Rule of thumb for mesh generation!

The mesh generation principle is a fundamental concept in numerical simulations and computational modeling. It involves the creation of a grid of interconnected points (elements) that cover the geometric domain of interest. This grid, known as the mesh, allows the representation of complex geometries as a discrete set of interconnected elements. The primary goal of mesh generation is to ensure accurate representation of the geometry and to capture the physics of the problem being simulated.

One crucial aspect considered during mesh generation is the "maximum aspect ratio." Aspect ratio refers to the ratio of the longest edge to the shortest edge in a single element of the mesh. In 2D simulations, this ratio is based on the edge lengths of triangles or quadrilaterals, while in 3D simulations, it considers the edge lengths of tetrahedra or hexahedra.

A low maximum aspect ratio is desired because it ensures that the elements are more uniform and closer to equilateral or regular shapes. Uniform elements lead to better accuracy and stability in simulations, as irregular elements can introduce numerical errors and result in incorrect solutions.

However, achieving a perfectly uniform mesh is often challenging, especially in complex geometries. In practice, engineers and researchers strike a balance between mesh refinement, computational cost, and simulation accuracy. Different meshing strategies and algorithms are employed to optimize the mesh, control the aspect ratio, and ensure accurate representation of the physics of interest.

The maximum aspect ratio for mesh generation is a parameter that can vary depending on the specific requirements of the simulation and the software being used. In general, a lower maximum aspect ratio is preferred for more accurate and stable simulations.

In many engineering and scientific simulations, a common rule of thumb is to aim for a maximum aspect ratio of around 3 to 4. This means that the longest edge of an element in the mesh should not be more than 3 to 4 times the length of the shortest edge. However, in some cases, such as simulations involving complex geometries or flow features, slightly higher aspect ratios may be acceptable.

It's important to note that the ideal maximum aspect ratio can differ based on the specific application, the geometry being simulated, and the level of accuracy required. Engineers and researchers often perform mesh sensitivity studies to determine the optimal mesh settings for their particular simulation.

Ultimately, achieving a balanced mesh with a reasonable maximum aspect ratio is essential for obtaining accurate and efficient numerical simulations. The goal is to ensure that the mesh is well-suited to capture the relevant flow features and physics while minimizing any adverse effects on the simulation results.