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  "body": "\n## Summary\n\nThe finite volume method discretizes a [[conservation law|8RA7AMWSAF]] by dividing the domain into small control volumes and keeping the average of the solution in each.\nThe [[divergence theorem|0JX86PSSA9]] turns the change of each average into a sum of fluxes through the faces of the volume.\nEach flux is computed once and used by the two volumes that share the face, so the scheme conserves the total amount exactly.\nThis makes it the standard method for shocks in gas dynamics and for transport in fluid mechanics; [[Godunov's scheme|43HZJ7DRT0]] is a classical example.\nSee the [[definition|CAB1ARHH31]].\n\n## Explanations\n\n### L1 human\n\nSplit a pipe into short sections and keep track of how much water each section holds.\nThe amount in a section changes only by what flows in or out through its two ends.\nWhatever leaves one section through a wall enters the neighbour through the same wall, so no water is created or lost.\nA finite volume method computes these flows from the amounts in the neighbouring sections and updates the amounts step by step.\n",
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