Ömer Oruç
A strong-form meshfree technique based on particle difference method (PDM) is developed to efficiently simulate coupled nonlinear advection–diffusion–reaction partial differential equations (PDEs) which describe modeling the transport and remediation of groundwater contaminants in the microbiological technology. In the PDM, differential operators are directly discretized at collocation points using Taylor series expansion along with moving least-square approximation. Since only collocation points are needed for discretization, irregular domains can be handled easily in the PDM. Also because the considered PDE is a time-dependent nonlinear equation, an implicit–explicit second-order backward difference formula (IMEX-BDF2) is combined with PDM to avoid solving nonlinear system of equations and achieve high accuracy. Several benchmark simulations are performed to show efficiency of the proposed method. To further show performance of the proposed method, some comparisons are made with finite element method, finite volume method and some other meshfree methods. The numerical simulations and comparisons made with available methods reveal that the suggested method is highly efficient and accurate to solve the considered problem which can be useful for removing the pollutants that have a health risk.