Lec: FD3
9 important questions on Lec: FD3
What would be good arguments to pick a certain L? What happens if you have a very small vs very wide plume
Gigantic wide plume, meaning gradients at sides would be really weak, advection is equally important, but diffusion is much smaller
Therefore, size/width of plume is important and L is taken as the width.
All information about our problem is captured in one dimensionless nr (D/uL)
Name the amazing quality of dimensionless nrs
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Why are dimensionless nrs handy:
- Compare processes
- Build scale models: as long as Peclet nr is the same, the size of u/L/D do not matter. Thus you don't have to build a lab with a 100 m wide river in it. If we then reduce L by factor 20, we need to increase u or decrease D accordingly in order to maintain Pe nr.
When is the explicit (Euler forward) time integration scheme stable? Give the formulas and Peclet nrs
u * dt/dx <=1
If diffusion dominates: 2Ddt/(dx)2 <=1
What happens if we do not keep to the stability rules as defined by CFL? Also make a drawing
What is the relation between the Peclet nr and stability analysis?
How do you make an equation dimensionless?
- Factor out all the typical magnitudes so everything has the same magnitudes/units/dimensions
- Make the formula dimensionless by multiplying with L/uS
At which Peclet nrs does diffusion/advection dominate and when are they equally influential?
Pe > 1 Diffusion is dominant
Pe < 1 Advection is dominant
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