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Patent number 8762117 is assigned to

The following quote was obtained by the news editors from the background information supplied by the inventors: "Fluid simulation is an essential technology in many areas of technology. For example, it may be used in engineering where dynamic fluid simulation enables testing, optimization and validation of various designs and constructions, or for educational purposes where dynamic fluid simulation enables virtual experiments and exploration based learning. Other examples include virtual reality training simulators (where dynamic fluid simulation enables realistic behavior of ships, vehicles and other machines and devices, as well as load and cargo, or body fluids in surgery training simulators, etc.), environment illustrations in motion pictures (where fluid simulation enable cost effective and spectacular computer generated visual effects of flooding, splashing, explosions and general representation of water and other fluids in containers, floods, lakes and oceans), and contemporary computer games, where interactive simulation of dynamic fluids enriches game play and enables special effects, such as water splashes and explosions.

"In a conventional method for pseudo particle based simulation of dynamic fluids, the motion of the simulated fluid is governed by penalty forces that act to preserve the fluid volume and mass density. In addition, the fluid velocity can be corrected by means of a projection of the velocities of a compressible fluid upon a velocity field of a corresponding incompressible fluid. The penalty force method sets severe restriction on the size of the time step of the time discrete computer simulation, since the time step must be small enough to resolve fluctuations of the fluid that propagate through the fluid with the speed of sound of the fluid. The fluid sound speed is often 10-100 times that of other relevant speed scales of the system.

"As will become apparent from the description below, conventional penalty force methods are computationally heavy and inefficient in representing dynamic near incompressible fluids. Furthermore, conventional penalty force methods commonly experience severe stabilization problems.

"Therefore, conventional methods use a variety of approaches for dealing with the described stability problem. Such methods may comprise a viscosity or damping force being added to the pressure force. The damping of velocities will stabilize the dynamic fluid simulation for larger pressure forces, and thus allow for simulation of more incompressible fluids. However, very large viscosity forces are needed to substantially stabilize these incompressible fluid simulations. In the limit of very large viscosity forces, these forces will themselves start to contribute instabilities to the simulation, and in addition such large viscosity forces will also give highly unrealistic simulations of even the most ordinary well known fluids that have relatively low internal viscosity.

"Thus, the overall effect on the dynamic fluid simulation of a very large viscosity is a slightly more stable simulation, a fluid with a still unrealistic degree of compressibility, and a fluid with too much internal viscosity to be realistic."

In addition to the background information obtained for this patent, VerticalNews journalists also obtained the inventors' summary information for this patent: "A problem to which the invention relates is the problem of simulating dynamic fluids with an improved computational efficiency.

"This problem is addressed by a method for simulating dynamic fluids comprising a plurality of pseudo particles. The method comprising the steps of: defining a fluid mass density of the pseudo particle masses; defining a mass density constraint such that the mass density on each pseudo particle is constrained to a reference mass density of a real fluid, whereby an instant propagation of density fluctuations through the entire fluid system is enabled; performing constraint stabilization on said mass density constraint using a time stepping function, wherein said time stepping function is arranged to conserve global physical symmetries and is stable for violations of said mass density constraint; solving a linear system of equations for said mass density constraint in order to calculate density constraint forces; calculating new time discrete pseudo particle velocities from previous pseudo particle velocities with addition of velocity increments calculated from said density constraint forces; and calculating new time discrete pseudo particle positions from the previous pseudo particle positions with additions of the position increments calculated from said new pseudo particle velocities.

"This problem is further addressed by an apparatus for simulating dynamic fluids, comprising a processing unit capable of generating a plurality of pseudo particles and performing a dynamic fluid simulation of said plurality of pseudo particles, said apparatus being adapted to define a fluid mass density of the pseudo particle masses, define a mass density constraint such that the mass density on each pseudo particle is constrained to a reference mass density of a real fluid, whereby an instant propagation of density fluctuations through the entire fluid system is enabled, perform constraint stabilization on said mass density constraint using a time stepping function, wherein said time stepping function is arranged to conserve global physical symmetries and is stable for violations of said mass density constraint, solving a linear system of equations for said mass density constraint, and calculating density constraint forces, calculating new time discrete pseudo particle velocities from previous pseudo particle velocities with addition of velocity increments calculated from said density constraint forces, and calculating new time discrete pseudo particle positions from the previous pseudo particle positions with additions of the position increments calculated from said new pseudo particle velocities.

"By having a combined time stepping, constraint stabilization and relaxation method that provides global conservation of physical symmetries of the dynamic simulated incompressible fluid and provides a robust physical and numerical stability under large constraint violations, the method according to the invention provides a substantial improvement in computational efficiency over other known methods.

"If the pseudo particles violate a boundary condition of a container, a body floating in the simulated fluid, the method may further comprises the steps of: adding a smoothed boundary density to boundary condition violating pseudo particles; defining a mass density constraint at the boundary such that the mass density of the pseudo particles violating the boundary condition to the reference mass density of the fluid are constrained; and adding this boundary mass density constraint to the mass density constraint.

"If the simulated fluid requires a lower degree of viscosity, the method may further comprise the step of: relaxing the mass density constraint such that the mass density constraint dissipates energy upon constraint violation and stabilization in dependence of the mass density constraint being satisfied on the average over time. If, however, the simulated fluid requires a higher degree of viscosity, the method may further comprise the step of: adding a kinematic constraint arranged to constrain the pseudo particle velocities of neighbouring particles.

"If a lower degree of fidelity and precision is required, the method may further comprise the step of: solving the linear system of equations by means of sequential solutions to each of the constraint equations, which utilizes the Gauss-Seidel iterative method for solution of linear systems of equations.

"If a higher degree of fidelity and precision is required, the method may further comprise the step of: solving the linear system of equations by means of the conjugate gradient iterative method or a direct sparse linear solver method.

"Additionally, the method may further comprise the steps of: implementing an interaction constraint, said interaction constraint being entirely consistent with the mass density constraint and with the linear equations, arranged to simulate the interaction between the simulated fluid and a plurality of rigid bodies containing the simulated fluid, floating on top of or inside the simulated fluid; and implementing a rigid body constraint, wherein said rigid body constraint is a non-penetration constraint and a dry friction constraint, arranged to simulate the interaction between rigid bodies, which in effect couples to the simulated fluid through those rigid bodies containing the simulated fluid, floating on top of or inside the simulated fluid. Thus, the rigid body simulation may be made an integral part of the fluid simulation by adding additional equations to the linear systems of equations, thus resulting in an entirely consistent simulation model.

"The method may also comprise the step of adding a rigid body inequality constraint, which extends the linear system of equations to a linear complimentarity problem, whereby the step of solving the linear system of equations further comprises an extension to corresponding projected versions far solving linear complimentarity problems.

"Further advantageous embodiments of the apparatus and computer program product are set forth in the dependent claims and correspond to the advantageous embodiments already set forth with reference to the previously mentioned method."

URL and more information on this patent, see: Bodin, Kenneth; Lacoursiere, Claude; Servin, Martin. Method, an Apparatus and Computer Program Product for Simulating Dynamic Fluids. U.S. Patent Number 8762117, filed

Keywords for this news article include: Technology,

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