A normalized iterative Smoothed Particle Hydrodynamics method

In this paper we investigate on a normalized iterative approach to improve the Smoothed Particle Hydrodynamics (SPH) estimate of a function. The method iterates on the residuals of an initial SPH approximation to obtain a more accurate solution. The iterative strategy preserves the matrix-free nature of the method, does not require changes on the kernel function and it is not affected by disordered data distribution. The iterative refinement is further improved by ensuring a linear approximation order to the starting iterative values. We analyze the accuracy and the convergence of the method with the standard and normalized formulation giving evidence of the improvements obtained with both uniform and non-uniform data density. Numerical experiments in 2D domain with different data sets are presented to validate the iterative approach