The quality of a mesh plays a significant role in the accuracy and stability of the numerical computation. Regardless of the type of mesh used in your domain, checking the quality of your mesh is a must. The ‘good meshes’ are the ones that produce results with fairly acceptable level of accuracy, considering that all other inputs to the model are accurate. While evaluating whether the quality of the mesh is sufficient for the problem under modeling, it is important to consider attributes such as mesh element distribution, cell shape, smoothness, and flow-field dependency.
Element Distribution
It is known that meshes are made of elements (vertices, edges and faces). The extent, to which the noticeable features such as shear layers, separated regions, shock waves, boundary layers, and mixing zones are resolved, relies on the density and distribution of mesh elements. In certain cases, critical regions with poor resolution can dramatically affect results. For example, the prediction of separation due to an adverse pressure gradient depends heavily on the resolution of the boundary layer upstream of the point of separation.
Cell Quality
The quality of a cell has a crucial impact on the accuracy of the entire mesh. The quality of cell is analyzed by the virtue of three aspects: Orthogonal quality, Aspect ratio and Skewness.
Orthogonal Quality: An important indicator of mesh quality is an entity referred to as the orthogonal quality. The worst cells will have an orthogonal quality close to 0 and the best cells will have an orthogonal quality closer to 1.
Aspect Ratio: Aspect ratio is an important indicator of mesh quality. It is a measure of stretching of the cell. It is computed as the ratio of the maximum value to the minimum value of any of the following distances: the normal distances between the cell centroid and face centroids and the distances between the cell centroid and nodes.
Skewness: Skewness can be defined as the difference between the shape of the cell and the shape of an equilateral cell of equivalent volume. Highly skewed cells can decrease accuracy and destabilize the solution.
Smoothness
Smoothness redirects to truncation error which is the difference between the partial derivatives in the equations and their discrete approximations. Rapid changes in cell volume between adjacent cells results in larger truncation errors. Smoothness can be improved by refining the mesh based on the change in cell volume or the gradient of cell volume.
Flow-Field Dependency
The entire effects of resolution, smoothness, and cell shape on the accuracy and stability of the solution process is dependent upon the flow field being simulated. For example, skewed cells can be acceptable in benign flow regions, but they can be very damaging in regions with strong flow gradients.
Correct Mesh Size
Mesh size stands out as one of the most common problems to an equation. The bigger elements yield bad results. On the other hand, smaller elements make computing so long that it takes a long amount of time to get any result. One might never really know where exactly is the mesh size is on the scale.
It is important to consider chosen analysis for different mesh sizes. As smaller mesh means a significant amount of computing time, it is important to strike a balance between computing time and accuracy. Too coarse mesh leads to erroneous results. In places where big deformations/stresses/instabilities take place, reducing element sizes allow for greatly increased accuracy without great expense in computing time.