Series

Discretization, meshes, boundary conditions and pressure–velocity coupling: the numerical backbone of a CFD solver.

2026.03.08 – 2026.10.14

1. 26.10.14Changing One Relaxation Factor Moved the Converged Solution — Where Rhie–Chow Face Velocities Remember Under-Relaxation
2. 26.10.13I Gave Curved Cells Their True Area and ∂x/∂x Stopped Being 1 — Why the Diagonal Cross-Product Area Fits Green–Gauss
3. 26.10.12Upgrading Only the Viscous Term to Second Order Made the Error 1.82x Worse — Why the Semi-Implicit Gear Scheme Extrapolates Convection

Riemann solvers, TVD flux limiters and MUSCL/WENO/TENO reconstruction for sharp, stable discontinuities.

2026.05.13 – 2026.10.07

1. 26.10.07The Same Code Gave 0.79 and 2.00 at Once — What Verification Cases Actually Measure
2. 26.08.25The Kinked String Was Fine, the Cut String Overshot by 9% — How the 1747 Wave-Equation Fight Ended Numerically
3. 26.08.18The Shock Never Left the Starting Line — Where Conservative and Primitive Forms Split

Low-Mach preconditioning, IMEX and dual-time stepping, and Krylov, Newton–Krylov and multigrid solvers for large systems.

2026.05.06 – 2026.10.30

1. 26.10.30A Steady-State Preconditioner Inside a Dual-Time Loop Took 19× More Inner Iterations — A Low-Mach Acoustic Pulse Test
2. 26.10.29A Ball Thrown at 5 m/s Passed Through a 20 mm Wall — Penalty Contact vs. the IPC Log Barrier
3. 26.10.21Halving the Grid Spacing Tripled the Error — What an Increment-Based Stopping Rule Hides in Jacobi Iteration

Diffuse-interface and five-equation models, interface capturing (VOF, THINC) and surface tension for compressible multiphase flow.

2026.03.04 – 2026.10.26

1. 26.10.26A Two-Cell Interface Loses 39% of Its Surface Tension — The Anisotropy of the Korteweg Stress
2. 26.10.20Adding 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 = 60
3. 26.10.02I asked for σ₁₂ = 1.00 and got 0.78 — where an absent phase leaks into the interface in three-component Allen–Cahn

The lattice Boltzmann method from kinetic theory: Chapman–Enskog expansion, collision operators, forcing terms and boundaries.

2026.05.25 – 2026.10.28

1. 26.10.28Velocity came out one sixth at τ=0.6 — dropping the half-force F/2 from Guo forcing
2. 26.10.23Changing only τ changed the density of a gas at rest — the (τ−½)² stress of Shan–Chen velocity-shift forcing
3. 26.10.19Giving Conduction Its Own τ Left Viscous Heating Stuck at Pr = 1 — The Quasi-Equilibrium g* in Two-Population LB

Finite element and discontinuous Galerkin formulations, basis functions and implementation.

2026.04.20 – 2026.09.14

1. 26.09.14One Integral Read as 0.1406 and 56.91 — Torsion Stress Function and Duct Laminar Flow
2. 26.08.31A 30° rigid rotation read -13% strain — conjugate stress-strain pairs in large-strain shells
3. 26.08.28Pushing the cell Péclet number to 2 drove the solution to -0.33 — where the energy to minimize disappeared

Fluid–structure interaction, immersed boundaries and particle methods such as SPH for moving bodies in flow.

2026.04.29 – 2026.08.13

1. 26.08.13The Weight Sits on Top and She Still Rights Herself — Metacentric Height and the Free Surface Effect
2. 26.08.03A Wall the Grid Never Sees — IBM Delta Kernels and Multi-Direct Forcing
3. 26.06.08When a Bullet Passes Straight Through a Wall — Continuous Collision Detection by Inclusion Bisection

Boundary layers, vortices, turbulence, heat transfer and combustion: the physics a simulation has to reproduce, and its history.

2026.03.25 – 2026.10.27

1. 26.10.27A Small Wobble in Mixture Fraction Drops the Mean Flame Temperature by 964 K — Presumed β-PDF and the Infinity at Z=0
2. 26.10.22Dividing the Reverse Rate by Kp Split 99.6% of AlO at 2500 K — The (p°/RT)^Δn Hidden in the Equilibrium Constant
3. 26.10.15A 1 μm Aluminum Particle Heated 4.6× Slower Than the Continuum Formula — Sherman Interpolation in the Knudsen Transition Regime

OpenFOAM case setup and verification examples.

2026.03.26 – 2026.08.10

1. 26.08.10Same Answer From 18% of the Cells — AMR Tagging Criteria and Coarse-Fine Refluxing
2. 26.07.17When Gradients Go Wrong on Skewed Meshes — Green–Gauss vs. Weighted Least-Squares Reconstruction
3. 26.06.12Solving an Impeller by Holding It Still — Rotating Frames and MRF

Selected CFD and fluid-mechanics papers, read through their key idea, equations and a reproduction script.

2026.03.24 – 2026.10.31

1. 26.10.31[Paper Review] A water-air interface in uniform flow produced an 8×10⁸ Pa pressure spike — the non-disturbance condition in a pressure-based BN model
2. 26.10.25[Paper Review] MSTACS with Slope 3 Blew Up After 255 Steps at Co=0.5 — Compressive Differencing and the Courant Limit
3. 26.10.24[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