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3D Realtime Fluid Animation by Navier-Stokes Equations

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3D Realtime Fluid Animation by Navier-Stokes Equations University of Central Florida STARS UCF Patents Technology Transfer 7-16-1996 3D realtime Fluid Animation by Navier-Stokes Equations Niels Da Vitoria Lobo Chen Jinxiong University of Central Florida Find similar works at: https://stars.library.ucf.edu/patents University of Central Florida Libraries http://library.ucf.edu This Patent is brought to you for free and open access by the Technology Transfer at STARS. It has been accepted for inclusion in UCF Patents by an authorized administrator of STARS. For more information, please contact [email protected]. Recommended Citation Da Vitoria Lobo, Niels and Jinxiong, Chen, "3D realtime Fluid Animation by Navier-Stokes Equations" (1996). UCF Patents. 3. https://stars.library.ucf.edu/patents/3 Illlll llllllll Ill lllll lllll lllll lllll lllll 111111111111111111111111111111111 US005537641A United States Patent 1191 [111 Patent Number: 5,537,641 da Vitoria Lobo et al. f451 Date of Patent: Jul. 16, 1996 [54) 3D REALTIME FLUID ANIMATION BY Helman et al, "Surface Representations of Two-and NAVIER-STOKES EQUATIONS Three-Dimensional Fluid Topologies", Visualizations (1990). [75] Inventors: Niels da Vitoria Lobo; Chen Jinxiong, both of Orlando, Fla. Primary Examiner-Almis R. Jankus [73] Assignee: University of Central Florida, Assistant Examiner-Rudolph J. Buchel Orlando, Fla. Attorney, Agent, or Finn-Brian S. Steinberger [21] Appl. No.: 158,442 [57] ABSTRACT [22] Filed: Nov. 24, 1993 This is a method for physically-based modeling of three 6 [51] Int. Cl. ..................................................... G06T 17/00 dimensional (30) general fluid animation in computer (52] U.S. Cl .............................................. 395/119; 395/152 graphics. By solving the two dimensional (20) Navier­ [58] Field of Search ..................................... 395/118, 119, Stokes equations using a Computational Fluid Dynamics 395/126, 152 method, we map it into 30 using the corresponding pres­ sures in the fluid flow field. The method achieves realistic [56] References Cited real-time fluid animation by solving the physical governing laws of fluids but avoiding the extensive 3D fluid dynamics U.S. PATENT DOCUMENTS computation. Unlike previous computer graphics fluid mod­ 4,469,601 9/1984 Beaver et al. .......................... 210/658 els, our approach can model many different fluid behaviors 4,809,202 2/1989 Wolfram ................................. 364/578 by changing the internal or external boundary conditions. It 4,817,039 3/1989 Frost . .. ................. ..... ......... ..... 364/420 can also model different kinds of fluids by varying the Reynolds number. In addition, we have generated several OTHER PUBLICATIONS ways to view the animation of fluid flow field, the streakline Ji et al, "The Boundary Element Method For Boundary of the flow field and the blending of fluids of different colors. Control of Linear Stokes Flow", Decision and Control Our model can serve as a testbed to simulate many more (1990). fluid phenomena which have never been successfully mod­ Kenwright, et al, "A 3-D Streamline Tracking Algorithm eled. Using Dual System Function," Visualizations (1992). Haggard, et al "Computational Fluid Dynamics on the Transputer; System Organization and Performance," System Theory (1990). 16 Claims, 8 Drawing Sheets r~ .. I . ~-··· • I I I ~. ·" I U.S. Patent Jul. 16, 1996 Sheet 1of8 5,537,641 j + l v i;j + l /2 j p u i;j i + l /2;j u v p j - l ·- i - l i + 1 Figure l: The staggered marker-and-cell mesh U.S. Patent Jul. 16, 1996 Sheet 2 of 8 5,537,641 update the external boundaries 21 O calculate current pressures: p 220 calculate velocities: u, v 230 update the internal boundaries 240 Figure 2 illustrates a program flow chart for calculating state-to-state calculations U.S. Patent Jul. 16, 1996 Sheet 3 of 8 5,537,641 initialize graphics and parameters Fig. 4 310 process the input information Fig. 5 320 calculate the current fluid field u, v, p, boundaries, etc. Fig. 2 330 draw current fluid frame (real-time animation) Fig. 6 340 No Yes Figure 3 illustrates the main program flowchart for 3D real-time animation U.S. Patent Jul. 16, 1996 Sheet 4 of 8 5,537,641 Start 400 initialize 3D graphics 410 initialize fluid boundary conditions 420 initialize fluid colors and other 430 Figure 4 illustrates an algorithm flowchart of the initialize graphics and parameters step of Fig. 3 U.S. Patent Jul. 16, 1996 Sheet 5 of 8 5,537,641 Start 500 ~ r -...., No update Re? \.. 510..1 Yes \ Raise or lower Re value (1-1000) 520 / \ 'I r " No I update ~t? ) \... 530 Yes \ I Raise or lower ~t value (0-0. l) 540 1/ ·' No Rotate the graphics? 