DERIVATION OF PIM SHAPE FUNCTION

DERIVATION OF PIM SHAPE FUNCTION

Figure 1 shows a domain of a flow. As shown, it contains five nodes which is uniformly distributed for simplification. The length of the domain is 5L. The size of support domain is decided as 3.5L, obtained by taking α_s=3.5. A support domain centered at a point of interest x=2.1L is graphically shown in the figure. Based on the figure, three nodes are included in the present support domain. For such an arrangement, a quadratic polynomial function is chosen, thus….

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DERIVATION OF PIM SHAPE FUNCTION