Figure 2.

Schematic of the staggered-grid layout of Eulerian degrees of freedom in two spatial dimensions. The pressures are approximated at cell centers, indicated by (i, j), the x₁-components of the velocity and force are approximated on the x₁-edges, ( $i-\frac{1}{2}$, j) or ( $i+\frac{1}{2}$, j), and the x₂-components of the velocity and force are approximated on the x₂-edges, (i, $j-\frac{1}{2}$) or (i, $j+\frac{1}{2}$).