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High-order accurate difference schemes for solving gasdynamic equations by the Godunov method with antidiffusion

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Abstract

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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  1. All-Russia Research Institute of Technical Physics, Russian Federal Nuclear Center, Box 245, Snezhinsk, 456770, Russia

    N. Ya. Moiseev & I. Yu. Silant’eva

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  1. N. Ya. Moiseev
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  2. I. Yu. Silant’eva
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Correspondence to N. Ya. Moiseev.

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Original Russian Text © N.Ya. Moiseev, I.Yu. Silant’eva, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 5, pp. 857–873.

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Moiseev, N.Y., Silant’eva, I.Y. High-order accurate difference schemes for solving gasdynamic equations by the Godunov method with antidiffusion. Comput. Math. and Math. Phys. 49, 827–841 (2009). https://doi.org/10.1134/S096554250905008X

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