Discretization in cylindrical coordinates, unit thickness for azimuth?

In summary, the conversation discusses setting up a numerical simulation for the heat equation in cylindrical coordinates with spatial variables of radius, height, and azimuth. The assumption is that there is no gradient along the azimuth direction and the problem is determining the appropriate thickness (Δø) for the element. However, it is later realized that the azimuth drops out of the differential equation, rendering the question irrelevant.
  • #1
geetar_king
26
0
I am setting up a numerical simulation from a 2D discretization of the heat equation in cylindrical coordinates.

my spatial variables are radius (r), height (z), and azimuth (ø).

The assumption is that there is no gradient along the azimuth direction (if temperature is T then dT/dø = 0)

My problem is that I do not know how to handle the thickness Δø of my element. If I were to instead have a problem with dT/dz = 0 I know that I would use Δz = 1, but for this problem do I do the same and use Δø=1 or should it be a thickness based on r?
 
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  • #2
I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
 
  • #3
I've realized the azimuth drops out of the differential equation so my question no longer applies.
 

1. What is discretization in cylindrical coordinates?

Discretization in cylindrical coordinates is the process of dividing a continuous space into a finite number of smaller elements or cells in order to numerically solve a problem. This is commonly used in scientific and engineering simulations where the geometry of the problem is in cylindrical coordinates.

2. How is discretization different in cylindrical coordinates compared to Cartesian coordinates?

Discretization in cylindrical coordinates is different from Cartesian coordinates because the geometry of the problem is represented using a different coordinate system. In cylindrical coordinates, there is an additional coordinate, the radius, which must be taken into account when discretizing the space.

3. What is the significance of using unit thickness for azimuth in cylindrical coordinates?

Unit thickness for azimuth refers to using a fixed thickness for the azimuthal direction in the discretization process. This is important because it ensures that the cells in the azimuthal direction are of equal thickness, which allows for more accurate calculations and reduces errors in the simulation.

4. How does the choice of unit thickness for azimuth affect the accuracy of the solution?

The choice of unit thickness for azimuth can greatly affect the accuracy of the solution. If the thickness is too large, it can result in a coarse discretization and lead to less accurate results. On the other hand, if the thickness is too small, it can significantly increase the computational cost without necessarily improving the accuracy.

5. Are there any limitations to using unit thickness for azimuth in cylindrical coordinates?

While unit thickness for azimuth is a commonly used approach in discretization for cylindrical coordinates, it may not be suitable for all problems. For example, if the problem has a varying thickness in the azimuthal direction, using a fixed unit thickness may not accurately represent the geometry. In such cases, alternative discretization methods may need to be used.

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