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Godunov flux from the local Riemann solution

Definition

For left/right states in the neighborhood of Local small-data Riemann solver near a strictly hyperbolic state, let $u (ξ)$ be its self-similar profile, $ξ = x / t$ . If the profile is continuous at $ξ = 0$ , define the Godunov flux by $G (u_{L}, u_{R}) = f (u (0))$ . If it has a jump there, let $u (0 -)$ and $u (0 +)$ be its one-sided traces and define $G (u_{L}, u_{R}) = f (u (0 -)) = f (u (0 +)) .$ These fluxes agree by Rankine–Hugoniot at speed zero, so the definition does not depend on the arbitrary point value assigned at the jump. This is a local definition on the data neighborhood where the local solver is established.

Depends on

Used by

The local Godunov flux is consistent and conservative Theorem

Dependency tree · two levels

10 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Randall J. LeVeque, Numerical Methods for Conservation Laws (standard reference, not scraped)