ALTERNATIVE DIRECT INTERPOLATION BOUNDARY ELEMENT METHOD APPLIED TO ADVECTIVE-DIFFUSIVE PROBLEMS WITH VARIABLE VELOCITY FIELD

Abstract

The wide range of physical phenomena of industrial interest which can be properly represented by advection-diffusion transport models motivates a constant effort in the development of new numerical methods capable of dealing with strong advective effects such as compressibility ones. The recent direct interpolation technique (DIBEM) proved to be an accurate and reliable tool for the representation of problems with constant velocity field and initial tests were also performed for problems with variable velocity field, where the results are reasonably satisfactory, but not so robust, since the integral relative to the velocity divergence, in general, seems to disturb the performance of the formulation. The current article presents a new formulation of the direct interpolation technique for solving variable velocity problems with non-zero velocity divergence. The accuracy of the new proposal is measured against a known analytical solution and, also, contrasted with the classical formulation of DIBEM and dual reciprocity technique (DRBEM) for the same case. Preliminary results show that the alternative DIBEM formulation proposed promotes a consistent improvement in precision, outperforming the two techniques in cross-comparison.