Towards an efficient meshfree solver

In this paper we focus on the enhancement in accuracy approximating a function and its derivatives via smoothed particle hydrodynamics. We discuss about improvements in the solution by reformulating the original method by means of the Taylor series expansion and by projecting with the kernel function and its derivatives. The accuracy of a function and its derivatives, up to a fixed order, can be simultaneously improved by assuming them as unknowns of a linear system. The improved formulation has been assessed with gridded and scattered data points distribution and the convergence has been analyzed referring to a case study in a 2D domain