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A core Course on Modeling

A core Course on Modeling. Introduction to Modeling 0LAB0 0LBB0 0LCB0 0LDB0 c.w.a.m.v.overveld@tue.nl v.a.j.borghuis@tue.nl P.14. Structural and quantitative confidence in the lantern model. Contents Scaffolding Correct qualitative behavior V arying cat.-I quantities

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A core Course on Modeling

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  1. A core Course on Modeling Introductionto Modeling 0LAB0 0LBB0 0LCB0 0LDB0 c.w.a.m.v.overveld@tue.nl v.a.j.borghuis@tue.nl P.14

  2. Structuralandquantitativeconfidence in the lantern model. • Contents • Scaffolding • Correct qualitativebehavior • Varying cat.-I quantities • Plottinggraphsusing the analysis tab • Correct asymptoticbehavior • Correct singularities • Convergence

  3. Scaffolding. • Build extra features in the model, not neededfor the calculation of the cat.-II quantities, but toinspect the validity of the model. • Lanterns: • brightnessdistribution over the road • differencebetween max and min intensity try! try!

  4. Scaffolding. • Build extra features in the model, not neededfor the calculation of the cat.-II quantities, but toinspect the validity of the model. • Lanterns: • brightnessdistribution over the road • differencebetween max and min intensity try! try!

  5. Scaffolding. • Build extra features in the model, not neededfor the calculation of the cat.-II quantities, but toinspect the validity of the model. • Lanterns: • brightnessdistribution over the road • differencebetween max and min intensity try! try!

  6. Correct qualitativebehavior. • Varying cat.-I quantities. Examples: dL=25 m; h=5.5 m; p  2.4 kW dL=25 m; h=12 m; p  2.4 kW: higherlanterns, solessfluctuations dL=15 m; h=12 m; p  2.4 kW: lanterns closer together: verylittlefluctuations dL=15 m; h=3 m; p  1 kW: shorterlanterns, soless energy/m ( 1/15 < 2.4/25) – but more fluctuations

  7. Correct qualitativebehavior. • Plottinggraphsusing the analysis-tab. Examples: Both maxIntandminInt are proportionalto P. Sotheirdifferencealso shouldbeproportionalto p. Tallerlanternscause more blending lessfluctuations Lanternsfurther apart givelargerfluctuations, solargerdifferencebetweenmaxIntandminInt.

  8. Correct asymptoticbehavior. • If the street is long enough (100m) comparedto the height of the lanterns (2 ... 32 m) we expecttosee the boundaryeffectsseparatedfrom the regularbehavior: h=2 m h=4 m hardlyany flat region flat region? h=8 m flat region flat region flat region h=16 m h=32 m

  9. Correct singularities. • IfdL is very large comparedto h, we canignoreaddingcontributions of multiple lanterns. • The maximum intensitycanthenbecalculated as p/h2: • p = 8069.5 W • h = 9.9 m • p/h2 = 82.3 W/m2 • ACCEL gives 84 W/m2. • OK because of • contribution of • otherlanterns.

  10. Correct convergence. • Suppose we increase performance bytakingfewerlanternsinto account. • allowsto set # lanternsto taken into account. Thisversion of the model

  11. Correct convergence. • Suppose we increase performance bytakingfewerlanternsinto account. • How few lanterns is enoughforreliableresult depends on regime dL=25 m; nr. neighbours = 0 dL=25 m; nr. neighbours = 2 dL=25 m; nr. neighbours = 3  no noticeabledifference, soleftand right 2 lanterns is enough.

  12. Correct convergence. • Suppose we increase performance bytakingfewerlanternsinto account. • How few lanterns is enoughforreliableresult depends on regime dL=1 m; nr. neighbours = 0 dL=1 m; nr. neighbours = 5 dL=1 m; nr. neighbours = 10 dL=1 m; nr. neighbours = 20: graphstill looks not smooth, we presumablyneed more lanterns.

  13. Summary: • Scaffoldingmaybeusefulto help ascertain the convincingness of the model; • Qualitativebehavor: think of configurationsthatcaneasilybeunderstood; • Asymptoticbehavior: can we separate ‘boundaryeffects’ thatcanbe ‘reasonedaway’; • Singularbehavior: are there cases where we can do the math even without a computer; • Convergence: do we take enough terms, steps, ... .

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