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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 8, Pages 1455–1469 (Mi zvmmf10447)  

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

M. S. Elaevaa, M. Yu. Zhukovbc, E. V. Shiryaevab

a 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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 213.01-11/2014-1


DOI: https://doi.org/10.7868/S0044466916080056

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

Bibliographic databases:

UDC: 516.634
Received: 24.10.2014

Citation: M. S. Elaeva, M. Yu. Zhukov, E. V. Shiryaeva, “Interaction of weak discontinuities and the hodograph method as applied to electric field fractionation of a two-component mixture”, Zh. Vychisl. Mat. Mat. Fiz., 56:8 (2016), 1455–1469; Comput. Math. Math. Phys., 56:8 (2016), 1440–1453

Citation in format AMSBIB
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\paper Interaction of weak discontinuities and the hodograph method as applied to electric field fractionation of a two-component mixture
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\yr 2016
\vol 56
\issue 8
\pages 1455--1469
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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