Simplified Smoothed Particle Hydrodynamics

• US 20120284002A1
• Filed: 01/20/2012
• Published: 11/08/2012
• Est. Priority Date: 05/05/2011
• Status: Active Grant

• Current Assignee: Siemens AG
• Original Assignee: Siemens Corp. (Siemens AG)
• Inventors: McDaniel, Richard Gary, Tamimi, Zakiya
• Granted Patent: US 8,831,916 B2
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: G06F 2111/08 Probabilistic or stochastic CAD
• CPC Class Codes: G06F 2111/10 Numerical modelling
• CPC Class Codes: G06F 30/20 Design optimisation, verification or simulation optimisation, verification or simulation of circuit designs G06F30/30

Abstract

For efficient smooth particle hydrodynamics using more particle information, virtual particles are created. Each virtual particle represents an averaging of properties for the fluid particles in a cell. For density, force, or other calculations for a given fluid particle, the interaction between the particles within a cell are calculated. For calculating the influence of particles outside the cell on the particle in the cell, the virtual particles from the neighboring cells are used. The interaction with these aggregate particles reduces the number of calculations while still including the influence from particles of other cells.

Claims

1. In a non-transitory computer readable storage medium having stored therein data representing instructions executable by a programmed processor for smooth particle hydrodynamics, the storage medium comprising instructions for:

dividing a simulation space into cells;

assigning fluid particles to the cells;

creating a virtual particle for each of the cells with at least one of the fluid particles, the virtual particle created from the fluid particles of the respective cell;

determining a mass of each of the virtual particles;

determining a surrounding density of each of the fluid particles as a function of the virtual particles of neighboring cells and particles of the cell of the fluid particle; and

advecting the fluid particles as a function of the densities of the fluid particles and the densities of the virtual particles.

2. The non-transitory computer readable storage medium of claim 1 wherein dividing and assigning comprises defining a three-dimensional distribution of the fluid particles grouped into the cells.

3. The non-transitory computer readable storage medium of claim 1 wherein creating the virtual particles comprises calculating a position of each of the virtual particles as an average of positions of the fluid particles in the respective cell.

4. The non-transitory computer readable storage medium of claim 1 wherein creating the virtual particles comprises calculating a radius of each of the virtual particles to include all the fluid particles of the respective cell.

5. The non-transitory computer readable storage medium of claim 1 wherein determining the mass comprises calculating the mass of each of the virtual particles as a function of a density of the virtual particle.

6. The non-transitory computer readable storage medium of claim 1 wherein determining the mass of each of the virtual particles comprises determining a density and volume only from fluid particles in the respective cell.

7. The non-transitory computer readable storage medium of claim 1 wherein determining the density of each of the fluid particles comprises calculating a contribution from the fluid particles in a same cell and not individual ones of the fluid particles of other cells and calculating a contribution from the virtual particles of the neighboring cells and not of the cell of the fluid particle.

8. The non-transitory computer readable storage medium of claim 1 wherein advecting comprises calculating a pressure force for each of the fluid particles, the pressure force being based on the densities of the fluid particles of the cell and the densities of the virtual particles of the neighboring cells.

9. The non-transitory computer readable storage medium of claim 1 wherein advecting comprises calculating a viscosity force for each of the fluid particles, the viscosity force being based on the densities of the fluid particles of the cell and the densities of the centroid particles of the neighboring cells.

10. The non-transitory computer readable storage medium of claim 1 wherein advecting comprises determining velocity and position of the fluid particles as a function of forces, the forces being a function of the densities of the fluid particles and the densities of the virtual particles.

11. The non-transitory computer readable storage medium of claim 1 wherein assigning, creating, determining the mass, determining the densities of the fluid particles, and advecting are repeated to simulate fluid flow.

12. The non-transitory computer readable storage medium of claim 1 wherein advecting comprises advecting as a function of an external force associated with a boundary.

13. A method for smooth particle hydrodynamics, the method comprising:

dividing, with a processor, a volume into sub-volumes;

populating the sub-volumes with fluid particles;

determining a virtual particle to represent the fluid particles for each of the sub-volumes; and

calculating force for each of the fluid particles based on the fluid particles in a same sub-volume as the fluid particle and virtual particles of adjacent sub-volumes, the calculating not being based on individual fluid particles of the adjacent sub-volumes.

14. The method of claim 13 wherein calculating comprises calculating the force for the fluid particles without contribution from non-adjacent sub-volumes.

15. The method of claim 13 wherein calculating comprises calculating a virtual force of the virtual particles as representing the forces within the respective cells and calculating the force for each of the fluid particles with contribution from the fluid particles in adjacent sub-volumes being the corresponding virtual forces.

16. The method of claim 13 wherein determining comprises:

calculating a position of each of the virtual particles as an average of positions of only the fluid particles in the respective sub-volume;

calculating a radius of each of the virtual particles to include all the fluid particles of the respective sub-volume;

calculating a density of each of the virtual particles only from fluid particles in the respective sub-volume; and

calculating a mass of each of the virtual particles as a function of the density of the virtual particle.

17. The method of claim 13 wherein calculating the force comprises:

calculating a pressure force for each of the fluid particles, the pressure force being based on densities of the fluid particles of the sub-volume and the densities of the virtual particles of the adjacent sub-volumes;

calculating a viscosity force for each of the fluid particles, the viscosity force being based on the densities of the fluid particles of the sub-volume and the densities of the virtual particles of the adjacent sub-volumes.

18. The method of claim 13 further comprising determining, iteratively, velocity and position of the fluid particles as a function of forces.

19. In a non-transitory computer readable storage medium having stored therein data representing instructions executable by a programmed processor for smooth particle hydrodynamics, the storage medium comprising instructions for:

defining first particles each representing one or more second particles; and

simulating, for each second particle, second particle-to-second particle interaction for the second particles within a range and second particle-to-first particle interaction of each second particle within the range with first particles outside of the range.

20. The non-transitory computer readable storage medium of claim 19 further comprising dividing a simulation space into cells, the second particles distributed within the cells throughout the simulation space, wherein the first particles represent all of the second particles in respective cells, wherein simulating the second particle-to-second particle interaction comprises interaction within one of the cells, and wherein simulating second-particle-to-first particle interaction comprises interaction with neighboring cells, the range defining the neighboring cells.