Abstract
This paper reviews some of the recent developments in upstream difference schemes through a unified representation, in order to enable comparison between the various schemes. Special attention is given to the Godunov-type schemes that result from using an approximate solution of the Riemann problem. For schemes based on flux splitting, the approximate Riemann solution can be interpreted as a solution of the collisionless Boltzmann equation.
Received by the editors March 29, 1982, and in revised form May 5, 1982. This research was sponsored by the National Aeronautics and Space Administration under contract NAS1-15810 while the first and third authors were in residence at ICASE, NASA Langley Research Center, Hampton, Virginia.
The work of this author was supported in part by the National Aeronautics and Space Administration under contract NCA2-OR525-001 at NASA Ames Research Center, Moffett Field, California, and by the U.S. Department of Energy under contract DE-AC02-76ER03077.
The work of this author was supported in part by the U.S. Department of Energy under contract DE-AC02-76ER03077.
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Harten, A., Lax, P.D., van Leer, B. (1997). On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws. In: Hussaini, M.Y., van Leer, B., Van Rosendale, J. (eds) Upwind and High-Resolution Schemes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60543-7_4
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DOI: https://doi.org/10.1007/978-3-642-60543-7_4
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