Divergence-Free SPH for Incompressible and Viscous Fluids

Area of Science:

• Computational Fluid Dynamics
• Numerical Simulation Methods

Background:

• Smoothed Particle Hydrodynamics (SPH) methods are used for fluid simulation.
• Existing SPH methods struggle with efficiently enforcing incompressibility, requiring either position or velocity level constraints.
• Maintaining constant density and divergence-free velocity is crucial for accurate incompressible flow simulation.

Purpose of the Study:

• To present a novel Smoothed Particle Hydrodynamics (SPH) method for efficient and stable incompressible fluid simulation.
• To improve simulation performance and stability by addressing limitations in existing SPH approaches.
• To introduce an integrated solver for simulating highly viscous fluids.

Main Methods:

• Developed a novel combination of two implicit pressure solvers to enforce low volume compression and a divergence-free velocity field.
• Implemented an optional third implicit solver for simulating highly viscous fluids with minimal numerical damping.
• Utilized Smoothed Particle Hydrodynamics (SPH) for particle-based fluid simulation.

Main Results:

• The proposed method significantly enhances simulation stability, allowing for larger time steps and reduced computational cost.
• Achieved substantial performance gains due to fewer required solver iterations and less frequent neighborhood searches.
• Demonstrated efficiency, robustness, and scalability in complex simulations, including turbulent and highly viscous fluid scenarios.

Conclusions:

• The novel SPH method provides efficient and stable simulations of incompressible fluids.
• The integrated approach allows for realistic simulation of highly viscous fluids with minimal damping.
• The method is robust and scalable for complex, large-scale fluid dynamics problems.