Relaxation method for unsteady convection-diffusion equations

Wensheng Shen, Changjiang Zhang, Jun Zhang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We propose and implement a relaxation method for solving unsteady linear and nonlinear convection-diffusion equations with continuous or discontinuity-like initial conditions. The method transforms a convection-diffusion equation into a relaxation system, which contains a stiff source term. The resulting relaxation system is then solved by a third-order accurate implicitexplicit (IMEX) RungeKutta method in time and a fifth-order finite difference WENO scheme in space. Numerical results show that the method can be used to effectively solve convection-diffusion equations with both smooth structures and discontinuities.

Original languageEnglish
Pages (from-to)908-920
Number of pages13
JournalComputers and Mathematics with Applications
Issue number4
StatePublished - Feb 2011


  • Convection-diffusion equation
  • Hyperbolic conservation laws
  • Implicit-explicit RungeKutta
  • Relaxation method
  • WENO scheme

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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