An analysis of the linear advection-diffusion equation using mesh-free and mesh-dependent methods

Boztosun I., Charafi A.

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, cilt.26, sa.10, ss.889-895, 2002 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 10
  • Basım Tarihi: 2002
  • Doi Numarası: 10.1016/s0955-7997(02)00053-x
  • Dergi Adı: ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.889-895
  • Anahtar Kelimeler: meshless methods, radial basis functions, thin plate spline, finite difference method, boundary element method, dual reciprocity method, partial differential equation, linear advection-diffusion problem, INTERPOLATION
  • Akdeniz Üniversitesi Adresli: Hayır

Özet

The numerical solution of advection-diffusion equations has been a long standing problem and many numerical methods that attempt to find stable and accurate solutions have to resort to artificial methods to stabilize the,solution. In this paper, we present a meshless method based on thin plate radial basis functions (RBF). The efficiency of the method in terms of computational processing time, accuracy and stability is discussed. The results are compared with the findings from the dual reciprocity/boundary element and finite difference methods as well as the analytical solution. Our analysis shows that the RBFs method, with its simple implementation, generates excellent results and speeds up the computational processing time, independent of the shape of the domain and irrespective of the dimension of the problem. (C) 2002 Elsevier Science Ltd. All rights reserved.