21.1.1 Averaging operators

Simple averaging operators are defined as follows:

   

$$\overline{\alpha_{i,k,j}}^\lambda \frac{\alpha_{i+1,k,j} + \alpha_{i,k,j}}{2}$$ = (21.1)

$$\overline{\alpha_{i,k,j}}^\phi \frac{\alpha_{i,k,j+1} + \alpha_{i,k,j}}{2}$$ = (21.2)

$$\overline{\alpha_{i,k,j}}^z \frac{\alpha_{i,k+1,j} + \alpha_{i,k,j}}{2}$$ = (21.3)

where $\alpha$ is any variable defined on grid points within T-cells or U-cells. It should be noted that the average is defined midway between the variables being averaged.