = 1. Used for wall distance and front propagation.
- EOS49 hits
- Equation of State. Closure relation p = f(ρ, e).
- Fast Marching20 hits
- Algorithm that computes distance or arrival-time fields by monotone propagation of the Eikonal equation.
- FDM11 hitswiki ↗
- Finite Difference Method. Discretization via nodal derivative approximations.
- FEM30 hitswiki ↗
- Finite Element Method. Discretization via variational weak form and shape functions.
- Finite Difference35 hits
- Numerical method that approximates derivatives with differences between grid values.
- Finite Element48 hits
- PDE discretization using element-wise basis functions and weak forms.
- Finite Volume85 hits
- CFD method that integrates conservation laws over cells and discretizes face fluxes.
- Five-Equation Model12 hits
- Compressible multiphase model tracking volume fraction plus mixture momentum and energy.
- Flux Limiter38 hits
- Nonlinear function that limits high-order corrections to suppress oscillations near steep gradients.
- FVM42 hitswiki ↗
- Finite Volume Method. Cell-wise conservative integration; the CFD workhorse.
- Galerkin15 hitswiki ↗
- Variational discretization where trial and test spaces coincide.
- GMRES31 hitswiki ↗
- Generalized Minimal Residual. Robust Krylov solver for general non-symmetric systems.
- Godunov50 hitswiki ↗
- Conservative finite-volume scheme that solves a Riemann problem at each cell interface to determine fluxes.
- Helmholtz10 hits
- Classical vortex theorem describing vortex-line conservation in inviscid barotropic flow.
- HLLC34 hits
- Harten–Lax–van Leer Contact. Approximate Riemann solver that captures contact discontinuities.
- IBM15 hitswiki ↗
- Immersed Boundary Method. Represents complex boundaries as body-force terms on Cartesian grids.
- ILU6 hitswiki ↗
- Incomplete LU factorization. Approximate triangular decomposition of sparse matrices; standard Krylov preconditioner.
- IMEX59 hits
- Implicit-Explicit splitting. Stiff terms (pressure, viscosity) implicit; non-stiff (advection) explicit.
- k-epsilon4 hits
- Two-equation RANS model solving turbulence kinetic energy k and dissipation epsilon.
- Kolmogorov12 hits
- Smallest scale in the turbulence energy cascade. η = (ν³/ε)^(1/4).
- Krylov32 hitswiki ↗
- Subspace spanned by {r₀, Ar₀, A²r₀, ...}. Foundation of CG/GMRES/BiCGSTAB.
- Lax-Wendroff21 hits
- Second-order linear advection scheme based on a time Taylor expansion.
- LBM120 hitswiki ↗
- Lattice Boltzmann Method. Boltzmann kinetics discretized on a lattice; highly parallelizable.
- LES21 hits
- Large Eddy Simulation. Resolves large vortices, models sub-grid scales.
- Level Set12 hits
- Interface-capturing method representing the interface as the zero contour of a signed-distance function.
- Mach127 hitswiki ↗
- Flow speed divided by sound speed. Indicates compressibility and shock formation.
- Multigrid3 hitswiki ↗
- Acceleration that cycles between coarse/fine grids to damp low+high frequency errors together.
- MUSCL43 hitswiki ↗
- Monotone Upstream-centered Schemes for Conservation Laws. 2nd-order spatial reconstruction with monotone Riemann fluxes.
- OpenFOAM53 hitswiki ↗
- Open-source CFD library based on finite volume method.
- PINN4 hits
- Physics-Informed Neural Network — embeds PDEs into the training loss.
- PISO4 hits
- Pressure Implicit with Splitting of Operators. Efficient for transient flows.
- Plateau-Rayleigh4 hitswiki ↗
- Surface-tension-driven instability that breaks a liquid jet into droplets.
- Poiseuille33 hits
- Analytical viscous internal flow driven by a pressure gradient.
- Quaternion2 hitswiki ↗
- Four-component hypercomplex number (w, x, y, z); gimbal-lock-free 3D rotations.
- Rankine Vortex
- Simple vortex model with a forced-vortex core and free-vortex exterior.
- RANS13 hits
- Reynolds-Averaged Navier–Stokes. Time-averaged form for turbulence modeling.
- Reynolds74 hitswiki ↗
- Ratio of inertial to viscous forces. Determines laminar–turbulent transition.
