Edge-based Meshless Methods for Compressible Flow Simulations

This work concerns the development of a highly accurate and efficient meshless flow solver for inviscid flow in two dimensions. Novel aspects of this work include the application of mesh-based reconstruction, diffusion, and convergence acceleration schemes within an edge-based meshless framework. Most notably, “multicloud,” a meshless counterpart to multigrid, has been implemented. Multicloud dramatically enhances convergence to steady state, resulting in a convergence rate which is nearly an order of magnitude faster than single cloud results. Results are presented which indicate good agreement with conventional finite volume results for several test cases, despite the absence of any formal proof of conservation. Correct shock jumps and locations are obtained for airfoils in transonic flow. Lift and drag coefficients also compare well to the finite volume results.