A fast multi-level convolution boundary element method for transient diffusion problems

2005 ◽  
Vol 62 (14) ◽  
pp. 1895-1926 ◽  
Author(s):  
C.-H. Wang ◽  
M. M. Grigoriev ◽  
G. F. Dargush
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Transient Diffusion ◽  
Multi Level ◽  
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.

A Boundary Element Method Formulation for Design Sensitivities in Steady-State Conduction-Convection Problems

1992 ◽  
Vol 59 (1) ◽  
pp. 182-190 ◽  
Author(s):  
Abhijit Chandra ◽  
Cho Lik Chan
Keyword(s):  
Steady State ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Machining Processes ◽  
Convection Diffusion ◽  
Design Sensitivities ◽  
Singular Kernels ◽  
Method Formulation ◽  
Diffusion Problems ◽  
Element Method

A Boundary Element Method (BEM) formulation for the determination of design sensitivities of temperature distributions to various shape and process parameters in steady-state convection-diffusion problems is presented in this paper. The present formulation is valid for constant or piecewise-constant convective velocities. This approach is based on direct differentiation (DDA) of the relevant BEM formulation of the problem. It retains the advantages of the BEM regarding accuracy and efficiency while avoiding strongly singular kernels. The BEM formulation is also observed to avoid any false diffusion. This approach provides a new avenue toward efficient optimization of steady-state convection-diffusion problems and may be easily adapted to investigate the thermal aspects of various machining processes.

Study on Chloride Diffusion in Concrete with Non-Homogenous Coefficient Using Meshless Boundary Element Method

2010 ◽  
Vol 650 ◽  
pp. 38-46
Author(s):  
Li Guo ◽  
Tang Chen ◽  
Jun Hong ◽  
Ling Qiao ◽  
Xiao Ming Guo
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Boundary Integral Equations ◽  
Numerical Technique ◽  
Boundary Integral ◽  
Chloride Diffusion ◽  
Weighted Residual Method ◽  
Transient Diffusion ◽  
Radial Basis Function Approximation ◽  
Element Method

A new robust numerical technique was proposed for analyzing chloride transient diffusion in concrete with non-homogenous coefficient. The method was based on a meshless boundary element method which results in an integral equation for explicitly evaluating field chloride quantities. Weighted residual method and Green’s function were adopted to derive domain and boundary integral equations. A radial integration method coupling with radial basis function approximation technology was used to convert domain integral into equivalent boundary integral. With central finite difference method, an explicit time iteration scheme was established for solving transient diffusion equation. Two numerical examples for 2D diffusion problem were given to demonstrate the robustness of the proposed method. Numerical results show that the non-homogenous diffusion coefficient causes the chloride distribution non-uniform, and the diffusion process is nonlinear with respect to time.

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