Abstract
For the full or isenthalpic Euler equations combined with the ideal-gas law, the flux-vector splitting presented here is, by a great margin, the simplest means to implement upwind differencing. For a polytropic gas law, with γ > 1, closed formulas have not yet been derived.
The scheme produces steady shock profiles with two interior zones. There is evidence [10] that, among implicit versions of upwind methods, those with a two-zone steady-shock representation give faster convergence to a steady solution than those with a one-zone representation.
A disadvantage in using any flux-vector splitting is that it leads to numerical diffusion of a contact discontinuity at rest. This diffusion can be removed; present research is aimed at achieving this with minimal computational effort.
Numerical solutions by first- and second-order schemes including the above split fluxes can be found in Refs. [6], [7] (one-dimensional) and [8], r91 (two-dimensional).
Research was supported under NASA Contract No. NAS1-15810 while the author was in residence at ICASE, NASA Langley Research Center, Hampton, VA 23665.
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© 1982 Springer-Verlag
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van Leer, B. (1982). Flux-vector splitting for the Euler equations. In: Krause, E. (eds) Eighth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11948-5_66
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DOI: https://doi.org/10.1007/3-540-11948-5_66
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