流体动画的形态保持理论与方法

Physically-based fluid animation has important application value, but often needs intensive computing cost. Since it takes a long time to produce high-resolution fluid animation, users often hope to first preview a low-resolution simulation result, iterativelly find suitable simulation paramaters, and then produce a high-resolution result with a similar shape as the low-resolution result. However, in practice, the fluid results from different resolution simulators often show large differences in fluid shape, which is an inherent shortcoming of traditional Eulerian simulation framework. Recent research works try to guide high-resolution simulation result to match the shape of low-resolution result, but loss physical accuracy of original high-resolution simulator, and increasing computational cost.In this proposal, we propose a novel research idea in opposite direction. Instead, we focus on conserving the shape of high-resolution result using low-resolution simulation, while decreasing computationalcost.We will systematically explore the theory and approach for fluid shape conservation. 1)analyze shape feature of fluid, and establish objective metrics for fluid shape;2)explore reasons and sources of shape deviation of low-resolution fluid simulation results, explain the regular patterns and mechanisms of fluid shape deviation，and formulate efficient shape correction method; 3）explore the influence of Poisson Solver on fluid shape and control it to correct shape, and develop fast preview and simulation framework that can quickly conserve high-resolution fluid shape using low resolution grid. This project will contribute novel fluid animation theory and methods for objective shape description, precise shape capturing, and efficient shape conservation for fluid simulation.

基于物理的流体动画具有重要应用价值，但计算开销大，制作高精度流体动画的周期长,用户常希望先用低精度模拟预览，迭代地设计好参数后，再计算得到形态一致的高精度结果。但在实际中，不同精度模拟的流体形态往往偏差很大，是传统欧拉模拟框架的一个固有缺陷。现有前沿研究试图引导高精度模拟与低精度形态匹配，但丢失了原高精度结果的物理准确性，并增加了计算量。本项目提出一个截然相反的新思路，着眼于利用低精度模拟保持原高精度准确形态，且减少高精度计算量，系统地探索流体动画的形态保持理论与方法。1)分析流体的形态特征，建立形态的客观表征和形态算子；2)探究不同精度流体形态偏差的根源，阐明流体形态偏差的规律和机理，建立有效的形态修正算子；3)探索泊松方程求解过程对流体形态的影响并修正控制，构建保持流体形态的快速预览和模拟新框架。预期将建立一套能客观描述形态、准确捕捉形态、高效保持形态的流体动画模拟的新理论和新方法。

基于物理的流体动画具有重要应用价值，但计算开销大，制作高精度流体动画的周期长, 用户常希望快速迭代地调整好参数后，再计算得到期望形态的高精度结果。但不同精度模拟生成的流体动画之间具有形态偏差，不利于流体动画的迭代设计控制。本项目针对流体形态问题进行了深入探索研究，提出了一系列能保持流体形态的流体动画模拟新方法。主要研究成果有：1）提出一种流体形态的客观度量和流体形态引导模拟方法；2）对流体动画数据分析，提出一种基于神经网络的流体动画快速模拟方法，能对流体模拟投影步的流体数据变换关系进行高效建模，在保持流体形态的同时提高计算速度；3）针对流体动画的投影步，提出了一种基于快速迭代正交投影的流体模拟方法，可显著加速流体模拟并较好地保持流体形态和精度；4）提出了一种预条件Schur Complement的流体模拟并行计算方法，支持对大规模流体动画的高效并行加速模拟和适应性优化计算；5）提出一种基于位置的流体控制方法，能根据动画设计师的需要，使流体形成快速变化的目标形态，并保持流体的自然运动。本项目深入探索了流体动画形态相关问题，贡献了一批流体模拟新方法，为后续相关研究与应用提供了基础。