This article is cited in 3 papers

Interaction of weak discontinuities and the hodograph method as applied to electric field fractionation of a two-component mixture

M. S. Elaeva^a, M. Yu. Zhukov^bc, E. V. Shiryaeva<sup>b

a</sup> Financial University under the Government of the Russian Federation, Moscow, Russia
^b Institute of Mathematics, Mechanics, and Computer Science, Southern Federal University, Rostov-on-Don, Russia
^c South Mathematical Institute, Vladikavkaz Research Center, Russian Academy of Sciences, Vladikavkaz, Russia

Abstract: The hodograph method is used to construct a solution describing the interaction of weak discontinuities (rarefaction waves) for the problem of mass transfer by an electric field (zonal electrophoresis). Mathematically, the problem is reduced to the study of a system of two first-order quasilinear hyperbolic partial differential equations with data on characteristics (Goursat problem). The solution is constructed analytically in the form of implicit relations. An efficient numerical algorithm is described that reduces the system of quasilinear partial differential equations to ordinary differential equations. For the zonal electrophoresis equations, the Riemann problem with initial discontinuities specified at two different spatial points is completely solved.

Key words: quasilinear hyperbolic equations, hodograph method, zonal electrophoresis, efficient numerical algorithm, Riemann problem.

UDC: 516.634

Received: 24.10.2014

DOI: 10.7868/S0044466916080056

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:8, 1440–1453

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