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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.

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Numerical Wave Damping in the Pencil Code

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Numerical Wave Damping in the Pencil Code