# Model Workshop

• There is nothing without reason. (Leibniz)
• One mathematical model says more than thousand words. (Dylan)
• Nature’s great book is written in mathematics. (Galileo)
• With four parameters I can fit an elephant, and with five I can make him     wiggle his trunk. (von Neumann)

Model Workshop opens to a problem based approach to learning, where tools and methods are collected as they are needed to handle specific cases of significance, rather than teaching  generalities first. For the young mind particularities can be more captivating than generalities and generalisation can come at a later stage by discovering similarities of particularities.

Model Workshop invites to an answer – question form of learning, where the student after having explored a simulation gets incentive to answer the questions: How is it done? What elements are included? What does the code express? How can I expand the simulation? It is like watching a magician showing a trick and then seeking to find out how it was done and how to repeat/modify it. This gives the student an active role in an open search for information on the web, to be compared with a the passive role in the traditional form of question – answer directed by teacher and book.

Explanation is thus kept sparse to give incentive to explore models by trial and error computation with inspiration from reality and web in learning-by-computing. Watch out: Can be Addictive!

You can enter Model Workshop with a minimal preparation of Basic Mathematics 16-29 assuming basic knowledge of decimal numbers and return to binary numbers later.

Check code to find explanation of model if not given directly. The models are carefully selected to be as simple as possible yet open windows to a complex world of many phenomena. Be confident that in retrospect you will see the scientific wealth buried in these (seemingly simple) models.

Add to Game Workshop using the physics of Model Workshop.

Run code by clicking arrow on upper left corner. Modify code, test and have fun!

(Sometimes restart is needed to activate mouse interaction).

List of topics:

1. Start: Space-Position Time-Motion
2. Population Dynamics
3. Mass-Spring Systems
4. Electrical Circuits
5. Resonance
6. Elastic Mechanics
7. Convection-Diffusion
8. Reaction-Diffusion
9. Fluid Mechanics
10. Coupled Fluid-Elastic Mechanics
11. Waves in Elastic Bodies
12. Waves in Fluids
13. Heat Conduction
14. ElectroMagnetics
15. Chemical Reactions
16. Chaos
17. Fractals and Representation
18. Parameter Identification
19. Music
20. Image
21. Cosmology
22. Atom Physics

### 9. Fluid Mechanics

1. Inspiration:The Secret of Flight, Incorrect Theories of Flight, D’Alembert’s Paradox, Potential Flow
2. Potential Flow around Square (1st type) (variant) (skew variant) (read me)
3. Potential Flow around Disc (2nd type) (with pressure) (around square)
4. Potential Flow around Disc as Real Part of z + 1/z (two discs)
5. Potential Flow around Elliptical Wing (2nd type)
6. Cauchy-Riemann Equations
7. Analytic Functions
8. Archimedes Principle
9. Meteorology: Wind-Pressure Map (compare with real global wind map)
10. Meteorology: Air Pollution
11. Titanic Ship Stability (catastrophical)
12. Compressible Flow: Burgers equation (zero pressure) 2d
13. Compressible Flow: Small velocity + viscosity (Stokes equations)
14. Incompressible Flow: Lid Driven Cavity 2d (variant) (see Computational Turbulent Incompressible Flow)
15. Incompressible Flow: Lid Driven Cavity 3d  (HD version)
16. Incompressible Flow: Variable Density Lid Driven Cavity 2d
17. Incompressible Flow: Ventilation
18. Incompressible Flow: Bluff Body No-Slip (Slip) (HD version)
19. Incompressible Flow Bluff Body Slip: Drag and Lift
20. Incompressible Box/Flat Plate Slip Density Check
21. Incompressible Flow: Periodic 2d
22. Incompressible Flow: Atmospheric Inversion
23. Compressible Flow: Euler equations for Ideal Gas (see Computational Thermodynamics)
24. Compressible Flow: Riemann Problem
25. Compressible Flow: Periodic boundary conditions + forcing
26. Compressible Flow: 3d
27. Compressible Flow: Bluff Body (HD-version)
28. Compressible Flow: Low Mach
29. Compressible Flow: Refrigerator1: Cooling by Expansion (see book)
30. Compressible Flow: Refrigerator2: Compression
31. Compressible Flow: Decay from Initial Random Momentum
32. Compressible vs Incompressible Flow
33. Compressible vs Incompressible Flow: Ventilation
34. Compressible vs Incompressible Flow: Decay from Random
35. Unified Compressible-Incompressible Bluff Body Flow (compare with std pressure equation for incompressible flow with slip and passive density check and with force)
36. Compressible Bluff Body Slip (Skew)
37. Unified Compressible-Incompressible Flow II: Compressible (HD and Skew) vs Incompressible (HD)
38. Flat Plate Wing (slip): Incompressible 1:6 (HD 1:10).
39. Compressible Flow: Joule’s Experiment  (HD) (see Computational Thermodynamics p. 29)

### 12. Waves in Fluids

1. Traffic Model as Conservation Law with Shock Formation (see also this)
2. Breaking Wave Model (1d Burgers equation
3. Shallow Water: Linearized Small Deviation (with periodic boundary cond)
5. Shallow Water: Coriolis Force + Periodic
6. Shallow Water: Ship Waves (HD version)
7. Tsunamis and Solitons (compare with this)

### 19. Music

1. Music: Pythagorean Scale (Compare sinus wave with square wave) Combine with Frequency Sound Generator
2. Play Tone
3. Play Something

### 21. Cosmology

1. Gravitational Collapse into Black Hole (scary)
2. Cosmology: Big Bang (compare with 14 and this post)
3. Cosmology: Spiral Galaxy
4. Cosmology:  3d Expansion – Contraction
5. Dark Energy: Repellation of galaxies with mass of different sign (compare with Attraction of galaxies with mass of same sign)
6. Unphysical Gravitational Collapse
7. Physical Gravitational Collapse  (see this post)