A pairwise-relaxing incompressible smoothed particle hydrodynamics scheme

We present a formulation of incompressible smoothed particle hydrodynamics (ISPH) method that utilizes pairwise-relaxing kernel to achieve approximately first-order consistency. Previous high-order formulations by using reproduced and corrected kernel function have had difficulties in ensuring momentum conservation. In the new scheme, relaxing constants for each kernel function are determined pair-wisely throughout the entire calculation domain by enforcing the Taylor-series consistency condition. We call this modified ISPH method Pairwise-Relaxing ISPH, or PR-ISPH. PR-ISPH retains high-order accuracy for non-uniform particle distributions. The spatial symmetry of the kernel function is kept in PR-ISPH thus momentum is strictly conserved. Several two-dimensional benchmark calculations are conducted to demonstrate the accuracy as well as the conservation property of the PR-ISPH.