Particle shifting with density invariant correction for stable and reliable particle simulations of free surface flow

While the particle method is suitable for representation of large and discontinuous deformations, it is prone to accuracy degradation and numerical instability due to issues with particle distribution. To solve this problem, SPH(2) has been proposed, which can perform highly accurate calculations even when there are disturbances in the particle distribution. But is still limited in overcoming numerical instability. From previous studies, it is found that more stable and accurate calculations can be achieved by using SPH(2) in combination with the particle shifting technique. However, the existing particle shifting technique tends to expand the volume in the long term smulations. Therefore, we propose a new particle rearrangement method that can simultaneously improve particle homogeneous distribution and volume conservation. For this purpose, it is also important to use the proposed method in combination with other stabilization techniques, and our policy is to sort out the roles of various stabilization techniques and eliminate unnecessary terms. In addition, the numerical stability and accuracy improvement of the proposed method are demonstrated by Rotating square patch fluid simulations and Dam break simulations.