A robust finite difference scheme for strongly coupled systems of singularly perturbed convection-diffusion equations

作者：Hsieh Po Wen; Yang Suh Yuh^*; You Cheng Shu

来源：Numerical Methods for Partial Differential Equations, 2018, 34(1): 121-144.

DOI：10.1002/num.22188

• boundary and interior layers
• Il'in-Allen-Southwell scheme
• magnetohydrodynamic duct flow
• singularly perturbed convection-diffusion equation
• strongly coupled system
• uniform convergence

This paper is devoted to developing an Il'in-Allen-Southwell (IAS) parameter-uniform difference scheme on uniform meshes for solving strongly coupled systems of singularly perturbed convection-diffusion equations whose solutions may display boundary and/or interior layers, where strong coupling means that the solution components in the system are coupled together mainly through their first derivatives. By decomposing the coefficient matrix of convection term into the Jordan canonical form, we first construct an IAS scheme for 1D systems and then extend the scheme to 21) systems by employing an alternating direction technique. The robustness of the developed IAS scheme is illustrated through a series of numerical examples, including the magnetohydrodynamic duct flow problem with a high Hartmann number. Numerical evidence indicates that the IAS scheme appears to be formally second-order accurate in the sense that it is second-order convergent when the perturbation parameter epsilon is not too small and when epsilon is sufficiently small, the scheme is first-order convergent in the discrete maximum norm uniformly in epsilon.

• 出版日期2018-1
• 单位中央民族大学