Asymptotic-numerical study of supersensitivity for generalized Burgers' equations

M. Garbey, H. G. Kaper

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

This article addresses some asymptotic and numerical issues related to the solution of Burgers' equation, -εuxx+ut+uux = 0 on (-1, 1), subject to the boundary conditions u(-1) = 1+δ, u(1) = -1, and its generalization to two dimensions, -εΔu+ut+uux+uuy = 0 on (-1, 1) × (-π, π), subject to the boundary conditions u|x=1 = 1 + δ, u|x=-1 = -1, with 2π periodicity in y. The perturbation parameters δ and ε are arbitrarily small positive and independent; when they approach 0, they satisfy the asymptotic order relation δ = Os(e-a/ε) for some constant a ∈ (0, 1). The solutions of these convection-dominated viscous conservation laws exhibit a transition layer in the interior of the domain, whose position as t → ∞ is supersensitive to the boundary perturbation. Algorithms are presented for the computation of the position of the transition layer at steady state. The algorithms generalize to viscous conservation laws with a convex nonlinearity and are scalable in a parallel computing environment.

Original languageEnglish (US)
Pages (from-to)368-385
Number of pages18
JournalSIAM Journal on Scientific Computing
Volume22
Issue number1
DOIs
StatePublished - 2000

Keywords

  • Asymptotic analysis
  • Burgers' equation
  • Domain decomposition
  • Supersensitivity
  • Transition layers
  • Viscous conservation laws

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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