Postprint version. Published in 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition Proceedings: Orlando Florida, January 4, 2011, pages 1 of 16-16 of 16.
The definitive version is available at https://doi.org/10.2514/6.2011-654.
A meshless solution algorithm for the full potential equation has been developed by applying the principles of the Taylor Least Squares (TLS) method. This method allows for a PDE to be discretized on a local cloud of scattered nodes without the need of connectivity data. The process for discretizing the full potential equation within a meshless framework is outlined along with a novel Hermite TLS technique for enforcement of Neumann boundary conditions. Several two-dimensional test cases were solved that compare well with analytical and benchmark solutions. The first test case solved for the subcritical compressible flow over a circular cylinder at a freestream Mach number of 0.375. The last two cases solved for the non-lifting and lifting subcritical flows over a NACA 0012 airfoil with freestream conditions (M∞= 0.72; α = 0°) and (M∞= 0.63; α = 2°) respectively.
2011 authors. First published by American Institute of Aeronautics and Astronautics, Inc..