# Dual-criteria time stepping for weakly compressible smoothed particle hydrodynamics

## TL;DR

This paper introduces a dual-criteria time-stepping method for weakly compressible smoothed particle hydrodynamics that enhances computational efficiency by decoupling particle interaction updates from pressure relaxation steps.

## Contribution

It proposes a novel dual-criteria time-stepping approach that improves efficiency in WCSPH simulations by using separate advection and acoustic time criteria.

## Key findings

- Reduced CPU cost in simulations
- Maintained accuracy in benchmark tests
- Potential for fluid-structure interaction modeling

## Abstract

Implementing particle-interaction configuration and time integration are performance intensive essentials of particle-based methods. In this paper, a dual-criteria time-stepping method is proposed to improve the computational efficiency of the weakly-compressible smoothed particle hydrodynamic (WCSPH) method for modeling incompressible flows. The key idea is to introduce an advection time criterion, which is based on fluid velocity field, for recreating the particle-interaction configuration. Within this time criterion, several steps of pressure relaxation determined by the acoustic time criterion, based on the artificial speed of sound, can be carried out without updating the particle interaction configuration and much larger time-step sizes compared with the conventional counterpart. The method has shown optimized computational performance through CPU cost analysis. Good accuracy and performance is obtained for the presented benchmarks implying promising potential of the proposed method for incompressible flow and fluid-structure interaction simulations.