The Riemann problem in the quasi-one-dimensional approximation
Михаил Владимирович Абакумов, Yu. P. Popov, П. В. Родионов · Computational Mathematics and Mathematical Physics · 2015
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.