Description

When the current CAE dimension is set to 2D, this diagnostic function is available for structured domains only. On the other hand, when the current CAE dimension is set to 3D, the function is available for structured and prism blocks.

The Jacobian is computed for each cell in the following way:

• Quadrilateral: The Jacobian is computed calculating the scalar triple product at each corner of a given cell using points from that cell and a normal vector computed from the bounding box of the grid system. The final Jacobian for the cell is the average of all the corner Jacobians.
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Caution: Since the normal to the cells is obtained from the bounding box of the grid system, the Jacobian computation is only accurate for the particular case of flat structured domains aligned with the positive direction of one of the main axes.

• Hexahedron: The Jacobian is computed by calculating the scalar triple product at each corner of a given cell using only other grid points from that cell and then calculating the average value of all the corner Jacobians.
• Prism: The Jacobian computation consists of computing the triple product at each cell corner using only other grid points from that cell and then computing the average value of all the corner Jacobians. The average value is then pre-multiplied by a coefficient of 0.5.
The options in the Options frame allows you to quickly decide which cells to visualize according to their Jacobian value (Positive, Positive Skew, Zero, Negative Skew, and Negative). You can also see the number and percentage of cells for each Jacobian Category.

Note: In general, we do not recommend toggling on all the Jacobian categories at once (shown above). Doing so, would cause all the cells in the domain or block to be rendered at the same time making it very cumbersome to distinguish bad cells from good cells. Furthermore, simultaneously displaying all cells in a large mesh can be computationally expensive.

Positive, Positive Skew, Zero, Negative Skew, and Negative Jacobian cells can be individually rendered in the Display window by toggling each type in the Options frame (shown above). The number and total percent of cells for each Jacobian Category can be seen in the Count and Percent columns. These cell Jacobians are classified according to the table shown below:

Jacobian Classification Average Value of Corner Jacobians Sign of Corner Jacobians
Positive Positive All Positive
Positive Skew Positive Mixed Signs
Zero Zero
Negative Skew Negative Mixed Signs
Negative Negative All Negative

Tip: If you note that your domain or block has all negative Jacobians, this is a sure sign that the computational orientation of your block is left-handed. Use the Edit, Orient command to correct the orientation and ensure that all of your domains and blocks are right-handed before exporting your mesh.