Investigating Castillo-Grone's Mimetic Difference Operators in Development of Geophysical Fluid Dynamics Models Implemented on GPGPUs

This research investigates the performance of Castillo-Grone's Mimetic (CGM) difference operators in 2D and 3D fully curvilinear grids. A software package is provided that assists the user in generating Laplacian operator in fully curvilinear grids using higher order CGM operators. Furthermore, a stability analysis is performed using von Neumann's analysis to understand the behavior of these operators in solving advection equation. A shallow water equation solver is provided that harnesses the power of the general purpose graphics processing units (GPGPUs) and some timing are provided.