A dynamic relaxation method with operator splitting and random-choice strategy for SPH

Abstract

In this paper, we propose an efficient dynamic relaxation method for smoothed particle hydrodynamics (SPH) to address the time-consuming issue when dealing with achieving the equilibrium of a dynamic system. First, an artificial-viscosity-based damping term is added into the momentum equation to dissipate the velocity gradient without losing the momentum conservation of the system. Two operator splitting methods, which update velocities implicitly, are then developed to discretize the added damping term for relaxing the time-step limit. To further improve the computational efficiency, a random-choice strategy is also introduced into the dynamic relaxation process, by which the damping is imposed randomly rather than each time step. Furthermore, a splitting cell-linked list scheme is proposed by dividing the conventional cell-linked list into several blocks to avoid the thread conflict when shared-memory parallelization is applied to accelerate the computation. A number of benchmark tests show the fast and efficient feature of the present method for dynamic systems achieving their equilibrium.