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  "body": "\n## Summary\n\nA total variation diminishing (TVD) scheme is a numerical scheme for a scalar [[conservation law|8RA7AMWSAF]] in one space dimension.\nIts discrete [[total variation|8QA5DEWNYD]] never increases from one time step to the next.\nThis copies a property of the exact entropy solutions, and it rules out the creation of new local extrema.\nSo the scheme gives no spurious oscillations near shocks.\nThe notion was introduced by Harten in 1983, and it is the design principle of the high-resolution schemes built with flux limiters.\n\n## Explanations\n\n### L1 human\n\nThe total variation of a list of numbers is the sum of the sizes of the jumps between neighbours: it measures how much the profile goes up and down.\nWiggles near a shock increase this sum.\nA TVD scheme guarantees that the sum never grows, so wiggles cannot appear.\nFor example, a step from $1$ to $0$ has total variation $1$, and a TVD scheme can smear the step but never turn it into an overshoot such as $1, 1.1, 0.4, 0$.\n",
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