Local Poisson SPH For Viscous Incompressible Fluids

Enforcing fluid incompressibility is one of the time‐consuming aspects in SPH. In this paper, we present a local Poisson SPH (LPSPH) method to solve incompressibility for particle based fluid simulation. Considering the pressure Poisson equation, we first convert it into an integral form, and then apply a discretization to convert the continuous integral equation to a discretized summation over all the particles in the local pressure integration domain determined by the local geometry. To control the approximation error, we further integrate our local pressure solver into the predictive‐corrective framework to avoid the computational cost of solving a pressure Poisson equation globally. Our method can effectively eliminate the large density deviations mainly caused by the solid boundary treatment and free surface topological change, and show advantage of a higher convergence rate over the predictive‐corrective incompressible SPH (PCISPH).

[1]  Brian A. Barsky,et al.  A New Concept and Method for Line Clipping , 1984, TOGS.

[2]  Martin Servin,et al.  Constraint Fluids , 2012, IEEE Transactions on Visualization and Computer Graphics.

[3]  Enhua Wu,et al.  Pressure corrected SPH for fluid animation , 2009, Comput. Animat. Virtual Worlds.

[4]  S. Cummins,et al.  An SPH Projection Method , 1999 .

[5]  S. Shao,et al.  INCOMPRESSIBLE SPH METHOD FOR SIMULATING NEWTONIAN AND NON-NEWTONIAN FLOWS WITH A FREE SURFACE , 2003 .

[6]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[7]  Renato Pajarola,et al.  A unified particle model for fluid–solid interactions: Research Articles , 2007 .

[8]  L. Libersky,et al.  Smoothed Particle Hydrodynamics: Some recent improvements and applications , 1996 .

[9]  Jessica K. Hodgins,et al.  A point-based method for animating incompressible flow , 2009, SCA '09.

[10]  L. Greengard.  The Rapid Evaluation of Potential Fields in Particle Systems , 1988 .

[11]  J. Monaghan.  Simulating Free Surface Flows with SPH , 1994 .

[12]  Nikolaus A. Adams,et al.  An incompressible multi-phase SPH method , 2007, J. Comput. Phys..

[13]  Philip Dutré,et al.  Mixing Fluids and Granular Materials , 2009, Comput. Graph. Forum.

[14]  Ross T. Whitaker,et al.  Particle‐Based Simulation of Fluids , 2003, Comput. Graph. Forum.

[15]  Matthias Teschner,et al.  Eurographics/ Acm Siggraph Symposium on Computer Animation (2007) Weakly Compressible Sph for Free Surface Flows , 2022 .

[16]  Yoshiaki Oka,et al.  A hybrid particle-mesh method for viscous, incompressible, multiphase flows , 2005 .

[17]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[18]  Renato Pajarola,et al.  A unified particle model for fluid–solid interactions , 2007, Comput. Animat. Virtual Worlds.

[19]  Greg Turk,et al.  Hybrid smoothed particle hydrodynamics , 2011, SCA '11.

[20]  Markus H. Gross,et al.  Particle-based fluid-fluid interaction , 2005, SCA '05.

[21]  J. Morris,et al.  Modeling Low Reynolds Number Incompressible Flows Using SPH , 1997 .

[22]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[23]  Leonidas J. Guibas,et al.  Adaptively sampled particle fluids , 2007, ACM Trans. Graph..

[24]  Mathieu Desbrun,et al.  Smoothed particles: a new paradigm for animating highly deformable bodies , 1996 .

[25]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[26]  Renato Pajarola,et al.  Predictive-corrective incompressible SPH , 2009, ACM Trans. Graph..

[27]  Matthias Teschner,et al.  A Parallel SPH Implementation on Multi‐Core CPUs , 2011, Comput. Graph. Forum.

[28]  Philip Dutré,et al.  Porous flow in particle-based fluid simulations , 2008, ACM Trans. Graph..

[29]  Markus H. Gross,et al.  Particle-based fluid simulation for interactive applications , 2003, SCA '03.

[30]  Markus H. Gross,et al.  Eurographics Symposium on Point-based Graphics (2005) a Unified Lagrangian Approach to Solid-fluid Animation , 2022 .

[31]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[32]  Ronald Fedkiw,et al.  Two-Way Coupled SPH and Particle Level Set Fluid Simulation , 2008, IEEE Transactions on Visualization and Computer Graphics.