When the sweeping ordering is considered, the spatial mesh is divided into different causality groups so that the nodes in each group are independent from the nodes in other groups. Therefore, the nodal sweeping in groups can be done in parallel [Fig. 3(a)]. For example, in Fig. 3(a), according to the flow direction, Triangles 1 to 5 form a causality group, Triangles 6 through 8 form a causality group, and Triangle 9 forms a causality group. During the sweeping transport, only the nodes within the same group are dependent. For example, the computation in the group with Triangles 1 through 5 should go sequentially from Triangle 1 to Triangle 5. Therefore, in parallelization, independent computations can be carried out simultaneously. That is the parallelization can be done on the nodes with the same color, i.e., on Triangle 1, 6, and 9 first, Triangle 2 and 7 next, then Triangle 3 and 8, then Triangle 4, and last Triangle 5.