An Improved CSPM Approach for Accurate Second-Derivative Approximations with SPH

We compare several approximations for second derivatives with Smoothed Particle Hydrodynamics (SPH). A first-order consistent approximation, derived from the zeroth-order consistent Corrective Smoothed Particle Method (CSPM), is proposed. The accuracy of the new method (ICSPM) is similar to that of the Finite Particle Method (FPM) and Modified Smoothed Particle Hydrodynamics (MSPH), but it is computationally less expensive. We demonstrate the accuracy of our method by studying heat conduction in a slab with discontinuous conductivity coefficients. We use both uniformly and pseudo-randomly distributed particles.