Which statement correctly describes a hybrid mesh?

A combination, e.g. prism or hexahedral layers at walls with tetrahedra in the core

A mesh where every node has the same number of neighbours

A mesh made only of tetrahedra with arbitrary connectivity

A mesh of only hexahedra addressed by (i,j,k)

What is an advantage of a structured mesh?

Low memory and fast solvers (ADI, line-SOR), with low numerical diffusion when aligned with the flow

Fully automatic meshing of any geometry

Easy local refinement without affecting other regions

Works best for car bodies and engine bays

Compared with a structured mesh, an unstructured mesh typically:

fits complex shapes and refines locally easily, but needs more memory and indirect addressing

needs more manual effort but uses less memory

has the same number of neighbours for each cell

always gives lower numerical diffusion

Practice · 6 marks

Structured, unstructured and hybrid meshes

Short answer

Structured meshes use regular hexahedra with low memory and fast solvers but require multi-block for complex shapes. Unstructured meshes use triangles/tetrahedra, automatically fit any shape, but need more cells and memory. Hybrid meshes combine prism layers near walls with tetrahedral core, giving good wall treatment and moderate effort.

Differentiate between structured, unstructured and hybrid meshes. Give the advantages, disadvantages and typical applications of each.

A mesh (grid) divides the flow domain into small cells on which the equations are solved. Its type affects accuracy, memory and effort.

 Structured        Unstructured       Hybrid
 +--+--+--+        /\  /\ /\          ||||||||  prism
 +--+--+--+       /__\/__\/__\        ||||||||  layers
 +--+--+--+       \  /\  /\  /        /\/\/\/\  tetra
 +--+--+--+        \/__\/__\/         core

Structured: cells are arranged in a regular pattern; each interior node has the same number of neighbours and is addressed by indices $(i,j,k)$ . Cells are quadrilaterals (2D) or hexahedra (3D).
Unstructured: cells (triangles/tetrahedra, or any polyhedra) have arbitrary connectivity, stored in a table; the number of neighbours varies.
Hybrid: a combination, e.g. thin prism or hexahedral layers next to walls and tetrahedral cells in the core, or structured blocks joined by unstructured regions.

Point	Structured	Unstructured	Hybrid
Geometry fit	Simple shapes; complex shapes need multi-block	Any complex shape	Complex shapes with good wall treatment
Meshing effort	High manual effort	Mostly automatic	Moderate
Accuracy per cell	High; aligned with flow	Lower; may need more cells	Good near walls
Memory/solver	Low memory, fast solvers (ADI, line-SOR)	More memory, indirect addressing	Medium
Local refinement	Hard, propagates through the block	Easy	Easy
Numerical diffusion	Low if aligned with flow	Higher	Low in boundary layer
Applications	Pipes, ducts, turbomachinery blades, finite difference codes	Car body, engine bay, buildings, electronics	Aircraft wings, vehicle aerodynamics, boundary-layer flows

✓ Answer checked by Claude Opus 5.5 (high effort)

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