- Rhie-Chow43 hits
- Face-velocity interpolation that suppresses pressure checkerboarding on collocated grids.
- Riemann77 hitswiki ↗
- 1-D initial discontinuity problem between two states. Foundation of numerical fluxes in CFD.
- Riemann Solver38 hits
- Algorithm that solves a local Riemann problem at a cell face to compute numerical flux.
- Roe50 hitswiki ↗
- Approximate Riemann solver that linearizes the Jacobian via Roe's average.
- Semi-Implicit24 hits
- Time integration that treats stiff terms implicitly and other terms explicitly.
- Shallow Water6 hits
- Depth-averaged free-surface flow equations for horizontal scales much larger than depth.
- SIMPLE29 hits
- Semi-Implicit Method for Pressure-Linked Equations. Incompressible pressure–velocity coupling.
- Speed of Sound359 hits
- Propagation speed of pressure disturbances; sensitive to phase fraction in compressible mixtures.
- SPH32 hitswiki ↗
- Smoothed Particle Hydrodynamics. Mesh-free discretization via particle interaction kernels.
- SST3 hits
- Turbulence model blending near-wall k-omega behavior with outer-flow k-epsilon behavior.
- Staggered Grid13 hits
- Grid arrangement that stores pressure and velocity components at different locations.
- TENO34 hits
- Targeted ENO. Lower-dissipation shock-capturing scheme (5/6th order) than WENO.
- TVD39 hits
- Total Variation Diminishing. Monotonicity condition preventing spurious oscillations.
- VOF43 hits
- Volume of Fluid. Tracks volume fractions of each phase in multiphase flow.
- Volume Fraction88 hits
- Fraction of a cell volume occupied by a particular phase in multiphase flow.
- Vorticity42 hits
- Curl of the velocity field; twice the local spin rate of a fluid particle.
- Wall Distance12 hits
- Distance from a cell or point to the nearest wall, needed by wall functions and turbulence models.
- WENO34 hits
- Weighted Essentially Non-Oscillatory. High-order non-oscillatory reconstruction near shocks.
- y+9 hits
- Nondimensional wall distance of the first cell; key metric for wall functions and wall-resolved CFD.
— A —
source posts
At acoustic CFL 10 the preconditioner multiplied the error by 100 every sweep — the one arrow a block preconditioner throws away×5[Paper Review] GMRES Ran 1000 Times and Still Wouldn't Stop — Physics-Based Block Preconditioning for an All-Speed Melt Pool×4What Jacobi Cannot Kill in 10,000 Sweeps, a V-Cycle Kills in 10 — The Real Secret of Multigrid×2Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB×2
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Same Answer From 18% of the Cells — AMR Tagging Criteria and Coarse-Fine Refluxing×9ρ and u Agree to the Last Digit While the Strain Rate Swells 45% — Nonequilibrium Rescaling at an LBM Refinement Interface×7Quadtree AMR — Letting the Mesh Grow Where It Needs To×7Moving refine one line below stream cost a 7.2x error — the recursive time cycle of LBM AMR×3What Jacobi Cannot Kill in 10,000 Sweeps, a V-Cycle Kills in 10 — The Real Secret of Multigrid×2
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Catching Shocks Without Multiplying a Matrix at Every Face — AUSM Flux Splitting×20[Paper Review] Tired of Differentiating Jacobians by Hand? — Operator-Overloading Automatic Differentiation (ADOO)×2From the Riemann Problem to Godunov's Scheme - The Essence of Numerical Flux×2Halving the mesh made the blow-up arrive twice as fast — complex eigenvalues in the 6-equation two-fluid model×1[Paper Review] Fooling a Nonlinear Flux Into Behaving Linearly — Jin–Xin & Suliciu Relaxation×1
— B —
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Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB×8Pushing the cell Péclet number to 2 drove the solution to -0.33 — where the energy to minimize disappeared×1Where Jacobi Dies on a Boundary-Layer Mesh — the Linelet Line-Implicit Preconditioner×1What Jacobi Cannot Kill in 10,000 Sweeps, a V-Cycle Kills in 10 — The Real Secret of Multigrid×1Implicit Diffusion and the Thomas Algorithm — Buying Stability with One Tridiagonal Solve×1
