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First-order finite-volume update using supplied HLL speeds

Definition

Let $F : A \to R^{m}$ be the flux of the one-dimensional system in Strictly hyperbolic conservation systems and characteristic families. On a periodic uniform mesh of $N \geq 2$ cells of width $h > 0$ , let $U_{i} \in A$ be the cell means and put $ν = Δ t / h \geq 0$ . At each face $(i + 1 / 2)$ choose explicit speeds $S_{L, i + 1 / 2} < 0 < S_{R, i + 1 / 2}$ and evaluate the middle branch of the HLL flux HLL two-wave approximate flux on $(U_{i}, U_{i + 1})$ . The first-order HLL update is $U_{i}^{+} = U_{i} - ν ({\hat{F}}_{i + 1 / 2} - {\hat{F}}_{i - 1 / 2}), i (m o d N) .$ The speeds are supplied data. Neither this definition nor later algebraic results assert that they enclose the wave speeds of an exact nonlinear Riemann solution.

Depends on

Used by

Dependency tree · two levels

4 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

D. I. Ketcheson, R. J. LeVeque, and M. J. del Razo, Riemann Problems and Jupyter Solutions (standard reference, not scraped)
D. I. Ketcheson, R. J. LeVeque, and M. J. del Razo, Riemann Problems and Jupyter Solutions (standard reference, not scraped)