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  "body": "\n## Summary\n\nGodunov's scheme is a finite volume method for hyperbolic systems of [[conservation laws|8RA7AMWSAF]].\nIt stores cell averages, solves the [[Riemann problem|GJWKX22VVE]] exactly at each cell interface, and averages the result again.\nIt is conservative, first-order accurate, and captures shocks without spurious oscillations.\nIts idea of using Riemann solvers is the basis of many modern high-resolution schemes.\nSee the [[definition|FBJ4JCP5SR]].\n\n## Explanations\n\n### L1 human\n\nDivide the line into cells and keep only the average of the solution in each cell.\nAt each cell boundary two constant values meet, and the exact evolution of such a jump is known.\nLet these jumps evolve for one short time step, then compute the new average in each cell.\nFor the equation $u_t + a u_x = 0$ with $a \u003e 0$, this gives the upwind scheme, which takes information from the left neighbour.\n",
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