Animating turbulent fluid with a robust and efficient high‐order advection method,Computer Animation and Virtual Worlds

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Animating turbulent fluid with a robust and efficient high‐order advection method
Computer Animation and Virtual Worlds ( IF 0.9 ) Pub Date : 2020-07-01 , DOI: 10.1002/cav.1951
Jian Zhu ₁ , Silong Li ₁ , Ruichu Cai ₁ , Zhifeng Hao _{1,

2} , Guoheng Huang ₁ , Bin Sheng ₃ , Enhua Wu ₄

Affiliation

The accuracy of advection has a great influence on the visual effect of fluid simulation. Constrained interpolation profile (CIP) method has been an important advection scheme because of its third‐order accuracy and the fact that it only needs to be performed over a compact stencil, but extending it to high‐dimensional advection equations is not easy, because it involves complex calculations and large memory overheads, and is usually unstable. In this article, we propose a stable and efficient three‐dimensional (3D) CIP scheme which can maintain high accuracy but requires low computation and memory cost. We first construct an efficient two‐dimensional (2D) CIP scheme based on dimensional splitting and local Taylor expansions, and then propose an effective way to extend it for 3D applications without decreasing the computational accuracy or affecting the stability. The experimental results show the advantages of our method over the state‐of‐the‐art advection schemes.

中文翻译：

使用稳健高效的高阶对流方法动画湍流

对流的准确性对流体模拟的视觉效果影响很大。约束插值剖面 (CIP) 方法一直是一种重要的平流方案，因为它的三阶精度以及它只需要在紧凑模板上执行的事实，但将其扩展到高维平流方程并不容易，因为它涉及复杂的计算和大的内存开销，并且通常不稳定。在本文中，我们提出了一种稳定高效的三维 (3D) CIP 方案，该方案可以保持高精度，但需要低计算和内存成本。我们首先构建了一个基于维度分裂和局部泰勒展开的高效二维 (2D) CIP 方案，然后提出一种有效的方法将其扩展到 3D 应用程序，而不会降低计算精度或影响稳定性。实验结果表明我们的方法优于最先进的对流方案。

更新日期：2020-07-01

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