550 -------. Yes set on/off indicating rotation 560 end 570 Figure 5 illustrates an algorithm flowchart for updating parameters for the user interface U.S. Patent Jul. 16, 1996 Sheet 6 of 8 5,537,641 Start 600 No Yes for every grid (i, j), l=i* gridscale, J j* gridscale, K=p(i, j)* heightscale draw vector from (I, J, K) to (l+u(i, j), J+v(i, j), K) 620 for every grid (i, j), l=i* gridscale, J j* gridscale, K=p(i, j)* heightscale using the graphics polygon tool to draw and shade the fluid flow field as a surface. 630 End 640 Figure 6 illustrates the 30 drawing process U.S. Patent Jul. 16, 1996 Sheet 7 of 8 5,537,641 Figure 7 U.S. Patent Jul. 16, 1996 Sheet 8 of 8 5,537,641 Figure 8 5,537,641 1 2 3D REALTIME FLUID ANIMATION BY Another object of the invention is to use a calculator based NAVIER-STOKES EQUATIONS numerical method based on the corresponding pressures and velocities of 2D coordinates to produce the coordinate value The present invention relates generally to three dimen­ of the third dimension. sional (3D) visual animation, and more specifically to simu- 5 Another object of this invention is to use computer lating 3D realtime fluid animation using pressure and veloc­ graphics to produce 3D displays of the realtime fluid ani­ ity obtained from a two dimensional (2D) representation mation. modelled by Navier-Stokes Equations. This application was Another object of this invention is to be able to simulate funded in part from U.S. Army contract N61339-92-K-0001. different kinds of fluids in a realtime graphics simulation. 10 BACKGROUND OF THE INVENTION Another object of the invention is to simulate different kinds of fluids in realtime by varying properties such as the Modelling fluid flow dynamics is helpful for designing Reynolds number. structures such as but not limited to ship hulls, pipelines and airfoils. Thus, three-dimensional (3D) animation of fluid Another object of this invention is to be able to show a 3D flow dynamics is necessary to represent for example, the 15 display of the animation of the fluid flow field, the streakline flow of water past a ship's hull, fluid in a pipeline, fluid flow of the flow field and the blending of fluids of different colors. of air past an airfoil, or fluid in blood vessels. Another object of this invention is to simulate specific Further, the movie and advertising industries, military and applications such as the effects of a motorized boat on a commercial training systems, virtual reality games and river, and blood within a vessel. entertainment, and scientific research have been increasingly 20 The file of this patent contains at least two drawings turning to 3D modeling to obtain realistic visual simulations executed in color. Copies of this patent with color drawings of physical phenomena. will be provided by the Patent and Trademark Office upon Present computer graphic processes can be used to model request and payment of necessary fee. some behavioral characteristics of fluid flow but cannot 25 model the 3D dynamics of flow, and the effects caused by the BRIEF DESCRIPTION OF THE FIGURES internal and external boundaries of the fluid flow. FIG. 1 illustrates a staggered marker-cell mesh for the Real-time animation of fluids is not available in existing arrangement of a fluid flow field. systems where the movement of fluids on a graphical FIG. 2 illustrates an algorithm flow chart for calculating computer is calculated and animated at the same time. 30 Real-time animation is difficult to achieve where calcula­ state-to-state calculations of current pressure and velocities. tions are intensive. Where the simulation calculations take FIG. 3 illustrates an algorithm flow chart for 3D realtime so much time to occur on a computer, they cannot be simulation of fluids. completed in regular intervals of time at the pace of the FIG. 4 illustrates an algorithm flow chart of the process physical process that is being simulated. Ideally, each frame 35 for initializing the 3D Graphics and boundary conditions. in animation must be calculated fast enough in order to FIG. 5 illustrates an algorithm flow chart for updating the achieve real-time animation. parameters by user interface. Thus, no present systems are known to exist that produce FIG. 6 illustrates an algorithm flow chart for the 3D realistic looking 3D modeling and simulation of fluid flows drawing process. in realtime. 4-0 FIG. 7 shows an animation frame of velocity vectors of Another problem with creating 3D animation in prior art the fluid flow field. systems is that layers of 2D grids(x,y) in the -z- axis must FIG. 8 shows an animation frame of a 3D fluid flow. be attached to form a 3D grid. Calculations for the third dimension must be calculated at each node on each 2D grid in the z direction. These calculations are numerous, exten- 45 DETAILED DESCRIPTION OF THE sive and time consuming. INVENTION A further problem is that no one has been able to actually Before explaining the disclosed embodiments of the solve Navier-Stokes equations for 3D simulation using present invention in detail it is to be understood that the numerical methods calculated by computer in realtime.
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