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Rankine–Hugoniot jumps and Lax shocks
Definition
For a system as in Strictly hyperbolic conservation systems and characteristic families, a discontinuity with constant states and speed is a Rankine–Hugoniot jump if For a system strictly hyperbolic on , states , and , it is a strict Lax -shock if it is a Rankine–Hugoniot jump and An empty family of inequalities is omitted. A linearly-degenerate contact has equal -speeds on both sides, so it is not a strict Lax shock.
Depends on
Used by
- A Roe jump property does not imply entropy admissibility Counterexample
- Godunov flux from the local Riemann solution Definition
- A contact discontinuity with equal velocity and pressure Example
- Positive-state Burgers shock and the monotone finite-volume baseline Example
- A linearly-degenerate characteristic curve is a contact wave Lemma
- A moving jump is a weak solution exactly under Rankine–Hugoniot Lemma
- Ideal-gas acoustic wave curves have the stated pressure response Lemma
- Local shock curve by an augmented Rankine–Hugoniot equation Lemma
- Local small-data Riemann solver near a strictly hyperbolic state Theorem
- The HLL flux follows from the conservative two-wave model Theorem
Dependency tree · two levels
3 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
- Alberto Bressan, Hyperbolic Conservation Laws: An Illustrated Tutorial (standard reference, not scraped)
- Randall J. LeVeque, Numerical Methods for Conservation Laws (standard reference, not scraped)