Prescribed Velocity Gradients for Highly Viscous SPH Fluids with Vorticity Diffusion

Area of Science:

• Computational physics
• Fluid dynamics
• Smoothed Particle Hydrodynamics (SPH)

Background:

• Simulating highly viscous Smoothed Particle Hydrodynamics (SPH) fluids requires robust methods.
• Prescribed velocity gradients offer efficient and independent control over shear rate, spin, and expansion rate.
• Existing methods sometimes struggle with accurate vorticity handling.

Purpose of the Study:

• To propose a novel variant of the prescribed-gradient method for SPH fluids.
• To introduce a physically motivated approach to vorticity handling within this framework.
• To compare the proposed vorticity diffusion with preservation and damping methods.

Main Methods:

• Development of a novel prescribed-gradient approach for SPH fluid simulation.
• Implementation and analysis of vorticity diffusion as a core component.
• Comparative study of vorticity diffusion against vorticity preservation and damping.
• Exploration of the relationship between prescribed velocity gradients and Laplacians.
• Investigation of the connection to implicit viscosity formulations.

Main Results:

• The proposed vorticity diffusion method is shown to be effective and physically motivated.
• Vorticity diffusion offers advantages over vorticity preservation in certain SPH simulations.
• The study clarifies the relationship between prescribed velocity gradients and Laplacians.
• The method's connection to implicit viscosity formulations is elucidated.

Conclusions:

• The novel prescribed-gradient method with vorticity diffusion enhances the simulation of highly viscous SPH fluids.
• This approach provides a more physically accurate and stable alternative for vorticity handling.
• The findings improve the understanding and application of prescribed-gradient techniques in fluid dynamics.