Geodesic
The Riemann problem in the quasi-one-dimensional approximation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 8, pp. 1391-1404 Cet article a éte moissonné depuis la source Math-Net.Ru

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The classical one-dimensional Riemann problem is generalized to the quasi-one-dimensional case. A plane slotted channel with a discontinuous cross section is considered. The resulting exact self-similar solution is compared with numerical results obtained for a system of quasi-onedimensional and two-dimensional equations. It is shown that they are in good qualitative agreement and, for certain parameters, also agree well quantitatively. 
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M. V. Abakumov; Yu. P. Popov; P. V. Rodionov. The Riemann problem in the quasi-one-dimensional approximation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 8, pp. 1391-1404. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a10/

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