In numerical analysis and computational fluid dynamics, Godunov's scheme is a conservative numerical scheme, suggested by S. K. Godunov in 1959, for solving partial differential equations. One can think of this method as a conservative Finite-volume_method which solves exact, or approximate Riemann_problems at each inter-cell boundary. In its basic form, Godunov's method is first order accurate in both space, and time, yet can be used as a base scheme for developing higher-order methods.
Read more about Godunov's Scheme: Basic Scheme, Linear Problem, Three Step Algorithm
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“Your scheme must be the framework of the universe; all other schemes will soon be ruins.”
—Henry David Thoreau (1817–1862)