Fleischmann, Nico; Adami, Stefan; Adams, Nikolaus A.
On an inconsistency of the arithmetic-average signal speed estimate for HLL-type Riemann solvers
In this short note, we highlight the sensitivity of the HLL-type Riemann solver with respect to the choice of signal speed estimates and demonstrate a major deficiency of the arithmetic-average estimate. The investigation of two essential Riemann problems and a classical bow shock simulation reveals that inherent inconsistencies of the arithmetic-average estimate may lead to unexpected behavior and erroneous results.
Approximate Riemann solver; HLL; HLLC; Signal speed estimates; Low-dissipation scheme