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

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.

Citation

Korkmaz, A. and Dağ, İ. (2012), "Cubic B‐spline differential quadrature methods for the advection‐diffusion equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 8, pp. 1021-1036. https://doi.org/10.1108/09615531211271844