A Meshless Finite Difference Scheme for Compressible Potential Flows

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.