Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/99125
標題: A robust finite difference scheme for strongly coupled systems of singularly perturbed convection‐diffusion equations
作者: Po-Wen Hsieh
Suh-Yuh Yang
Cheng-Shu You
謝博文
關鍵字: boundary and interior layers;Il'in‐Allen‐Southwell scheme;magnetohydrodynamic duct flow;singularly perturbed convection‐diffusion equation;strongly coupled system;uniform convergence
Project: Numerical Methods for Partial Differential EquationsVolume 34, Issue 1
摘要: 
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 2D 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 ϵ is not too small and when ϵ is sufficiently small, the scheme is first‐order convergent in the discrete maximum norm uniformly in ϵ.
URI: http://hdl.handle.net/11455/99125
DOI: 10.1002/num.22188
Appears in Collections:應用數學系所

Files in This Item:
File Description SizeFormat Existing users please Login
131.pdf6.52 MBAdobe PDFThis file is only available in the university internal network    Request a copy
Show full item record
 

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.