Tanay Kumar Karmakar, Durga Charan Dalal
The patch dynamics scheme in equation-free multiscale modelling has the potential to efficiently predict the macroscopic behaviours by simulating the microscale problem in a fraction of the space-time domain. The patch dynamics schemes developed so far are mainly on rectangular domains with uniform grids and uniform rectangular patches. In real-life problems, the geometry of the domain is not regular or simple, where rectangular and uniform grids or patches may not be useful. To address this kind of complexity, for the first time, a generalised orthogonal curvilinear coordinate system is employed in the patch dynamics scheme, applicable to both rectangular domains with non-uniform grids and non-rectangular domains; while applying this, the concept of non-uniform and non-rectangular patch configurations in the physical domain is also adopted for the first time. An explicit representation of a patch dynamics scheme on a generalised curvilinear coordinate system in a two-dimensional domain is proposed for unsteady, linear, heterogeneous convection-diffusion-reaction (CDR) problems. The proposed scheme is validated through heterogeneous convection-diffusion-reaction and non-axisymmetric diffusion problems on generalised curvilinear coordinate systems. The results demonstrate excellent accuracy and show that the method significantly outperforms full-domain simulations in terms of computational efficiency, memory usage and overall performance.