Direct interpolation boundary element method applied for solving steady-state convection-diffusion-reaction problems with variable velocity field

Abstract

Motivated by the superior results achieved by the Direct Interpolation Boundary Element Method (DIBEM) in solving important scalar field models such as the Poisson and Helmholtz problems, this article presents the performance of the mentioned technique applied in Diffusive-Advective-Reactive issues, considering the spatial variation of the velocity field. Aiming the evaluation of the numerical model's robustness, the effect of advection is gradually increased relative to the diffusive phenomena, despite the limitations imposed by interpolation with radial basis functions, which restrict the fluid flow representation to creeping flow. The accuracy and stability are checked using benchmark problems with widely known analytical solutions and compared with other methods. Assuming that the fluid flow occurs to a low Mach number, compressible effects also could be considered, and its impact in numerical solution is analyzed.