A RATIONALE OF THE STABILIZED ISPH METHOD II –AN OPTIMIZATION OF RELAXATION COEFFICIENT BASED ON ERROR ESTIMATES–

Abstract

The stabilized ISPH method is a particle method for the incompressible Navier–Stokes equations and has a characteristic of adding a relaxation term with respect to a particle density in the pressure Poisson equation. The relaxation term contributes to keeping uniformness of particle distribution, then, enhancements of stability, volume conservation, and accuracy are confirmed by numerical results. For the stabilized ISPH method, it was shown by our previous study that the stabilization term is theoretically derived as an approximate solution of an energy minimization problem with respect to errors of incompressibility of fluid and uniformness of particle distributions weighted by a relaxation coefficient. However, a theoretical derivation of the optimal value of the relaxation coefficient remained unsolved. Then, this paper derives an optimal relaxation coefficient in the sense that minimizing an upper bound of errors derived by error analysis. Moreover, it is shown that the value and tendency of the optimal relaxation coefficient coincide with experimental results.