p1184

# p1184 - GCI = 1 25 | 6 h | 2 1 78 − 1 = 0 51 | 6 h | 124...

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11.84. CHAPTER 11, PROBLEM 84 123 11.84 Chapter 11, Problem 84 Figure 11.41 shows the opening screen for Program POTFLOW DATA . Figure 11.41: Opening screen of Program POTFLOW DATA . Executing Program POTFLOW and examining the program output confirms that for 101, 201 and 401 grid points the velocity at x =0 and y =2 a is u (0 , 2 a ) = 1.236173, 1.231433 and 1.232812, respectively. 11.84(a): Since the number of finite-difference cells is 100, 200 and 400 for the three computations, the grid-refinement ratio is r =2 . So, identifying φ = u (0 , 2 a ) ,wehave φ r 2 h =1 . 236173 , φ rh =1 . 231433 , φ h =1 . 232812 The order of accuracy is p = f n | ( φ rh φ r 2 h ) / ( φ rh φ h ) | f nr = f n | (1 . 231433 1 . 236173) / (1 . 231433 1 . 232812) | f n 2 =1 . 78 11.84(b): Using the fact that the order of accuracy is 1.78, the grid convergence index is

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Unformatted text preview: GCI = 1 . 25 | 6 h | 2 1 . 78 − 1 = 0 . 51 | 6 h | 124 CHAPTER 11. POTENTIAL FLOW For the 401-point grid, the GCI expressed in percent is thus GCI = 51 e e e e e φ h − φ rh φ h e e e e e = 0 . 06% 11.84(c): Based on Richardson extrapolation, the error for the 401-point grid is E h = 1 3 ( φ h − φ rh ) = 1 3 (1 . 232812 − 1 . 231433) = 0 . 000460 Hence, as a percentage, there follows 100 E h φ h = 0 . 04% The error estimates are similar because the numerical solution is nearly second-order accurate at this point in the flowfield....
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p1184 - GCI = 1 25 | 6 h | 2 1 78 − 1 = 0 51 | 6 h | 124...

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