Accuracy and efficiency of higher-order boundary element methods for steady convective heat diffusion in three-dimensions

Higher-order boundary element methods (BEM) are presented for three-dimenisonal steady corrective heat diffusion at high Peclet numbers. The boundary element formulation is facilitated by the definition of an influence domain due to convective kernels. This approach essentially localizes the surface integrations only within the domain of influence which becomes more narrowly focused as the Peclet number increases. The outcome of this phenomenon is an increased sparsity and improved conditioning of the global matrix. Therefore, iterative solvers for sparse matrices become a very efficient and robust tool for the corresponding boundary element matrices. In this paper, we consider an example problem with an exact solution and investigate the accuracy and efficiency of the higher-order BEM formulations for high Peclet numbers in the range from 1000 to 100,000. The bi-quartic boundary elements included in this study are shown to provide very efficient and extremely accurate solutions to this problem, even on a single engineering workstation.