Mesh Quality Best Practices

Mesh quality plays a significant role in the accuracy and stability of numerical computations. While the Discovery mesh size defaults are intended to provide a reasonable mesh quality based on the defined physics, checking the quality of your mesh is essential to ensure an accurate solution. The following are indicators of mesh quality along with best practices.

Structural Mesh Metrics


Mesh Quality Indicator	Description	Best Practice
Element quality	It provides a composite quality metric that ranges between 0 and 1. A value of 1 indicates a perfectly shaped element while a value of 0 indicates that the element has a zero or negative volume. Learn more about Element Quality.	The optimal Element quality is 1.0, and a high-quality mesh typically avoids elements with an Element quality less than 0.05. Elements with element quality less than 0.05 should be avoided in regions with large stress gradients but may be acceptable if the primary result of interest is displacement.
Jacobian ratio	It compares the shape of a given element to that of an ideal element. If an element has a poor Jacobian ratio, the element may not map well from element space to real space, thereby making computations based on the element shape less reliable. Learn more about Jacobian Ratio.	The optimal Jacobian ratio is 1.0, and a high-quality mesh typically has a Jacobian ratio ranging from 1 to 10 for most of its elements. Elements with large Jacobian ratios (>30) should be avoided in regions with large stress gradients but may be acceptable if the primary result of interest is displacement.
Aspect ratio	A measure of the stretching of an element. It is a measure of the ratio of the longest dimension to the shortest dimension of an element. Learn more about Aspect Ratio.	An aspect ratio of 1 is ideal, and values less than 5 are acceptable. Elements with large aspect ratios (>20) should be avoided in regions with large stress gradients but may be acceptable in areas of low stress gradients or if the primary result of interest is displacement.
Mesh element distribution	The density and arrangement of mesh elements within a computational domain.	The proper resolution of the mesh depends on the desired structural results. For accurate displacement values, a coarser mesh may be acceptable, whereas accurate stress and strain results require more mesh refinement. The mesh should be fine enough to minimize the change stress and strain from element to element especially in regions of stress concentrations.

Fluid Flow Mesh Metrics


Mesh Quality Indicator	Description	Best Practice
Orthogonality	A measure of how close the worst cells are to an ideal orthogonal state. Learn more about Orthogonal Quality.	The worst cells will have an orthogonal quality closer to 0, with the best cells closer to 1. The minimum orthogonal quality for all types of cells should be more than 0.01, with an average value that is significantly higher. Cells with an orthogonal quality of less than 0.1 can affect the rate of solution convergence.
Skewness	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. Learn more about Skewness.	Keep the maximum skewness for a tetrahedral mesh below 0.95, with an average value that is significantly lower. A maximum value above 0.95 may lead to convergence difficulties and may require changing the solver options. Highly skewed cells can decrease accuracy and destabilize the solution.
Aspect ratio	A measure of the stretching of an element. It is a measure of the ratio of the longest dimension to the shortest dimension of an element. Learn more about Aspect Ratio.	Avoid sudden and large changes in cell aspect ratios in areas where the flow field exhibits large changes or strong gradients. High aspect ratios are not an issue if the direction of the stretch is in the direction of the flow.
Mesh element distribution	The density and arrangement of mesh elements within a computational domain.	Ensure proper resolution of the mesh for both laminar and turbulent flows. The mesh should be fine enough to minimize the change in flow variables from cell to cell, especially in regions of large gradients. No flow passage should be represented by fewer than 5 cells.
Smoothness	The smoothness of the change in cell size during mesh generation or refinement. An abrupt change in cell size can result in solution instability and inaccuracy.	Improve the smoothness of the mesh by refining it based on the change in cell volume or the gradient of cell volume. Rapid changes in cell volume between adjacent cells translate into larger truncation errors. The application uses a default growth ratio of 1.2 for fluid meshing. It ensures that the change in size between cells is less than 20%.