Efficiency of boundary element methods for time‐dependent convective heat diffusion at high Peclet numbers

Abstract

SUMMARYA higher-order boundary element method (BEM) recently developed by the current authors (Comput Methods Appl Mech Eng 2003; 192:4281-4298; 4299-4312; 4313-4335) for time-dependent convective heat di usion in two-dimensions appears to be a very attractive tool for e cient simulations of transient linear ows. However, the previous BEM formulation is restricted to relatively small time step sizes (i.e. t 6 4Ä=V2 ) owing to the convergence issues of the time series for the kernel representation within a time interval. This paper extends the boundary element formulation in a way to allow time step sizes several orders of magnitude larger than in the previous approach. We consider an example problem of thermal propagation, and investigate the accuracy and e ciency of BEM formulations for Peclet numbers in the range from 10 3 to 10 5 .

Time‐domain BEM solution of convection–diffusion‐type MHD equations

“…t = 1.0, 2.0) in this procedure since the time-dependent fundamental solution is used. [3]). We solve the convection-diffusion equation…”

“…t = 1.0, 2.0) in this procedure since the time-dependent fundamental solution is used. [3]). We solve the convection-diffusion equation 4(1 + t))], 0<x<1 The exact solution is given by The boundary of the square region [0, 1] × [0, 1] is discretized with 20 constant boundary elements and 25 equally spaced interior points.…”

“…N. BOZKAYA AND M. TEZER-SEZGIN to be solved by using another numerical scheme for the time derivative in the governing equation, and usually finite difference method (FDM) is chosen for the time integration. But, due to the stability problems very small time increment must be used and this is computationally expensive and time consuming.The BEM applications of the time-dependent convection-diffusion problems are due to Grigoriev and Dargush [1][2][3]. In these studies, they have used time-dependent fundamental solution together with higher-order boundary elements.…”

“…The BEM applications of the time-dependent convection-diffusion problems are due to Grigoriev and Dargush [1][2][3]. In these studies, they have used time-dependent fundamental solution together with higher-order boundary elements.…”

A boundary element numerical scheme for the two‐dimensional convection–diffusion equation

“…Using the fundamental solution (11) in the integral equation (6) and applying Gauss' theorem make it possible to obtain an integral equation for the function :…”