Higher-order boundary element methods for unsteady convective transport phenomena.

摘要

Despite the significant number of publications on boundary element methods (BEM) for time-dependent problems of heat diffusion and convective diffusion, there still remain issues that need to be addressed, most importantly accuracy of the numerical modelling. Although very precise for steady-state problems, the common boundary element methods applied to transient problems do not yield highly accurate numerical solutions.;First, this work investigates the reasons that prohibit achievement of a high level of accuracy for transient diffusion problems with continuous temperature and bounded heat flux solutions. We propose higher-order time interpolation functions, including quadratic and quartic approximations. We show that the use of higher-order time functions greatly reduces the numerical error concentrated in the comer regions, and results in very good uniformity of the flux and temperature distributions along the boundaries for problems where uniform distributions are expected.;In order to highlight the importance of proper resolution both in time and space for the transient problems, we consider one- and two-dimensional formulations. For the two-dimensional case, single- and poly-region formulations are utilized. While the latter approach employs the hexagonal mesh introduced by Grigoriev and Dargush (1999) for steady viscous flows at high Reynolds numbers, the former approach makes use of both a hexagonal mesh and a regular mesh of rectangles throughout the volume.;A finite-flux boundary element method (BEM) for transient heat diffusion phenomena is extended to problems involving instantaneous rise of temperature on a portion of the boundary. The new boundary element formulation involves the use of an infinite flux function in order to properly capture the singular response of the flux. It is shown that the conventional finite flux BEM formulation, as well as a commercial FEM code, results in a large first time step numerical error that cannot be reduced by mesh or time step refinement.;Higher-order boundary element methods for the time-dependent convective diffusion problems are presented. The time-dependent convective diffusion free-space fundamental solutions originally proposed by Carslaw and Jaeger (1957) are used to obtain the boundary integral formulation. A complete set of closed form time integrals for the one-dimensional formulation are presented here for the first time in the literature. Solutions are obtained for four different problems of unsteady convection-diffusion, including shock wave propagation. (Abstract shortened by UMI.).