A consistent δ-Plus-ULPH model towards higher accuracy and lower numerical dissipation with fewer neighboring particles

This paper proposes a novel consistent δ+- Updated Lagrangian Particle Hydrodynamics (ULPH) model. Although the Smoothed Particle Hydrodynamics (SPH) model has gained recognized achievements, it is afflicted by excessive numerical dissipation when the neighboring particles are insufficient. The present proposed consistent δ+-ULPH model has advantages in overcoming this problem. To improve the accuracy, efficiency, stability, and energy conservation, several new techniques are introduced to the consistent δ+-ULPH model. A novel extended support domain technique is proposed to achieve higher accuracy with fewer neighboring particles. An optimal matrix for the velocity divergence is proposed to improve the free-surface stability. A consistent particle shifting technique for the ULPH scheme is proposed to maintain a uniform and regular particle distribution and obtain superior conservation. In addition, an acoustic damper term for the ULPH scheme is introduced to improve the pressure field stability. Five benchmark tests were carried out to validate the consistent δ+-ULPH model. The conventional ULPH and the consistent δ+-SPH results are presented for comparison. Results indicate that the proposed consistent δ+-ULPH model can accurately simulate both gentle waves and violent sloshing flows and shows higher accuracy and lower numerical dissipation when using fewer neighboring particles, even in long-term and long-distance wave propagation simulations. Additionally, the computational ef­ ficiency of the consistent δ+-ULPH model is enhanced visibly because of fewer neighboring particles.