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Why a Rougher Ball Flies Farther — The Drag Crisis and Boundary-Layer Separation×13Measure the Drag, Get the Heat Transfer — The Reynolds Analogy×12When the Stream Breaks — Reynolds' Critical Number and the Layered Turbulent Boundary×9A 9% Smaller Drag Coefficient Left the Droplet 35% Slower — Where the Distortion and Vaporization Corrections Attach×4How Far Must Water Flow Before It Becomes a Parabola — Entrance Length and Hagen–Poiseuille×3
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[Paper Review] Fooling a Nonlinear Flux Into Behaving Linearly — Jin–Xin & Suliciu Relaxation×5The Shock Never Left the Starting Line — Where Conservative and Primitive Forms Split×3CFL = 1 takes ten thousand steps, CFL = 100 explodes — Switched Evolution Relaxation×2When Explicit Blows Up, Solve Implicit Without Inverting the Matrix — LU-SGS×2When Characteristics Collide, a Shock Is Born — Burgers and the (x,t) Plane×2
— C —
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[Paper Review] Split Newton in Two and Free-Surface Becomes Solvable — Casulli–Zanolli (2012)×6[Paper Review] Beating the Storm Clock — Casulli–Walters (2000) Semi-Implicit Shallow Water on Unstructured Orthogonal Grids×5The bill for a 1001x larger time step — why a semi-implicit pressure scheme is not L∞ stable×1The Weight Sits on Top and She Still Rights Herself — Metacentric Height and the Free Surface Effect×1
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CFL = 1 takes ten thousand steps, CFL = 100 explodes — Switched Evolution Relaxation×41At acoustic CFL 10 the preconditioner multiplied the error by 100 every sweep — the one arrow a block preconditioner throws away×39[Paper Review] The Pressure Went Implicit and Δt Still Shrank 100× — the Second 1/M² Hiding in the Relative Velocity×11[Paper Review] The Capillary Shackle Came Off and CFL 0.05 Was Still There — The Real Ceiling on VOF Interface Advection×11Mass Is Conserved Exactly, Yet the Density Is Negative — The Positivity-Preserving Flux Limiter×11
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Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB×15At acoustic CFL 10 the preconditioner multiplied the error by 100 every sweep — the one arrow a block preconditioner throws away×7One Integral Read as 0.1406 and 56.91 — Torsion Stress Function and Duct Laminar Flow×4[Paper Review] The Same Point Read 0.544 Apart Along Two Paths — Curl Involutions on a Staggered Grid×1Pushing the cell Péclet number to 2 drove the solution to -0.33 — where the energy to minimize disappeared×1
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1950 — When von Neumann Deliberately Smeared the Shock: Artificial Viscosity and Odd-Even Decoupling×3Changing One Relaxation Factor Moved the Converged Solution — Where Rhie–Chow Face Velocities Remember Under-Relaxation×2The Man Who Erased Pressure — Chorin's Projection Method and Fractional Step×1Rhie-Chow Interpolation for Compressible Multiphase Flows×1
— D —
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One Fewer Quadrature Point and the Solution Blew Up — DG's Integration Floor and the Taylor Basis×14[Paper Review] Suspect the Cell After Solving It — A Posteriori MOOD Subcell Limiter for DG×12[Paper Review] When the Sound Speed Diverges and the Time Step Survives — Orlando–Bonaventura (2024) AP-IMEX for Non-Ideal Gases×6FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques×3Discontinuous Galerkin Method (DGM): High-Precision Discretization for Unstructured Grid Compressible Flow Analysis×2
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Interface Capturing Methods: VOF vs Level Set vs Diffuse Interface×6Un-smearing the Interface Every Step — Implementing Anti-Diffusion Sharpening (IST)×3[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×2Fewer Equations, and It Stopped Blowing Up — The Four-Equation Model and the Interface Equilibrium Condition×2Why a Shout Above Water Never Reaches Below — Acoustics Across a Diffuse Interface×2
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Turbulence Runs Three Rulers at Once — The Kolmogorov Cascade and the -5/3 Law×8[Paper Review] When a Microbubble Burns Like a Star — Keller–Miksis and the Secondary Bjerknes Force×3Reynolds Number and Flow Transition, Through Visualization×3The Outlet Is Open, Yet the Wave Comes Back — NSCBC and the Price of σ×2[Paper Review] When 30 K Breaks Boussinesq — Demou (2018) NOB Natural Convection and the Pressure Split×2
