A core Course on Modeling

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A core Course on Modeling. Introduction to Modeling 0LAB0 0LBB0 0LCB0 0LDB0 [email protected]e.nl [email protected] 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

Introductionto Modeling

0LAB0 0LBB0 0LCB0 0LDB0

[email protected]

[email protected]

P.14

Structuralandquantitativeconfidence in the lantern model.

• Contents
• Scaffolding
• Correct qualitativebehavior
• Varying cat.-I quantities
• Plottinggraphsusing the analysis tab
• Correct asymptoticbehavior
• Correct singularities
• Convergence

Scaffolding.

• Build extra features in the model, not neededfor the calculation of the cat.-II quantities, but toinspect the validity of the model.
• Lanterns:
• differencebetween max and min intensity

try!

try!

Scaffolding.

• Build extra features in the model, not neededfor the calculation of the cat.-II quantities, but toinspect the validity of the model.
• Lanterns:
• differencebetween max and min intensity

try!

try!

Scaffolding.

• Build extra features in the model, not neededfor the calculation of the cat.-II quantities, but toinspect the validity of the model.
• Lanterns:
• differencebetween max and min intensity

try!

try!

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

Correct qualitativebehavior.

• Plottinggraphsusing the analysis-tab. Examples:

Both maxIntandminInt are proportionalto P.

Sotheirdifferencealso

shouldbeproportionalto p.

Tallerlanternscause more blending lessfluctuations

Lanternsfurther apart givelargerfluctuations, solargerdifferencebetweenmaxIntandminInt.

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

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.

Correct convergence.

• Suppose we increase performance bytakingfewerlanternsinto account.
• allowsto set # lanternsto taken into account.

Thisversion of the model

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.

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.

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, ... .