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The Finite Difference Method for transient convection-diffusion problems

100%

Majchrzak E. , Turchan Ł.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2012

tom Vol. 11, nr 1

63-72

The convection-diffusion equation (1D problem) is considered. At first, the unknown temperature T is expanded into a Taylor series with respect to time taking into account its three components. Next, using the convection-diffusion equation and equation obtained from the differentiation of this equation, the way of temperature T computations is shown. In this new equation the high order derivatives with respect to spatial co-ordinate appear and the approximation of these derivatives is also discussed. The explicit scheme is used and the stability criteria are formulated. Finally, the results of computations are shown.

Exact difference schemes and schemes of higher order of approximation for convection-diffusion equation. I

100%

Lapinska-Chrzczonowicz M. , Matus P.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

2013

tom Vol. 13, no. 1

37--51

The initial-boundary value problem for a convection-diffusion equation [formula] is considered. The difference scheme, approximating this problem, is constructed. It is shown that for traveling wave solutions the scheme is exact (EDS). The monotonicity of the scheme is also taken into consideration. Presented numerical experiments illustrate the theoretical results investigated in the paper.

A Neumann problem for a convection-diffusion equation on the half-line

100%

Biler P. , Karch G.

Annales Polonici Mathematici

2000

tom 74

nr 1

79-95

We study solutions to a nonlinear parabolic convection-diffusion equation on the half-line with the Neumann condition at x=0. The analysis is based on the properties of self-similar solutions to that problem.

A research study on unsteady state convection diffusion flow with adoption of the finite volume technique

63%

Patel M. R. , Pandya J. U.

Journal of Applied Mathematics and Computational Mechanics

2021

tom Vol. 20, nr 4

65--76

This research paper is an attempt to solve the unsteady state convection diffusion one dimension equation. It focuses on the fully implicit hybrid differencing numerical finite volume technique as well as the fully implicit central differencing numerical finite volume technique. The simulation of the unsteady state convection diffusion problem with a known actual solution is also used to validate both the techniques, respectively, the fully implicite hybrid differencing numerical finite volume technique as well as the fully implicit central differencing numerical finite volume technique by giving a particular example and solving it using the appropriate, particular technique. It is observed that the numerical scheme is an outstanding deal with the exact solution. Numerical results and graphs are presented for different Peclet numbers.