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  "body": "\n## Summary\n\nNumerical diffusion is the smearing of a computed solution caused by the discretisation itself.\nIt acts like an extra diffusion term that the original equation does not have.\nIt is most visible in advection problems: a sharp front that should move without change of shape spreads out more and more.\nIt is measured by the coefficient of the second-derivative term in the modified equation of the scheme.\nIt is typical of first-order schemes such as the [[upwind scheme|MTCRZC5QKT]].\nSome numerical diffusion is often needed for stability, but too much of it destroys the resolution of fine features.\n\n## Explanations\n\n### L1 human\n\nImagine a square pulse of dye carried by a steady current.\nThe exact pulse keeps its shape, but a simple computer simulation shows its edges blurring, as if the dye were also spreading by diffusion.\nThis blur is not physics; it is an error of the method, and it behaves like a diffusion whose strength shrinks with the grid size.\nFor the upwind scheme, the extra diffusion coefficient is $\\frac{a \\Delta x}{2}(1 - \\nu)$, where $a$ is the speed and $\\nu = a \\Delta t / \\Delta x$.\n",
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