A Comparison of Various Meshless Schemes Within a Unified Algorithm

An algorithm for use with several meshless schemes is presented based on a local extremum diminishing property. The scheme is applied to the Euler equations in two dimensions. The algorithm is suitable for use with many meshless schemes, three of which are detailed here. First, a method based on Taylor series expansion and least squares is highlighted. Next, a similar least squares method is used, but using polynomial basis functions with fixed Gaussian weighting. A third method makes use of the Hardy multiquadric radial basis functions on a local cloud of points. Results indicate that all three methods perform essentially equally well for flows without shocks. For flows with shocks, the least squares methods perform significantly better than the radial basis method, which displays discrepancies in shock location and magnitude. All methods are compared to an established finite volume method for validation purposes.