Boundary element methods for transient convective diffusion. Part II: 2D implementation

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

“…Recently, Grigoriev and Dargush [1][2][3] presented higher-order boundary element methods for unsteady convective di usion problems using the time-dependent convective-di usion kernels originally obtained by Carslaw and Jaeger [13]. Similar to their earlier work [14], linear, quadratic and quartic time interpolation functions were utilized for a temporal discretization of the boundary integral equation.…”

“…Recent studies [1][2][3][4][5][6][7][8][9][10][11][12] have revealed that the use of convective kernels within the boundary element framework provides an automatic upwinding in the most natural way for the entire range of Reynolds (or, Peclet) number, from zero to inÿnity. Despite the attractiveness of the convective boundary element methods (BEM) a proper numerical implementation of the convective fundamental solutions appears extremely di cult.…”

“…Similar to their earlier work [14], linear, quadratic and quartic time interpolation functions were utilized for a temporal discretization of the boundary integral equation. In References [1][2][3], the authors considered both one-and two-dimensional BEM formulations. Although the implicit time marching formulation utilized in References [2,3] did not impose any restrictions on the time step size t, the applicability of the numerical algorithm was restricted to the following time step sizes:…”

“…Consequently, the BEM became less e cient and even in some cases failed to converge if the time steps were too large. In this paper, the formulation presented in References [1][2][3] is extended to alleviate constraint (1). The use of time steps up to three orders of magnitude larger than t c is facilitated by splitting the time interval t into singular and non-singular intervals.…”

“…The use of time steps up to three orders of magnitude larger than t c is facilitated by splitting the time interval t into singular and non-singular intervals. For the singular part, the integration is performed according to the approach presented in Reference [2]. Whereas, numerical time integration is found to be su ciently accurate for the remaining non-singular portion of the time interval.…”