Relaxation method for unsteady convection-diffusion equations

Authors:
Wensheng Shen;Changjiang Zhang;Jun Zhang
Affiliations:
Department of Computational Science, SUNY Brockport, Brockport, NY 14420, USA;Department of Computer Science, University of Kentucky, Lexington, KY 40506-0046, USA;Department of Computer Science, University of Kentucky, Lexington, KY 40506-0046, USA
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

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 implicit-explicit (IMEX) Runge-Kutta 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.