A practical, general‐purpose, two‐state HLL Riemann solver for hyperbolic conservation laws

We construct a general-purpose Riemann solver for hyperbolic conservation laws that does not involve extensive characteristic analysis of governing equations but can nevertheless sharply resolve discontinuities. To achieve this goal, we revisit the class of two-state HLL schemes and show that inexpensive, accurate solvers within this class can be designed using only geometric interpretations of the Rankine-Hugoniot conditions. We argue that the small cost and nearly uniform algorithmic complexity of resulting methods make them attractive for quick computations of practical, especially very complex, problems for which more accurate solvers are either not available or their development cost is not justified