Effects of small viscosity and far field boundary conditions for hyperbolic systems

Huey Er Lin, Jian Guo Liu, Wen Qing Xu

Research output: Contribution to journalArticle

Abstract

In this paper we study the effects of small viscosity term and the far-field boundary conditions for systems of convection-diffusion equations in the zero viscosity limit. The far-field boundary conditions are classified and the corresponding solution structures are analyzed. It is confirmed that the Neumann type of far-field boundary condition is preferred. On the other hand, we also identify a class of improperly coupled boundary conditions which lead to catastrophic reflection waves dominating the inlet in the zero viscosity limit. The analysis is performed on the linearized convection-diffusion model which well describes the behavior at the far field for many physical and engineering systems such as fluid dynamical equations and electro-magnetic equations. The results obtained here should provide some theoretical guidance for designing effective far field boundary conditions.

Original languageEnglish
Pages (from-to)267-290
Number of pages24
JournalCommunications on Pure and Applied Analysis
Volume3
Issue number2
Publication statusPublished - 2004 Jun 1

Keywords

  • Boundary layer
  • Convection-diffusion equations
  • Far field boundary condition
  • Hyperbolic equations
  • Zero viscosity limit

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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