Application of the Space–Time Conservation Element and Solution Element Method to One-Dimensional Convection–Diffusion Problems

2000 ◽  
Vol 165 (1) ◽  
pp. 189-215 ◽  
Author(s):  
Sin-Chung Chang ◽  
Xiao-Yen Wang ◽  
Wai-Ming To
Keyword(s):  
Space Time ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Solution Element ◽  
Diffusion Problems ◽  
Element Method

Numerical modelling of convection-diffusion problems with first-order chemical reaction using the dual reciprocity boundary element method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Salam Adel Al-Bayati ◽  
Luiz C. Wrobel
Keyword(s):  
Steady State ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Content Type ◽  
Convection Diffusion ◽  
First Order ◽  
Order Chemical Reaction ◽  
First Order Chemical Reaction ◽  
Diffusion Problems ◽  
Element Method

Purpose The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one- and two-dimensional steady-state problems, to analyse transient convection–diffusion problems associated with first-order chemical reaction. Design/methodology/approach The mathematical modelling has used a dual reciprocity approximation to transform the domain integrals arising in the transient equation into equivalent boundary integrals. The integral representation formula for the corresponding problem is obtained from the Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. The finite difference method is used to simulate the time evolution procedure for solving the resulting system of equations. Three different radial basis functions have been successfully implemented to increase the accuracy of the solution and improving the rate of convergence. Findings The numerical results obtained demonstrate the excellent agreement with the analytical solutions to establish the validity of the proposed approach and to confirm its efficiency. Originality/value Finally, the proposed BEM and DRBEM numerical solutions have not displayed any artificial diffusion, oscillatory behaviour or damping of the wave front, as appears in other different numerical methods.

scholarly journals Mixed and Hybrid Finite Element Methods for Convection-Diffusion Problems and Their Relationships with Finite Volume: The Multi-Dimensional Case

2017 ◽  
Vol 9 (1) ◽  
pp. 68 ◽  
Author(s):  
Michel Fortin ◽  
Abdellatif Serghini Mounim
Keyword(s):  
Finite Volume ◽  
Numerical Approximation ◽  
Dimensional Case ◽  
Parabolic Problems ◽  
Finite Volume Schemes ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Hybrid Finite Element ◽  
The One ◽  
Diffusion Problems

We introduced in (Fortin & Serghini Mounim, 2005) a new method which allows us to extend the connection between the finite volume and dual mixed hybrid (DMH) methods to advection-diffusion problems in the one-dimensional case. In the present work we propose to extend the results of (Fortin & Serghini Mounim, 2005) to multidimensional hyperbolic and parabolic problems. The numerical approximation is achieved using the Raviart-Thomas (Raviart & Thomas, 1977) finite elements of lowest degree on triangular or rectangular partitions. We show the link with numerous finite volume schemes by use of appropriate numerical integrations. This will permit a better understanding of these finite volume schemes and the large number of DMH results available could carry out their analysis in a unified fashion. Furthermore, a stabilized method is proposed. We end with some discussion on possible extensions of our schemes.

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