Application of the generalized finite difference method to solve the advection–diffusion equation

• Published in: Journal of computational and applied mathematics Vol. 235; no. 7; pp. 1849 - 1855
• Main Authors: Prieto, Francisco Ureña, Benito Muñoz, Juan José, Corvinos, Luis Gavete
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Kidlington Elsevier B.V 01.02.2011; Elsevier
• Subjects: Advection-diffusion equation; Computational fluid dynamics; Convergence; Criteria; Exact sciences and technology; Explicit method; Finite difference method; Generalized finite differences; Irregular grids; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Sciences and techniques of general use; Stability; Truncation errors; Advection-diffusion equation; Explicit method; 65M06; 74S20; Generalized finite differences; Irregular grids; 65M12; 80M20; Grid pattern; Fluid dynamics; Advection diffusion equation; Stability criterion; Truncation error; Convergence; Numerical analysis; Applied mathematics; Finite difference method
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2010.05.026

The study of the advection–diffusion equation continues to be an active field of research. The subject has important applications to fluid dynamics as well as many other branches of science and engineering. This paper shows the application of the generalized finite difference method to solve the advection–diffusion equation by the explicit method. The convergence of the method has been studied and the truncation error over irregular grids is given. An example has been solved using the explicit finite difference formulae and the criterion of stability.