The derivative of a given variable is used to discretize the convection and diffusion terms of the equations of motion. The gradient is computed using the Green-Gauss theorem as
where is the value of at the cell face centroid, and the summation is over all the faces enclosing the cell.
Cell-Based Derivative Evaluation
By default, the face value, , in Equation 24.2-22 is taken from the arithmetic average of the values at the neighboring cell centers, i.e.,
To use this option, select Cell-Based under Gradient Option in the Solver panel.
Node-Based Derivative Evaluation
Alternatively, can be computed by the arithmetic average of the nodal values on the face.
where is the number of nodes on the face.
The nodal values, in Equation 24.2-24, are constructed from the weighted average of the cell values surrounding the nodes, following the approach originally proposed by Holmes and Connel[ 105] and Rauch et al.[ 207]. This scheme reconstructs exact values of a linear function at a node from surrounding cell-centered values on arbitrary unstructured meshes by solving a constrained minimization problem, preserving a second-order spatial accuracy.
The node-based averaging scheme is known to be more accurate than the default cell-based scheme for unstructured meshes, most notably for triangular and tetrahedral meshes.
To use this option, select Node-Based under Gradient Option in the Solver panel.