— E —
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[Paper Review] When the Sound Speed Diverges and the Time Step Survives — Orlando–Bonaventura (2024) AP-IMEX for Non-Ideal Gases×20Compressible Multiphase Flow CFD: Why It's Hard, Why It Matters×10Filling an Interface with a Fluid That Isn't There — The Ghost Fluid Method×4[Paper Review] Solve with Two Pressures, Merge to One — Saurel (2009) on Multiphase Pressure Relaxation×45-Equation Model Implementation Guide: Building a Multiphase Flow Solver in Python×4
— F —
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FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques×17FEM for Rigid Body Dynamics: Quaternion-based Rotation Handling and Inertia Tensors×4Discontinuous Galerkin Method (DGM): High-Precision Discretization for Unstructured Grid Compressible Flow Analysis×2One Integral Read as 0.1406 and 56.91 — Torsion Stress Function and Duct Laminar Flow×1A 30° rigid rotation read -13% strain — conjugate stress-strain pairs in large-strain shells×1
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FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques×14[Paper Review] Tired of Differentiating Jacobians by Hand? — Operator-Overloading Automatic Differentiation (ADOO)×6Poiseuille Flow: Analytical Solution Derivation and Finite Difference Validation×4Dean Flow: Analytical Solution and CFD Validation for Helical Pipe Flow×3Pushing the Frame to 0.2 Cut the Viscosity by 5.97% — The Missing Third Moment in LBM Equilibria×1
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FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques×20Pushing the cell Péclet number to 2 drove the solution to -0.33 — where the energy to minimize disappeared×4One Fewer Quadrature Point and the Solution Blew Up — DG's Integration Floor and the Taylor Basis×4FEM for Rigid Body Dynamics: Quaternion-based Rotation Handling and Inertia Tensors×4A 30° rigid rotation read -13% strain — conjugate stress-strain pairs in large-strain shells×3
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FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques×19I Gave Curved Cells Their True Area and ∂x/∂x Stopped Being 1 — Why the Diagonal Cross-Product Area Fits Green–Gauss×6One Fewer Quadrature Point and the Solution Blew Up — DG's Integration Floor and the Taylor Basis×6Saving Gradients on Unstructured Grids — Moving Least-Squares Approximation×4[Paper Review] When WENO Smears Small Eddies — Fu (2019) Low-Dissipation TENO Finite-Volume Scheme×4
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[Paper Review] Stop letting sound speed swallow your CFL — Peluchon (2017) acoustic-transport IMEX×55-Equation Model Implementation Guide: Building a Multiphase Flow Solver in Python×3Un-smearing the Interface Every Step — Implementing Anti-Diffusion Sharpening (IST)×2Interface Capturing Methods: VOF vs Level Set vs Diffuse Interface×1Compressible Multiphase Flow CFD: Why It's Hard, Why It Matters×1
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When Lax–Wendroff Shook at a Step — Building a 2nd-Order TVD Advection Scheme with Flux Limiters×10Advecting Without Splitting Directions — The Bell-Colella-Glaz Unsplit Upwind Scheme×6Refining the Grid 8x Never Moved 2.4674 — Two Constants Fourier Left Behind in 1807×3Mass Is Conserved Exactly, Yet the Density Is Negative — The Positivity-Preserving Flux Limiter×3[Paper Review] Suspect the Cell After Solving It — A Posteriori MOOD Subcell Limiter for DG×3
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FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques×16I Gave Curved Cells Their True Area and ∂x/∂x Stopped Being 1 — Why the Diagonal Cross-Product Area Fits Green–Gauss×6Saving Gradients on Unstructured Grids — Moving Least-Squares Approximation×4[Paper Review] Physics-Informed Neural Networks for Turbulence Modeling×3When Gradients Go Wrong on Skewed Meshes — Green–Gauss vs. Weighted Least-Squares Reconstruction×2
— G —
