Geodesic
High-accuracy difference schemes for solving gasdynamic equations by the Godunov method with antidiffusion
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 5, pp. 857-873 Cet article a éte moissonné depuis la source Math-Net.Ru

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A technique is proposed for improving the accuracy of the Godunov method as applied to gasdynamic simulations in one dimension. The underlying idea is the reconstruction of fluxes arsoss cell boundaries (“large” values) by using antidiffusion corrections, which are obtained by analyzing the differential approximation of the schemes. In contrast to other approaches, the reconstructed values are not the initial data but rather large values calculated by solving the Riemann problem. The approach is efficient and yields higher accuracy difference schemes with a high resolution. 
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     title = {High-accuracy difference schemes for solving gasdynamic equations by the {Godunov} method with antidiffusion},
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N. Ya. Moiseev; I. Yu. Silant'eva. High-accuracy difference schemes for solving gasdynamic equations by the Godunov method with antidiffusion. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 5, pp. 857-873. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_5_a7/

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