Eularian numerical methods introduce a numerical error that can lead to energy dissipation. The exact form of this dissipation can be very complex and depends on the spatial and temporal resolution. For the simple linear wave we perform numerical experiments and determine the numerical viscosity and diffusion coefficient.

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.