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Variable arrangement

After we have settled the grids of the simulation, it is time for us to put system variables in the grid system. The simplest and most natural way to do it is to put all variables on each of the nodes. Besides this, there are also many other ways for us to put variables. Figure 3 shows the common methods to set variables in a two dimensional grid system. According to different computational schemes which we will discuss below, different variables may choose different arrangement in the grid system to achieve the best numerical result.

Figure 3: Different types of arrangement of variable in grid system.