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FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques×5One Fewer Quadrature Point and the Solution Blew Up — DG's Integration Floor and the Taylor Basis×2[Paper Review] Suspect the Cell After Solving It — A Posteriori MOOD Subcell Limiter for DG×2[Paper Review] When the Sound Speed Diverges and the Time Step Survives — Orlando–Bonaventura (2024) AP-IMEX for Non-Ideal Gases×2Discontinuous Galerkin Method (DGM): High-Precision Discretization for Unstructured Grid Compressible Flow Analysis×2
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Solving Without Inverting the Matrix — GMRES and the Arnoldi Subspace×16[Paper Review] GMRES Ran 1000 Times and Still Wouldn't Stop — Physics-Based Block Preconditioning for an All-Speed Melt Pool×9Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB×4I Added 64x the Cores and Weak-Scaling Efficiency Fell to 16.3% — The Trap of Measuring It by Refining the Grid×1The Man Who Erased Pressure — Chorin's Projection Method and Fractional Step×1
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Godunov's Method — One Tiny Shock Tube Inside Every Cell×12[Paper Review] Second-Order Accuracy in a Single Stage — A GRP Solver for the Kapila Multiphase Model×6Numerical Dungeon: Learn Numerical Methods Through a Game×6From the Riemann Problem to Godunov's Scheme - The Essence of Numerical Flux×6[Paper Review] Tired of Differentiating Jacobians by Hand? — Operator-Overloading Automatic Differentiation (ADOO)×4
— H —
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The Man Who Erased Pressure — Chorin's Projection Method and Fractional Step×3Two Faces of a Whirl — Free Vortex, Forced Vortex, and Helmholtz×2The bill for a 1001x larger time step — why a semi-implicit pressure scheme is not L∞ stable×1Same Answer From 18% of the Cells — AMR Tagging Criteria and Coarse-Fine Refluxing×1Waves Hanging in the Sky — The Kelvin-Helmholtz Instability×1
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[Paper Review] One Scheme Can't Handle Every Wave — Chamarthi (2025)×12What You Give Up the Exact Riemann Solution For — the Roe Solver and the Entropy Fix×6From the Riemann Problem to Godunov's Scheme - The Essence of Numerical Flux×4Letting Sound and Matter Flow Separately — Acoustic-Convective Splitting (Lagrange-Projection)×2Godunov's Method — One Tiny Shock Tube Inside Every Cell×2
— I —
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Where Jacobi Dies on a Boundary-Layer Mesh — the Linelet Line-Implicit Preconditioner×2Shuffling Cell Numbers Made LU-SGS 2.8× Slower — RCM Reordering and the Start Cell That Sets Sweep Direction×1I Added 64x the Cores and Weak-Scaling Efficiency Fell to 16.3% — The Trap of Measuring It by Refining the Grid×1Solving Without Inverting the Matrix — GMRES and the Arnoldi Subspace×1Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB×1
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[Paper Review] When the Sound Speed Diverges and the Time Step Survives — Orlando–Bonaventura (2024) AP-IMEX for Non-Ideal Gases×11[Paper Review] Not Killing Sound at Low Mach — An AP IMEX Wave Scheme×10The Mach Number Goes to Zero, the Time Step Doesn't Budge — Reproducing an IMEX TVD Scheme×8Water's 1625 m/s Sound Speed Became 18 m/s in the Pressure Subsystem — Where Toro–Vázquez Splitting Moves the Stiffness×7[Paper Review] Stop letting sound speed swallow your CFL — Peluchon (2017) acoustic-transport IMEX×4
— K —
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When the Stream Breaks — Reynolds' Critical Number and the Layered Turbulent Boundary×1[CFD Q&A] When simpleFoam Pressure Residual Fails to Converge×1[OpenFOAM Tutorial] Backward Facing Step Flow Analysis — Capturing Recirculation Zones with simpleFoam×1[Paper Review] Physics-Informed Neural Networks for Turbulence Modeling×1
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I Added 64x the Cores and Weak-Scaling Efficiency Fell to 16.3% — The Trap of Measuring It by Refining the Grid×7[Paper Review] GMRES Ran 1000 Times and Still Wouldn't Stop — Physics-Based Block Preconditioning for an All-Speed Melt Pool×6Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB×5[Paper Review] Tired of Differentiating Jacobians by Hand? — Operator-Overloading Automatic Differentiation (ADOO)×4Solving Without Inverting the Matrix — GMRES and the Arnoldi Subspace×4
— L —
