The document discusses numerical wave damping in the Pencil Code, focusing on the concept of numerical diffusion. It highlights the relationship between numerical diffusion and grid resolution through analytical and experimental approaches, concluding that numerical viscosity and diffusion can be analytically calculated. The findings emphasize a power law of -3 related to wave damping in Alfven wave simulations.

1. Numerical Wave Damping
in the Pencil Code
Simon Candelaresi, Eilidh Ryan
101
102
n
10−8
10−7
10−6
10−5
10−4
10−3
λ
∗
n−3

2. What is Numerical Diffusion?
2
Everyone is talking about it,
but no one knows what is really is.

3. Analytical Approach
3

4. Local Truncation Error
4
discretized exact
This is solved exactly.
(see: Naveen)

5. Numerical Diffusion
5
How does the numerical diffusion
depend on the grid resolution?
numerical diffusion:

6. Alfvén Wave Damping
6
wave propagation:
wave damping
damping parameter:
numerical damping:
Perform linear Alfven wave simulations
and measure the numerical damping.

7. Inviscid Navier-Stokes 3d
7
101
102
n
10−8
10−7
10−6
10−5
10−4
10−3
λ
∗
n−3

8. Numerical Experiments
8

9. Wave Damping
9

10. Conclusions
simon.candelaresi@gmail.com
●
Numerical viscosity and diffusion can be calculated analytically.
●
Find numerical diffusion in numerical experiments.
●
Power law of -3.