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Journal cover: International Journal of Numerical Methods for Heat & Fluid Flow

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Online from: 1991

Subject Area: Mechanical & Materials Engineering

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Cubic B-spline differential quadrature methods for the advection-diffusion equation


Document Information:
Title:Cubic B-spline differential quadrature methods for the advection-diffusion equation
Author(s):Alper Korkmaz, (Department of Mathematics, Çankiri Karatekin University, Çankiri, Turkey and Department of Mathematics and Computer Sciences, Eskisehir Osmangazi University, Eskisehir, Turkey), Idris Dag, (Department of Mathematics and Computer Sciences, Eskisehir Osmangazi University, Eskisehir, Turkey)
Citation:Alper Korkmaz, Idris Dag, (2012) "Cubic B-spline differential quadrature methods for the advection-diffusion equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 Iss: 8, pp.1021 - 1036
Keywords:Advection-diffusion equation, B-spline, Differential equations, Differential quadrature method, Diffusion
Article type:Research paper
DOI:10.1108/09615531211271844 (Permanent URL)
Publisher:Emerald Group Publishing Limited
Abstract:

Purpose – Cubic B-spline differential quadrature methods have been introduced. As test problems, two different solutions of advection-diffusion equation are chosen. The first test problem, the transportion of an initial concentration, and the second one, the distribution of an initial pulse, are simulated. The purpose of this paper is to simulate the test problems.

Design/methodology/approach – The cubic B-spline functions are chosen as test functions in order to construct the differential quadrature method. The error between the numerical solutions and analytical solutions are measured using various error norms.

Findings – The cubic B-spline differential quadrature methods have produced acceptable solution for advection-diffusion equation.

Originality/value – The advection-diffusion equation has never been solved by any differential quadrature method based on cubic B-splines.



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