This chapter introduces meshing as a numerical modeling activity rather than a geometric one. The purpose of the mesh, common meshing strategies, and practical quality metrics are summarized without reference to software-specific procedures. Emphasis is placed on understanding why different mesh types and controls exist, when they should be used, and how mesh quality directly affects accuracy, stability, and physical fidelity in CFD simulations.

What the Mesh Really Is

In CFD, the mesh is:

The numerical representation of the physical domain
The structure on which conservation laws are enforced
A key part of the mathematical model itself

CFD solvers:

Do not “see” CAD
Do not “see” smooth surfaces
Only see cells, faces, and connectivity

As a result:

A bad mesh cannot be fixed by a good solver.

Purpose of the Mesh

A good mesh must balance three competing goals:

Accuracy
- Resolve gradients where physics demands it
- Near walls, interfaces, shocks, and separation
Efficiency
- Use fine cells only where needed
- Keep cell count manageable
Numerical robustness
- Avoid pathological cell shapes
- Ensure stable convergence

Every meshing decision is a compromise between these three.

Where Mesh Refinement Actually Matters

Refinement is physically justified in regions with:

High velocity or pressure gradients
Boundary layers
Curvature or small geometric features
Flow separation or recirculation
Heat transfer or species gradients

Uniform refinement everywhere is numerically expensive and physically meaningless.

Mesh Topology: The Big Picture

Unstructured vs Structured Thinking

Unstructured meshes
Flexible, robust, geometry-friendly
Higher numerical diffusion
Structured / semi-structured meshes
Aligned with flow, lower numerical error
Require geometric discipline

Modern CFD uses hybrid meshes by default.

Core Mesh Element Types (When to Use What)

Tetrahedra

Excellent for complex geometry
Automatic and robust
Higher numerical diffusion
Not ideal near walls unless combined with inflation

Use when: geometry complexity dominates.

Prisms / Wedges (Inflation Layers)

High aspect-ratio cells near walls
Resolve boundary-layer gradients
Essential for turbulence and heat transfer

Use whenever walls matter (which is almost always).

Hexahedra

Best numerical accuracy per cell
Low numerical diffusion
Aligned with flow direction

Use when geometry allows it, especially in ducts and channels.

Hybrid Meshes

Tets in the core
Prisms near walls
Hex where possible

This is the industrial default.

Patch Conforming vs Patch Independent (Conceptual)

Patch Conforming

Mesh follows CAD surfaces exactly
Preserves geometric detail
Requires clean geometry

Good for: high-quality CAD, when small features matter.

Patch Independent

Mesh ignores small geometric details
Geometry is approximated within tolerance
More robust for dirty CAD

Good for: early design, scanned geometry, complex assemblies

Hex Meshing Strategies

Sweep Meshing

Extrudes a 2D mesh through a volume
Requires topological similarity
Produces high-quality hex/wedge cells

Ideal for: pipes, channels, turbomachinery passages.

Multizone Meshing

Automatically decomposes geometry
Produces mostly hex meshes
Less control than manual blocking

Good compromise between quality and automation.

Inflation Layers: Why They Matter

Near walls:

Gradients scale with wall distance
Turbulence models assume proper wall-normal resolution

Inflation layers:

Provide controlled growth away from the wall
Maintain orthogonality
Reduce numerical stiffness

Without inflation:

Wall-bounded CFD results are rarely trustworthy.

Mesh Quality Metrics (The Real Cheat Sheet)

These metrics matter more than cell count.

Skewness

Measures deviation from ideal cell shape
High skewness → solver instability

Rule of thumb:
Low is good. Avoid extreme values near walls and interfaces.

Orthogonality

Measures alignment of face normals and cell centers
Poor orthogonality increases discretization error

Critical for: pressure–velocity coupling.

Aspect Ratio

Ratio of longest to shortest cell dimension
High aspect ratio acceptable only in boundary layers

Bad in the core, good near walls (when intentional).

Smoothness (Growth Rate)

Controls how fast cell size changes
Abrupt changes harm convergence

Gradual transitions improve solver robustness.

Mesh Quality vs Mesh Density

More cells ≠ better solution.

A coarser but well-shaped mesh often outperforms:

A very fine mesh with bad skewness
A mesh with poor wall resolution

Mesh refinement should always be physics-driven, not guilt-driven.

Meshing as Part of the CFD Loop

Mesh generation is not a one-shot step.

Typical workflow:

Generate baseline mesh
Run preliminary solution
Inspect gradients and flow features
Refine selectively
Re-run and compare

Mesh independence is a process, not a checkbox.

Engineering Intuition

The mesh is part of the numerical model
Boundary layers deserve special treatment
Hex cells are gold, but not always feasible
Inflation is non-negotiable for wall physics
Quality beats quantity
A solver cannot fix a bad mesh

Study Priorities

If short on time, remember:

Where refinement matters physically
Why inflation layers exist
Patch conforming vs independent
Hybrid meshing philosophy
Skewness, orthogonality, growth rate

Key Takeaways

Meshing is a modeling decision, not a technical step.
The solver only sees cells and faces.
Hybrid meshes are the industrial standard.
Boundary layers require structured resolution.
Mesh quality controls accuracy and stability.
Good CFD starts with good meshing judgment.

Introduction to CFD Chapter 2: Meshing Foundations