Ansys Rocky SPH: comparisons of weakly-compressible and incompressible approaches

"Ansys Rocky has a native Smoothed-Particle Hydrodynamics (SPH) solver, which is a mesh-free numerical method. Unlike traditional grid-based methods, SPH represents fluid as a collection of particles that interact with each other through a kernel function, and that are tracked in a Lagrangian frame of reference. SPH is widely used for simulating complex fluid flows due to its ability to handle free surfaces, moving boundaries, and complex geometries. Additionally, SPH can simulate both compressible and incompressible fluids and can handle large deformations and high Reynolds numbers. Moreover, the nature of the SPH method allows it to be easily parallelized, making it well-suited for high-performance computing applications.

The current implementation in Ansys Rocky is the so-called Weakly Compressible SPH (WCSPH). In the formulation, the fluid pressure is solved from an equation of state, and the equations of motion are integrated explicitly. The drawback is that one is usually restricted to smaller timesteps, aiming to avoid numerical stability issues. On the other hand, the incompressible SPH (ISPH) approach allows for larger timesteps, but requires the implicit solution of a Poisson equation for the pressure, representing an inherent performance loss.

This study presents numerical validations of some cases where the incompressible and weakly-compressible SPH approaches are compared in terms of accuracy and performance. "