Application of the meshless generalised RKPM to the transient advection-diffusion-reaction equation

A variety of physical problems may be expressed using the advection-diffusion-reaction (ADR) equation that encompasses transport processes into a porous or nonporous material. Finding a theoretical solution to the ADR equation is difficult with time-dependent nonlinear coefficients, complicated geometries, general initial value and/or boundary conditions. In this paper a meshless model is developed by adapting the generalised reproducing kernel particle method to the strong and weak integral forms of ADR equation. Moreover, mixed-type boundary conditions are directly enforced via generalising the corrected collocation method. The model is validated using existing analytical solutions and shown to be both accurate and efficient.