Osher’s approximate Riemann solver is one of the earliest in the literature. The bases of the approach were communicated in the papers by Engquist and Osher in 1981 [185] and Osher and Solomon the following year [372]. Applications to the Euler equations were published later in a paper by Osher and Chakravarthy [370]. Since then the scheme has gained increasing popularity, particularly within the CFD community concerned with Steady Aerodynamics; see for example the works of Spekreijse [458], [459], Hemker and Spekreijse [247], Koren and Spekreijse [290], Qin et. al. [393], [394], [395], [396], [390], [391], [392]. One of the attractions of Osher’s scheme is the smoothness of the numerical flux; the scheme has also been proved to be entropy satisfying and in practical computations it is seen to handle sonic flow well. A distinguishing feature of the Osher scheme is its performance near slowly–moving shock waves; see Roberts [406], Billett and Toro [60] and Arora and Roe [19].
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Toro, E.F. (2009). The Riemann Solver of Osher. In: Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b79761_12
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DOI: https://doi.org/10.1007/b79761_12
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