Types of mesh

A mesh partitions space into elements (or cells or zones) over which the equations can be solved, which then approximates the solution over the larger domain.

Computationally poor elements will have sharp internal angles or short edges or both.

The basic 3-dimensional element are the tetrahedron, quadrilateral pyramid, triangular prism, and hexahedron.

A nonplanar quadrilateral face can be considered a thin tetrahedral volume that is shared by two neighboring elements.

A quadrilaterally-based pyramid has 5 vertices, 8 edges, bounded by 4 triangular and 1 quadrilateral face.

A cuboid, a topological cube, has 8 vertices, 12 edges, and 6 quadrilateral faces, making it a type of hexahedron.

The pyramid and triangular prism zones can be considered computationally as degenerate hexahedrons, where some edges have been reduced to zero.

This model is highly space efficient, since the neighbourhood relationships are defined by storage arrangement.

The choice of mesh element type affects both discretization and solution error.

The speed of each iteration grows (linearly) with the number of elements, and the number of iterations needed depends on the local solution value and gradient compared to the shape and size of local elements.

One can selectively refine the mesh in areas where the solution gradients are high, thus increasing fidelity there.

A faster rate of convergence means smaller error with fewer iterations.

A mesh of inferior quality may leave out important features such as the boundary layer for fluid flow.

The density of the mesh is required to be sufficiently high in order to capture all the flow features but on the same note, it should not be so high that it captures unnecessary details of the flow, thus burdening the CPU and wasting more time.

Quad and Hex cells can be stretched where the flow is fully developed and one-dimensional.

Based on the skewness, smoothness, and aspect ratio, the suitability of the mesh can be decided.

This method applies to all cell and face shapes and is almost always used for prisms and pyramids Another common measure of quality is based on equiangular skew.

For Hex and quad cells, skewness should not exceed 0.85 to obtain a fairly accurate solution.

Having a large aspect ratio can result in an interpolation error of unacceptable magnitude.