Meshless and analytical solutions to the time-dependent advection-diffusion-reaction equation with variable coefficients and boundary conditions

Abstract

• The unsteady ADR equation is formulated and solved by the meshless generalised RKPM. • A general Robin BC is formulated and precisely enforced in a novel approach. • An analytical solution is derived for 1D problem with temporally changing Robin BC. • A normalisation procedure is introduced to interpret the results to relevant applications. A variety of physical problems in science may be expressed using the advection-diffusion-reaction (ADR) equation that covers heat transfer and transport of mass and chemicals into a porous or a nonporous media. In this paper, the meshless generalised reproducing kernel particle method (RKPM) is utilised to numerically solve the time-dependent ADR problem in a general n -dimensional space with variable coefficients and boundary conditions. A time-dependent Robin boundary condition is formulated and precisely enforced in a novel approach. The accuracy and robustness of the meshless solution is verified against finite element simulations and a general one-dimensional analytical solution obtained in this study.