ADAPTIVE GRID REFINEMENT USING THE GENERALISED FINITE-DIFFERENCE METHOD

The combination of the Generalised Finite Difference Method (GFDM), and adaptive grid refinement is applied to solve 2D fluid flow problems. The accuracy of this combination is demonstrated by solving the 2D lid-driven cavity flow, and 2D backward-facing step flow problems, and comparing the results against the benchmarks. This new Computational Fluid Dynamics (CFD) formulation is applied to solve a 2D meter flow application to determine the velocity profiles through the centre of the meter for higher Reynolds numbers. To verify the accuracy of this combnation, analytical 2D and 3D Laplace partial differential equations (PDE's) are solved by two methods. The first method uses the Finite Difference Method (FDM) over a uniform grid of nodes, and the second method uses the GFDM over a non-uniform grid of nodes. Computational cost and accuracy comparisons are made for both methods.