Boundary Element Method for Laminar Viscous Flow and Convective Diffusion Problems

1985 ◽  
pp. 209-229
Author(s):  
K. Onishi ◽  
T. Kuroki ◽  
M. Tanaka
Keyword(s):  
Boundary Element Method ◽  
Viscous Flow ◽  
Boundary Element ◽  
Convective Diffusion ◽  
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.

scholarly journals Two-Dimensional Incompressible Viscous Flow Simulation Using Velocity-Vorticity Dual Reciprocity Boundary Element Method

2004 ◽  
Vol 20 (3) ◽  
pp. 177-185 ◽  
Author(s):  
T. I. Eldho ◽  
D. L. Young
Keyword(s):  
Boundary Element Method ◽  
Viscous Flow ◽  
Boundary Element ◽  
Computational Domain ◽  
Two Dimensional ◽  
Flow Problems ◽  
Poisson Equations ◽  
Incompressible Viscous Flow ◽  
Vorticity Transport ◽  
Element Method

AbstractThis paper describes a computational model based on the dual reciprocity boundary element method (DRBEM) for the solution of two-dimensional incompressible viscous flow problems. The model is based on the Navier-Stokes equations in velocity-vorticity variables. The model includes the solution of vorticity transport equation for vorticity whose solenoidal vorticity components are obtained by solving Poisson equations involving the velocity and vorticity components. Both the Poisson equations and the vorticity transport equations are solved iteratively using DRBEM and combined to determine the velocity and vorticity vectors. In DRBEM, all source terms, advective terms and time dependent terms are converted into boundary integrals and hence the computational domain of the problem reduces by one. Internal points are considered wherever solution is required. The model has been applied to simulate two-dimensional incompressible viscous flow problems with low Reynolds (Re) number in a typical square cavity. Results are obtained and compared with other models. The DRBEM model has been found to be reasonable and satisfactory.

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