This paper presents an enhanced version of the well-known SPH (Smoothed Particle Hydrodynamics) open-source code DualSPHysics both in CPU and GPU for the simulation of free-surface fluid flows, i.e., DualSPHysics+ [1]. The Optimized Particle Shifting (OPS) scheme is implemented to improve the accuracy of particle shifting vectors in the free-surface region. To mitigate energy dissipation and maintain consistency, the artificial viscosity in δ-SPH is substituted with a Riemann stabilization term, leading to the δR-SPH. The Velocity-divergence Error Mitigating (VEM) and Volume Conservation Shifting (VCS) schemes are adopted to mitigate the velocity-divergence error and improve the volume conservation, and hence to enhance the resolution of the continuity equation. To further reduce the errors in the velocity divergence field, a Hyperbolic/Parabolic Divergence Cleaning (HPDC) scheme is incorporated in addition to the VEM scheme. Validations in terms of accuracy, energy conservation are shown via classical benchmarks. The results show that the non-zero and relatively unsmooth velocity divergence field in the result by δR-SPH-OPS-VCS is enhanced by the incorporation of VEM and then further improved by simultaneous application of VEM and HPDC, which mitigates the instantaneous and accumulated velocity divergence errors, respectively. The energy of the fluid system in the artificial-viscosity simulation drops continuously, while that in the Riemann-term simulation conserves and matches well with the analytical solution. The predicted pressure history by δR-SPH-OPS-VCS-VEM-HPDC converges to the reference result much faster than those by δR-SPH-OPS-VCS-VEM and δR-SPH-OPS-VCS, which indicates the effectiveness of the proposed schemes in suppressing pressure noises.

References
[1] Y. Zhan, M. Luo, A. Khayyer. DualSPHysics+: An enhanced DualSPHysics with improvements in accuracy, energy conservation and resolution of the continuity equation. Computer Physics Communications, 306, 109389, 2025.

Smoothed Particle Hydrodynamics; DualSPHysics+; Volume conservation