cfd-mesh

name	cfd-mesh
description	CFD meshing — structured vs. unstructured, inflation layers, y+ calculation, domain sizing, mesh independence study, overset/chimera mesh, moving mesh (ALE, remesh).
metadata	{"priority":7,"promptSignals":{"phrases":["CFD mesh","inflation layer","y plus","CFD domain","mesh independence","boundary layer mesh","CFD grid"],"minScore":4}}

CFD Meshing — Complete Skill

Domain Sizing (External Flows)

Bluff Body / Vehicle Aerodynamics

Inlet: 5-10 body lengths upstream Outlet: 15-20 body lengths downstream (long wake) Sides/Top: 5 body lengths from model (blockage < 2-5%) Blockage ratio: A_body / A_domain_cross-section < 5% (avoids wall interference)

Airfoil / Wing

Inlet: 10-20 chords upstream (circular or C-type domain) Wake: 20-30 chords downstream Farfield: 15-20 chords normal to freestream

Internal Flow (Duct, Pipe)

Inlet: 10-20 hydraulic diameters upstream (for fully-developed profile) Outlet: 10-20 D_h downstream of last feature (prevent outlet BCs from affecting results) Or: apply developed velocity profile as BC (reduces domain length)

Inflation Layer Design (Boundary Layer)

Target y⁺ Calculation

Step 1: Estimate skin friction coefficient C_f Flat plate: C_f = 0.074 Re_L^(-1/5) (turbulent, 5×10⁵ < Re_L < 10⁷) or C_f = 0.0592 Re_L^(-1/5) (simpler Prandtl) Pipe: C_f = 0.316 Re_D^(-1/4) (Blasius, smooth)

Step 2: Wall shear τ_w = C_f × ½ρU²

Step 3: Friction velocity u_τ = √(τ_w/ρ)

Step 4: First cell height y₁ = y⁺_target × ν / u_τ

Example: Air at 30 m/s, L = 1 m, target y⁺ = 1 Re_L = 30×1/1.5e-5 = 2×10⁶ C_f = 0.074 × (2e6)^(-0.2) = 0.00368 τ_w = 0.00368 × ½ × 1.2 × 900 = 1.99 Pa u_τ = √(1.99/1.2) = 1.29 m/s y₁ = 1 × 1.5e-5 / 1.29 = 1.16×10⁻⁵ m = 0.0116 mm

Inflation Layer Parameters

First cell height: y₁ (from y⁺ calculation above) Growth ratio r: 1.2 (conservative, smooth), 1.3 (typical), 1.5 (max acceptable) Number of layers: enough to capture full boundary layer thickness δ

Boundary layer thickness: δ ≈ 0.37 L Re_L^(-1/5) [turbulent flat plate] Required layers n: δ/y₁ = r^n - 1/(r-1) → n = log(1 + δ(r-1)/y₁) / log(r)

Quick estimate: 12-20 inflation layers typical for y⁺ = 1 design

Mesh Independence Study (Grid Convergence Index — GCI)

Richardson Extrapolation

Use 3 systematically refined meshes (refine factor r = 2 typical) h₁ < h₂ < h₃ (fine → coarse) f_exact ≈ f₁ + (f₁ - f₂)/(r^p - 1) p = ln[(f₃-f₂)/(f₂-f₁)] / ln(r) [observed order of convergence]

Grid Convergence Index (Roache): GCI_12 = F_s |ε₁₂| / (r^p - 1) [ε₁₂ = (f₂-f₁)/f₁] F_s = 1.25 (safety factor for 3 meshes) GCI < 5%: grid-independent solution

Asymptotic range check: GCI_23 / (r^p × GCI_12) ≈ 1 → converged

Practical Study

Mesh	Cells	C_d	Δ% from prev
Coarse	500K	0.315	—
Medium	1.5M	0.296	-6.0%
Fine	4M	0.292	-1.4%
Medium → Fine < 2%: use Medium for production runs

Structured vs. Unstructured for CFD

Structured (Hexahedral)

All cells hexahedral; requires blocking strategy Pros: lower cell count for same accuracy, better near-wall performance, lower numerical diffusion Cons: complex for irregular geometry; time-consuming to create Tools: ICEM CFD, POINTWISE, Gridgen

Unstructured (Tetrahedral/Poly)

Auto-generated; handles any geometry Pros: fast to create, handles complex geometry Cons: 2-3× more cells needed for same accuracy; diffusion in wrong direction Polyhedral (Fluent/STAR-CCM+): average 5-7 faces/cell; better than TET, nearly as good as HEX for unit cost

Recommendation: HEX for simple geometry (pipes, ducts, airfoils), POLY for complex 3D geometry

Moving Mesh and ALE

ALE (Arbitrary Lagrangian-Eulerian)

Mesh moves with fluid partially; handles large deformations Applications: piston motion, valve opening, fluid-structure interaction Smoothing + remeshing when cells become too distorted

Sliding Mesh (Rotating Machinery)

Rotor zone rotates relative to stator zone Sliding interface: interpolates fluxes across moving/stationary boundary Fully unsteady — captures rotor-stator interaction Used for: fans, pumps, turbines (transient)

MRF (Multiple Reference Frame): steady-state approximation Adds Coriolis and centrifugal source terms in rotating zone No actual rotation — faster, less accurate for strong unsteady effects

Overset/Chimera Mesh

Multiple overlapping meshes; fringe cells interpolate between them Body-fitted mesh moves through background mesh Used for: complex maneuvers, 6-DOF ship/aircraft motion, propellers

Mesh Topology Patterns

O-grid (Circular Bodies)

Circular topology wrapping around cylinder/airfoil Excellent orthogonality at wall; preferred for aerodynamics

C-grid / H-grid (Airfoils)

C-grid: wraps around leading edge, exits at trailing edge H-grid: rectangular; wake captured inline; simpler for multi-element

Polyhedral Mesh (STAR-CCM+, Fluent)

Convert tet mesh to poly automatically Reduces cell count 3-5× vs. TET, maintains accuracy Currently best automatic meshing approach for complex geometry

Cell Count Estimation Guide

Application	Cells (2D)	Cells (3D full)
Simple pipe flow	5,000	100,000–500K
Airfoil 2D	50,000–200K	—
External aero (car)	—	20M–100M
HVAC room	—	1M–10M
Turbomachinery stage	—	5M–50M
Combustor	—	10M–100M (LES)

Output

Provide: domain size [m], first cell height y₁ [mm] for target y⁺, inflation layers count, total estimated cell count, GCI from mesh independence study [%], recommended mesh type (hex/poly/tet).