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Unformatted text preview: 1 Atms 502 Numerical Fluid Dynamics Thu., Oct. 12, 2006 10/18/06 Atms 502  Fal 2006  Jewett 2 Test case Cone • Upstream method • Refinement: 3x True Feedback No feedback 10/18/06 Atms 502  Fal 2006  Jewett 3 True Feedback No feedback Test case Square / top hat • LaxWendroff • Refinement: 3x Looks a bit ugly Error 50% less than upstream Note nest only on right half of square 10/18/06 Atms 502  Fal 2006  Jewett 4 Update frequency Below: error scores vs update frequency Frequent updates  lower error Less frequent updates  increasing error Hmm… 2 10/18/06 Atms 502  Fal 2006  Jewett 5 Oscillations • How long for features to move 1 ∆ x ??? s=vt ; time = distance/speed; t=s/v Total time to go distance ∆ x = ∆ x/c # time steps to go ∆ x = 1/ ν (why?) • So, every 5 time steps … The cone peak moves one grid distance. What does this say about our “true” solution? 10/18/06 Atms 502  Fal 2006  Jewett 6 Oscillations • Every 5 time steps the (exact) solution moves one grid length. • At right: 2 periods in 10 steps (1) What are these oscillations? • Projecting an exact solution on a finite grid results in errors  in the “true” solution !! n N+2 N+4 N+6 N+8 N+10 10/18/06 Atms 502  Fal 2006  Jewett 7 Question 3: update frequency Below: error scores vs update frequency Program 2b  cone  LaxWendroff Frequent updates  lower error Less frequent updates  increasing error total error after 200 steps  NX=70 case 10/18/06 Atms 502  Fal 2006  Jewett 8 Question 3: update frequency • In 60 steps the middle of the cone is on the right nest domain edge. • In 30 steps , when the error starts rapidly rising, the right edge of the cone (and of trunc. error) hits the nest edge. • In 20 steps , the nest border is still ahead of the cone’s leading edge. 60 steps 30 steps 20 2 10/18/06 Atms 502  Fal 2006  Jewett 5 Oscillations • How long for features to move 1 ∆ x ???...
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 Spring '09
 JEWETT
 ATMs, Jewett

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