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When Lax–Wendroff Shook at a Step — Building a 2nd-Order TVD Advection Scheme with Flux Limiters×12When FTCS Trembles, Upwind Goes Numb — First-Order Advection, Artificial Viscosity, and the CFL Trade×4[Paper Review] Second-Order Accuracy in a Single Stage — A GRP Solver for the Kapila Multiphase Model×3The Shock Never Left the Starting Line — Where Conservative and Primitive Forms Split×1Advecting Without Splitting Directions — The Bell-Colella-Glaz Unsplit Upwind Scheme×1
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Giving every species its own tau threw the total mass off by 16.8% — correction velocity in multicomponent LBM×9Entropy Stops the Blow-Up — Karlin's Entropic Lattice Boltzmann×8Degree six returned 9 where 15 was required — the three Hermite roots that fixed D2Q9×7One node pushed the error from 0.21% to 76% — local relaxation time in power-law LBM×7Nine Arrows of Maxwell–Boltzmann — Why LBM's Equilibrium Is a Polynomial×7
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How to Make an Outflow Stop Reflecting Sound — Navier–Stokes Characteristic Boundary Conditions×5One χ=50, two temperatures: 1759 K and 818 K — where a flamelet library folds×3Turbulence Runs Three Rulers at Once — The Kolmogorov Cascade and the -5/3 Law×2Reynolds Number and Flow Transition, Through Visualization×2A Small Wobble in Mixture Fraction Drops the Mean Flame Temperature by 964 K — Presumed β-PDF and the Infinity at Z=0×1
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Interface Capturing Methods: VOF vs Level Set vs Diffuse Interface×8Mobility Up 10×, Interface Width Unchanged — The Anti-Diffusion Term in Conservative Allen–Cahn×1[Paper Review] A Droplet Sends Almost Every Sound Wave Back — Acoustic Impedance and a Sharp-Interface Two-Phase Solver×1Filling an Interface with a Fluid That Isn't There — The Ghost Fluid Method×1From the Riemann Problem to Godunov's Scheme - The Essence of Numerical Flux×1
— M —
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Four Shocks Beat One — The Oblique Shock Train in a Supersonic Inlet×21[Paper Review] Why Roe breaks at low Mach — Hope–Collins (2022) and three artificial-diffusion scalings×21[Paper Review] GMRES Ran 1000 Times and Still Wouldn't Stop — Physics-Based Block Preconditioning for an All-Speed Melt Pool×11[Paper Review] When the Sound Speed Diverges and the Time Step Survives — Orlando–Bonaventura (2024) AP-IMEX for Non-Ideal Gases×8[Paper Review] Fooling a Nonlinear Flux Into Behaving Linearly — Jin–Xin & Suliciu Relaxation×5
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[Paper Review] Pick the Reconstruction with Smaller Jumps — Deng (2018) MUSCL-THINC-BVD×17[Paper Review] One Scheme Can't Handle Every Wave — Chamarthi (2025)×7[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×3[Paper Review] Suspect the Cell After Solving It — A Posteriori MOOD Subcell Limiter for DG×3FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques×2
— N —
— O —
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Rhie-Chow Interpolation for Compressible Multiphase Flows×5Same Answer From 18% of the Cells — AMR Tagging Criteria and Coarse-Fine Refluxing×3Poiseuille Flow: Analytical Solution Derivation and Finite Difference Validation×3[OpenFOAM Tutorial] Backward Facing Step Flow Analysis — Capturing Recirculation Zones with simpleFoam×3Solving an Impeller by Holding It Still — Rotating Frames and MRF×2
— P —
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A 1% Error in Diameter Is a 4% Error in Flow Rate — Half a Cell of Wall and Poiseuille's Constant×11Where Half the Force Goes in LBM — Four Forcing Schemes and 1−1/(2τ)×4How Far Must Water Flow Before It Becomes a Parabola — Entrance Length and Hagen–Poiseuille×4Dean Flow: Analytical Solution and CFD Validation for Helical Pipe Flow×4Poiseuille Flow: Analytical Solution Derivation and Finite Difference Validation×3
— Q —
— R —
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Turbulence Runs Three Rulers at Once — The Kolmogorov Cascade and the -5/3 Law×3Where Turbulence Stops Speeding Up a Flame — Damköhler's Wrinkling Hypothesis and Bending×2When the Stream Breaks — Reynolds' Critical Number and the Layered Turbulent Boundary×2Solving Wall Distance in O(N log N): Eikonal Equation and Fast Marching×2Reynolds Number and Flow Transition, Through Visualization×2
