Research Initiation Award: Physically-based Modeling and Animating 3D Behaviors in Real-Time Using the Navier-Stokes Equations

9410459 Lobo计算机图形学中对流体建模真实感的需求日益增加，这就需要基于物理的技术。此外，这些技术不可能像计算流体动力学那样需要大量资源。该建议涉及一种方法的开发，该方法既能保证实时性能，又能在模拟流体表面的3D行为时提供物理真实性。该方法基于使用交错标记和单元来求解完整的二维不可压缩、粘性的Navier-Stokes方程，从而在模拟的二维有限差分网格中产生压力和二维速度。然后，利用计算得到的压力来提高流体的表面，从而提供流体流动的三维效果和行为，而无需进行全三维计算。正如我们的初步结果所示，这种方法能够在常用工作站（如Silicon Graphics Indigo）上实现逼真的实时流体模拟。在初步结果的基础上，提出了进一步发展该方法的研究。为了使这种方法更有用，我们建议提高它的灵活性、稳定性和能力。我们还建议将该方法用于开发算法，以模拟不同流体的混合，流体，在移动容器中晃动，以及模拟液态金属。＊＊＊

9410459 Lobo The increased need for realism in fluid modeling in computer graphics calls for physically-based techniques. In addition, these techniques cannot be as resource-demanding as those on computational fluid dynamics. This proposal concerns the development of an approach that promises real-time performance while providing physical authenticity in modeling the 3D behaviors of the surface of fluids. THe approach is based on solving the full 2D incompressible, viscous, Navier-Stokes equations using a staggered marker-and-cell, to yield the pressure and 2D velocity throughout the modeled 2D finite difference grid. Then, the computed pressures are used to raise the surface of fluid, thus providing the 3D effects and behaviors pf fluid flow, without the exorbiant expense of full 3D computation. As our initial results show, this approach is capable of achieving realistic real-time fluid simulation on a commonly available workstation such as a Silicon Graphics Indigo. Based on our promising intital results, research is proposed to develop this appproach further. To make this approach more useful, we are proposing to improve its flexibility, its stability, and its capabilities. We are also proposing to use the approach in developing algorithms that model blending of different fluids, fluids, that slosh in moving containers, and modeling liquid metals. ***