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Spectral Methods in CFD

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Electronics Spectral methods in CFD Ans 1) Ans 4) Ans 5) 5)a) Program in file ‘task5.m ’. 5)c) Plot of FFT : 0 10 20 30 40 50 60 70 80 90 100 0 100 200 300 Magnitude 0 10 20 30 40 50 60 70 80 90 100 -200 -100 0 100 200 Phase Plot of y v/s t(IFFT): 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 5)d) For N=8, 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3 -2 -1 0 1 2 3x 10 -16 For N=128, 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3 -2 -1 0 1 2 3x 10 -16 5)e) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3 -2 -1 0 1 2 3x 10 -16 Ans 6) Matlab Results : m1 = Columns 1 through 5 65.3336 19.4182 9.4182 6.2467 4.6791 Columns 6 through 10 3.7433 3.1213 2.6781 2.3464 2.0890 Columns 11 through 15 1.8835 1.7158 1.5764 1.4588 1.3582 Columns 16 through 20 1.2714 1.1956 1.1291 1.0701 1.0176 Columns 21 through 25 0.9706 0.9282 0.8899 0.8552 0.8235 Columns 26 through 30 0.7946 0.7680 0.7436 0.7212 0.7004 Columns 31 through 35 0.6813 0.6635 0.6470 0.6317 0.6174 Columns 36 through 40 0.6042 0.5918 0.5803 0.5696 0.5596 Columns 41 through 45 0.5502 0.5415 0.5334 0.5258 0.5187 Columns 46 through 50 0.5122 0.5061 0.5004 0.4952 0.4903 Columns 51 through 55 0.4859 0.4818 0.4781 0.4747 0.4716 Columns 56 through 60 0.4689 0.4665 0.4643 0.4625 0.4610 Columns 61 through 65 0.4597 0.4587 0.4580 0.4576 0.4575 Columns 66 through 70 0.4576 0.4580 0.4587 0.4597 0.4610 Columns 71 through 75 0.4625 0.4643 0.4665 0.4689 0.4716 Columns 76 through 80 0.4747 0.4781 0.4818 0.4859 0.4903 Columns 81 through 85 0.4952 0.5004 0.5061 0.5122 0.5187 Columns 86 through 90 0.5258 0.5334 0.5415 0.5502 0.5596 Columns 91 through 95 0.5696 0.5803 0.5918 0.6042 0.6174 Columns 96 through 100 0.6317 0.6470 0.6635 0.6813 0.7004 Columns 101 through 105 0.7212 0.7436 0.7680 0.7946 0.8235 Columns 106 through 110 0.8552 0.8899 0.9282 0.9706 1.0176 Columns 111 through 115 1.0701 1.1291 1.1956 1.2714 1.3582 Columns 116 through 120 1.4588 1.5764 1.7158 1.8835 2.0890 Columns 121 through 125 2.3464 2.6781 3.1213 3.7433 4.6791 Columns 126 through 128 6.2467 9.4182 19.4182 >> Ans 7) 0 200 400 600 800 1000 1200 0 0.2 0.4 0.6 0.8 FFT versus DFT N Time 0 200 400 600 800 1000 1200 0 0.5 1x 10 -3 N Time

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