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Bugs Swim in Honey — The World of Flow Changed by Reynolds Number×8Reynolds Number and Flow Transition, Through Visualization×82.0000 in laminar flow, 1.0322 in turbulent — the coefficient in front of the velocity head×6How Far Must Water Flow Before It Becomes a Parabola — Entrance Length and Hagen–Poiseuille×6Turbulence Runs Three Rulers at Once — The Kolmogorov Cascade and the -5/3 Law×6
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Rhie-Chow Interpolation for Compressible Multiphase Flows×30When Pressure Rings in a Checkerboard — SIMPLE and Rhie-Chow Coupling×9Changing One Relaxation Factor Moved the Converged Solution — Where Rhie–Chow Face Velocities Remember Under-Relaxation×1Upgrading Only the Viscous Term to Second Order Made the Error 1.82x Worse — Why the Semi-Implicit Gear Scheme Extrapolates Convection×1I dropped K and the water compressed 1.86x too much — an interface error that refinement does not remove×1
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From the Riemann Problem to Godunov's Scheme - The Essence of Numerical Flux×16[Paper Review] Second-Order Accuracy in a Single Stage — A GRP Solver for the Kapila Multiphase Model×9Godunov's Method — One Tiny Shock Tube Inside Every Cell×7Filling an Interface with a Fluid That Isn't There — The Ghost Fluid Method×6[Paper Review] Prying Advection and Pressure Fully Apart — TV Flux Splitting for Baer–Nunziato×4
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From the Riemann Problem to Godunov's Scheme - The Essence of Numerical Flux×8The Star That Started Moving — Well-Balanced FVM and Angular Momentum in Polar Coordinates×6FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques×4I dropped K and the water compressed 1.86x too much — an interface error that refinement does not remove×2[Paper Review] Prying Advection and Pressure Fully Apart — TV Flux Splitting for Baer–Nunziato×2
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What You Give Up the Exact Riemann Solution For — the Roe Solver and the Entropy Fix×10[Paper Review] Why Roe breaks at low Mach — Hope–Collins (2022) and three artificial-diffusion scalings×9Catching Shocks Without Multiplying a Matrix at Every Face — AUSM Flux Splitting×8The Euler Eigensystem in an Arbitrary Direction — Three Waves, Two Repeats, One Singularity×6From the Riemann Problem to Godunov's Scheme - The Essence of Numerical Flux×4
— S —
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Upgrading Only the Viscous Term to Second Order Made the Error 1.82x Worse — Why the Semi-Implicit Gear Scheme Extrapolates Convection×6The bill for a 1001x larger time step — why a semi-implicit pressure scheme is not L∞ stable×4[Paper Review] Suspect the Cell After Solving It — A Posteriori MOOD Subcell Limiter for DG×4[Paper Review] Beating the Storm Clock — Casulli–Walters (2000) Semi-Implicit Shallow Water on Unstructured Orthogonal Grids×4Dividing the Reverse Rate by Kp Split 99.6% of AlO at 2500 K — The (p°/RT)^Δn Hidden in the Equilibrium Constant×2
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When Pressure Rings in a Checkerboard — SIMPLE and Rhie-Chow Coupling×8Changing One Relaxation Factor Moved the Converged Solution — Where Rhie–Chow Face Velocities Remember Under-Relaxation×6Rhie-Chow Interpolation for Compressible Multiphase Flows×3[Paper Review] GMRES Ran 1000 Times and Still Wouldn't Stop — Physics-Based Block Preconditioning for an All-Speed Melt Pool×2[CFD Q&A] When simpleFoam Pressure Residual Fails to Converge×2
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To Go Supersonic, Widen the Pipe — The De Laval Nozzle and Choking×30[Paper Review] Half Water, Half Air, and Sound Crawls at 24 m/s — The K∇·u Term in the Murrone–Guillard Five-Equation Model×22[Paper Review] A Droplet Sends Almost Every Sound Wave Back — Acoustic Impedance and a Sharp-Interface Two-Phase Solver×18Above Mach 1, You Must Widen to Speed Up — The Laval Nozzle Paradox×18Supersonic Flow Can't See Upstream — Characteristics and Sound Waves in the Euler Equations×14
