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Reference.org
Godunov's scheme
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<p>In <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a> and <a href="/facts/Computational_fluid_dynamics/zuWdtNJp">computational fluid dynamics</a>, Godunov's scheme is a <a href="/facts/Conservation_law/6g1Ay2FR">conservative</a> <a href="/facts/Numerical_analysis/QT9cYa9z">numerical scheme</a>, suggested by <a href="/facts/Sergei_Godunov/IaYktIaI">Sergei Godunov</a> in 1959, for solving <a href="/facts/Partial_differential_equation/DyPsBlv7">partial differential equations</a>. One can think of this method as a conservative <a href="/facts/Finite_volume_method/6JfQMucX">finite volume method</a> which solves exact, or approximate <a href="/facts/Riemann_problem/PHv1268A">Riemann problems</a> 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. </p>