At this numerical grid resolution, the solution amplitude will decay exponentially with time.

Numerical Diffusion at Fine Grid Resolution

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Question: Consider a 1d diffusion equation. The diffused profile is solved on a very coarse grid with a spatial step h for Courant=0.4 for the scheme from the Matlab activity. Consider a wavelength to grid spacing ratio, λ/h=3. What will happen at this numerical grid resolution with the solution amplitude as the time evolves?

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At this numerical grid resolution, the solution amplitude will decrease over time as the diffusion process smoothes out the initial profile. This decrease will become more pronounced as the wavelength to grid spacing ratio increases.

Answered by text-davinci-003

Feb. 22, 2023, 7:13 a.m.

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1d diffusion equation Courant=0.4 Matlab activity wavelength to grid spacing ratio λ/h=3 numerical grid resolution solution amplitude time evolves

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Published: Wednesday, February 22, 2023

Numerical Diffusion at Fine Grid Resolution

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