
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 GreenGauss theorem as
where is the value of at the cell face centroid, and the summation is over all the faces enclosing the cell.
CellBased Derivative Evaluation
By default, the face value, , in Equation 24.222 is taken from the arithmetic average of the values at the neighboring cell centers, i.e.,
(24.223) 
To use this option, select CellBased under Gradient Option in the Solver panel.
NodeBased 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 24.224, 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 cellcentered values on arbitrary unstructured meshes by solving a constrained minimization problem, preserving a secondorder spatial accuracy.
The nodebased averaging scheme is known to be more accurate than the default cellbased scheme for unstructured meshes, most notably for triangular and tetrahedral meshes.
To use this option, select NodeBased under Gradient Option in the Solver panel.