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

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• 作者：M. S. Elaeva ; M. Yu. Zhukov ; E. V. Shiryaeva
• 关键词：quasilinear hyperbolic equations ; hodograph method ; zonal electrophoresis ; efficient numerical algorithm ; Riemann problem
• 刊名：Computational Mathematics and Mathematical Physics
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：56
• 期：8
• 页码：1440-1453
• 全文大小：747 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1555-6662
• 卷排序：56

文摘

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.