A Shock-Adaptive Godunov Scheme Based on the Generalised Lagrangian Formulation

Application of the Godunov scheme to the Euler equations of gas dynamics based on the Eulerian formulation of flow smears discontinuities, sliplines especially, over several computational cells, while the accuracy in the smooth flow region is of the order O(h), where h is the cell width. Based on th...

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Bibliographic Details
Published in:Journal of computational physics 1995-12, Vol.122 (2), p.291-299
Main Authors: Lepage, C.Y., Hui, W.H.
Format: Article
Language:English
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Summary:Application of the Godunov scheme to the Euler equations of gas dynamics based on the Eulerian formulation of flow smears discontinuities, sliplines especially, over several computational cells, while the accuracy in the smooth flow region is of the order O(h), where h is the cell width. Based on the generalised Lagrangian formulation (GLF) of Hui et al., the Godunov scheme yields superior accuracy. By the use of coordinate streamlines in the GLF, the slipline—itself a streamline—is resolved crisply. Infinite shock resolution is achieved through the splitting of shock-cells. An improved entropy-conservation formulation of the governing equations is also proposed for computations in smooth flow regions. Finally, the use of the GLF substantially simplifies the programming logic resulting in a very robust, accurate, and efficient scheme.
ISSN:0021-9991
DOI:10.1006/jcph.1995.1214