Application of the meshless generalised RKPM to the transient advection-diffusion-reaction equation. (December 2017) - Gharib, M.; Khezri, M.; Foster, S.J.; Castel, A.
Highlights: Adaptation of meshless method to the transient advection–diffusion-reaction equation. ADR equation is cast in both strong and weak form for a general n -dimensional domain. Generalised RKPM with Lagrangian kernel for discretisation of weighted integrals. Solution of unsteady ADR equation with general initial value boundary conditions. Abstract: 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.