Song Oh-young, Kim Doyub, Ko Hyeong-Seok
Department of Digital Contents, Sejong University, Kwangjin-gu, Seoul, Korea.
IEEE Trans Vis Comput Graph. 2007 Jul-Aug;13(4):711-9. doi: 10.1109/TVCG.2007.1022.
We present a new fluid simulation technique that significantly reduces the nonphysical dissipation of velocity. The proposed method is based on an apt use of particles and derivative information. We note that a major source of numerical dissipation in the conventional Navier-Stokes equations solver lies in the advection step. Hence, starting with the conventional grid-based simulator, when the details of fluid movements need to be simulated, we replace the advection part with a particle simulator. When swapping between the grid-based and particle-based simulators, the physical quantities such as the level set and velocity must be converted. For this purpose, we develop a novel dissipation-suppressing conversion procedure that utilizes the derivative information stored in the particles, as well as in the grid points. For the fluid regions where such details are not needed, the advection is simulated using an octree-based constrained interpolation profile (CIP) solver, which we develop in this work. Through several experiments, we show that the proposed technique can reproduce the detailed movements of high-Reynolds-number fluids such as droplets/bubbles, thin water sheets, and whirlpools. The increased accuracy in the advection, which forms the basis of the proposed technique, can also be used to produce better results in larger scale fluid simulations.
我们提出了一种新的流体模拟技术，该技术可显著减少速度的非物理耗散。所提出的方法基于对粒子和导数信息的恰当运用。我们注意到，传统的纳维 - 斯托克斯方程求解器中数值耗散的一个主要来源在于平流步骤。因此，从传统的基于网格的模拟器开始，当需要模拟流体运动的细节时，我们用粒子模拟器替换平流部分。在基于网格的模拟器和基于粒子的模拟器之间切换时，诸如水平集和速度等物理量必须进行转换。为此，我们开发了一种新颖的抑制耗散的转换过程，该过程利用存储在粒子以及网格点中的导数信息。对于不需要此类细节的流体区域，使用我们在这项工作中开发的基于八叉树的约束插值剖面（CIP）求解器来模拟平流。通过多个实验，我们表明所提出的技术能够再现高雷诺数流体的详细运动，如液滴/气泡、薄水片和漩涡。构成所提出技术基础的平流精度的提高，也可用于在更大规模的流体模拟中产生更好的结果。