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[Paper Review] 0.333 in Tension, 0 in Compression — Where SPH Particles Start Pairing Up×13SPH Without Tears — Solving Fluids with Particles, from Kernel to Artificial Viscosity×10Saving Gradients on Unstructured Grids — Moving Least-Squares Approximation×7[Paper Review] The Tetrahedron That Led With One Sphere Never Broke Apart — A Bluntness Index for Mach 20 Fragment Clusters×1FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques×1
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1950 — When von Neumann Deliberately Smeared the Shock: Artificial Viscosity and Odd-Even Decoupling×4[Paper Review] The Same Point Read 0.544 Apart Along Two Paths — Curl Involutions on a Staggered Grid×3[Paper Review] Suspect the Cell After Solving It — A Posteriori MOOD Subcell Limiter for DG×3Advecting Without Splitting Directions — The Bell-Colella-Glaz Unsplit Upwind Scheme×1Why a Shout Above Water Never Reaches Below — Acoustics Across a Diffuse Interface×1
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[Paper Review] When WENO Smears Small Eddies — Fu (2019) Low-Dissipation TENO Finite-Volume Scheme×15[Paper Review] Drawing Shocks with tanh — Implementing TENO-THINC Reconstruction×13[Paper Review] The Tetrahedron That Led With One Sphere Never Broke Apart — A Bluntness Index for Mach 20 Fragment Clusters×1[Paper Review] Two Fragments Flew Together Instead of Pushing Apart — The 144° Equilibrium of a Mach 20 Sphere Pair×1[Paper Review] The Capillary Shackle Came Off and CFL 0.05 Was Still There — The Real Ceiling on VOF Interface Advection×1
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The Mach Number Goes to Zero, the Time Step Doesn't Budge — Reproducing an IMEX TVD Scheme×18When Lax–Wendroff Shook at a Step — Building a 2nd-Order TVD Advection Scheme with Flux Limiters×6[Paper Review] Drawing Shocks with tanh — Implementing TENO-THINC Reconstruction×4Mass Is Conserved Exactly, Yet the Density Is Negative — The Positivity-Preserving Flux Limiter×2Numerical Dungeon: Learn Numerical Methods Through a Game×2
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Interface Capturing Methods: VOF vs Level Set vs Diffuse Interface×10I dropped K and the water compressed 1.86x too much — an interface error that refinement does not remove×6[Paper Review] The Capillary Shackle Came Off and CFL 0.05 Was Still There — The Real Ceiling on VOF Interface Advection×6[Paper Review] Two-Phase Flow Without a Poisson Solver — Coupling the General Pressure Equation with MSTACS×6[Paper Review] MSTACS with Slope 3 Blew Up After 255 Steps at Co=0.5 — Compressive Differencing and the Courant Limit×3
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Giving Each Phase Its Own Equations — The Baer–Nunziato Seven-Equation Model×13[Paper Review] Half Water, Half Air, and Sound Crawls at 24 m/s — The K∇·u Term in the Murrone–Guillard Five-Equation Model×8[Paper Review] Second-Order Accuracy in a Single Stage — A GRP Solver for the Kapila Multiphase Model×8[Paper Review] Two-Phase Flow Without a Poisson Solver — Coupling the General Pressure Equation with MSTACS×6[Paper Review] One Scheme Can't Handle Every Wave — Chamarthi (2025)×5
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Two Faces of a Whirl — Free Vortex, Forced Vortex, and Helmholtz×12Where Total Pressure Dropped 1,080 Pa, Dissipation Was Zero — When the Bernoulli Constant Crosses Streamlines×10Where Turbulence Stops Speeding Up a Flame — Damköhler's Wrinkling Hypothesis and Bending×6Why a Spinning Ball Curves — Circulation, Magnus, and the Kutta–Joukowski Theorem×6Viscosity Is Not What Kills a Vortex — Newton's 1/r and the Lamb–Oseen Core×5
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[Paper Review] When WENO Smears Small Eddies — Fu (2019) Low-Dissipation TENO Finite-Volume Scheme×12[Paper Review] One Scheme Can't Handle Every Wave — Chamarthi (2025)×3FDM vs FEM vs FVM: The Essential Differences Between Three Discretization Techniques×3[Paper Review] Drawing Shocks with tanh — Implementing TENO-THINC Reconstruction×2[Paper Review] Pick the Reconstruction with Smaller Jumps — Deng (2018) MUSCL-THINC-BVD×2
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