Method and system for performing computer graphic simulation of a fluid using target-driven control

A system for performing computer graphic simulation of an incompressible fluid in motion, the system comprising:

• a simulator module having an input for receiving data that includes a scalar field that defines a physical property of the fluid or of matter suspended therein and a sequence of target scalar fields that define a desired temporal evolution of the scalar field;
• said simulator module being adapted to calculate a velocity vector u of the fluid at a plurality of points in the simulated fluid, at a plurality of time intervals, wherein said calculation is performed by solving an equation:
• ut=−u·∇u−∇p+f*+F
• where:
• p=hydrostatic pressure,
• f*=combination of forces acting on the fluid;
• F=a computed driving force that is defined by a predetermined function having closed-form terms based on an instantaneous state of the simulation at each simulation time step and that propels the fluid in such a manner that the resulting flow carries the scalar field towards the next target scalar field in said sequence thus avoiding any need for non-linear optimization,
• ut=is the vector of time derivatives of the velocity field u;
• an advection unit coupled to the computing unit for and being responsive to said velocity values at each time interval to advect the scalar field;
• a renderer module coupled to the advection unit and being responsive to the scalar field for producing a sequence of animation frames;
• and
• a storage unit coupled to the renderer module for storing the sequence of animation frames for subsequent display.

A program storage device readable by machine, tangibly embodying a program of instructions executable by the machine to perform method steps for performing computer graphic simulation of an incompressible fluid in motion, the method comprising:

• providing to a simulator module input data that includes a scalar field that defines a physical property of the fluid or of matter suspended therein and a sequence of target scalar fields that define a desired temporal evolution of the scalar field;
• simulating fluid motion by calculating a velocity vector u of the fluid at a plurality of points in the simulated fluid, at a plurality of time intervals, wherein said calculation is performed by solving an equation:
• ut=−u·∇u−∇p+f*+F
• where:
• p=hydrostatic pressure,
• f*=combination of forces acting on the fluid;
• F=a computed driving force that is defined by a predetermined function having closed-form terms based on an instantaneous state of the simulation at each simulation time step and that propels the fluid in such a manner that the resulting flow carries the scalar field towards the next target scalar field in said sequence thus avoiding any need for non-linear optimization;
• ut=is the vector of time derivatives of the velocity field u;
• using said velocity values at each time interval to advect the scalar field;
• sending the scalar field to a renderer module for producing a sequence of animation frames;
• and;
• storing the sequence of animation frames for subsequent display.

A computer storage medium having computer readable program code embodied therein for performing computer graphic simulation of an incompressible fluid in motion, the computer readable program code comprising:

• computer readable program code for causing the computer to provide input data to a simulator module, the input data including a scalar field that defines a physical property of the fluid or of matter suspended therein and a sequence of target scalar fields that define a desired temporal evolution of the scalar field;
• computer readable program code for causing the computer to simulate fluid motion by calculating a velocity vector u of the fluid at a plurality of points in the simulated fluid, at a plurality of time intervals, wherein said calculation is performed by solving an equation:
• where:
• ut=−u·∇u−∇p+f*+F
• where:
• p=hydrostatic pressure,
• f*=combination of forces acting on the fluid;
• F=a computed driving force that is defined by a predetermined function having closed-form terms based on an instantaneous state of the simulation at each simulation time step and that propels the fluid in such a manner that the resulting flow carries the scalar field towards the next target scalar field in said sequence thus avoiding any need for non-linear optimization;
• ut=is the vector of time derivatives of the velocity field u;
• computer readable program code for causing the computer to use said velocity values at each time interval to advect the scalar field;
• computer readable program code for causing the computer to render the scalar field so as to produce a sequence of animation frames;
• and
• computer readable program code for causing the computer to store the sequence of animation frames for subsequent display.