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Implicit incompressible SPH.

Markus Ihmsen1, Jens Cornelis1, Barbara Solenthaler2

  • 1University of Freiburg, Freiburg.

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|January 18, 2014
PubMed
Summary
This summary is machine-generated.

We introduce a new projection method for Smoothed Particle Hydrodynamics (SPH) that enhances solver convergence and time-integration robustness. This improved SPH formulation handles large time steps and small density deviations effectively.

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Area of Science:

  • Computational physics
  • Fluid dynamics
  • Numerical methods

Background:

  • Smoothed Particle Hydrodynamics (SPH) is a mesh-free Lagrangian method widely used in fluid dynamics.
  • Existing projection methods for SPH face challenges in convergence rate and time-integration robustness.
  • Accurate and efficient simulation of fluid behavior requires robust numerical schemes.

Purpose of the Study:

  • To develop a novel projection method for Smoothed Particle Hydrodynamics (SPH) that improves computational efficiency and stability.
  • To enhance the convergence rate of the pressure Poisson equation (PPE) solver within SPH.
  • To increase the robustness of the time-integration scheme for SPH simulations.

Main Methods:

  • A symmetric SPH pressure force formulation was combined with an SPH discretization of the continuity equation.
  • A discretized form of the pressure Poisson equation (PPE) was derived, explicitly including pressure force computation.
  • Density deviation was computed based on velocities rather than positions to improve time-integration robustness.

Main Results:

  • The novel formulation demonstrated improved convergence rates compared to previous projection schemes.
  • The method successfully handled large time steps and small density deviations (down to 0.01%).
  • Simulations involving up to 40 million SPH particles showcased the practical relevance and scalability of the approach.

Conclusions:

  • The proposed SPH projection method offers superior performance over existing schemes.
  • The explicit inclusion of pressure force computation and velocity-based density deviation enhance solver accuracy and stability.
  • This formulation represents a significant advancement for large-scale SPH simulations in fluid dynamics.