Efficient implementation of transport velocity formulation

The standard smoothed particle hydrodynamics (SPH) method suffers from tensile instability, resulting in particle clumping and void regions under negative pressure. In this study, we extend the transport-velocity formulation (TVF) by Adami et al. (2013) [1], which is able to effectively suppress the tensile instability for the weakly-compressible SPH (WCSPH) method. Rather than relying on the physical parameter of background pressure, our proposed formulation scales the TVF correction directly to the pure numerical parameter of smoothing length, making it suitable for general simulations, such as those involving multi-resolution and dual-criteria time integration. Additionally, we introduce a limiter to prevent over-correction, especially for flows with small velocities. Extensive numerical tests demonstrate that the proposed formulation offers a general and accurate solution for multi-physics SPH simulations. © 2025 The Author(s)     «

The standard smoothed particle hydrodynamics (SPH) method suffers from tensile instability, resulting in particle clumping and void regions under negative pressure. In this study, we extend the transport-velocity formulation (TVF) by Adami et al. (2013) [1], which is able to effectively suppress the tensile instability for the weakly-compressible SPH (WCSPH) method. Rather than relying on the physical parameter of background pressure, our proposed formulation scales the TVF correction directly t...     »