On the optimal implementation of the boundary element dual reciprocity method—multi-domain approach for 3D problems

In this paper, aspects regarding implementation of the boundary element dual reciprocity method—multi-domain approach (DRM-MD), in respect to 3D problems are reviewed. Results of numerical tests on a 3D advection–diffusion problem with non-uniform velocity field are presented. The sensitivity of the accuracy and stability of the codes to the continuity of the elements, scaling, internal DRM nodes and mesh refinement have been tested. The results show that scaling is essential and that mesh refinement and/or internal DRM nodes improve the accuracy when the non-homogeneous term of the governing equation becomes dominant. The computer code implemented with discontinuous elements offers higher accuracy, especially for advection dominant transport, but is much slower than the computer code with continuous elements. At the present stage, the discontinuous element code has the advantage of flexibility since it can solve non-homogeneous domains.