在复杂几何边界下基于带权最小二乘径向基函数的无网格格子玻尔兹曼流体仿真方法及其可视化研究

项目名称： 在复杂几何边界下基于带权最小二乘径向基函数的无网格格子玻尔兹曼流体仿真方法及其可视化研究

项目编号： No.61502305

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 计算机科学学科

项目作者： 刘晓培

作者单位： 上海科技大学

项目金额： 20万元

中文摘要： 计算机图形学里基于物理的流体仿真与渲染在需要高可信度流体动画的工业与研究中被大量应用，其中一大新型应用在电影特效。现有流体解法常依赖网格，在复杂边界下遇到挑战。粒子（无网格）解法更加灵活，却牺牲了精度。该研究项目将提出一种基于格子玻尔兹曼模型的无网格流体解法，在复杂边界下保证精度，易于求解。传统格子玻尔兹曼方法实现简单便于并行，但难以扩展到复杂边界。通过开发一种全新带权最小二乘径向基函数方案，我们将把传统格子玻尔兹曼方法转变为具有足够精度和稳定性的无网格流体解法。我们也会开发合适的湍流模型，在较小计算开销的情况下保留流体细节。另外，我们将开发全新的自适应网格索引将基于无网格算法的采样点搜索高效并行化，大大提升整体系统的效率。同时，我们还将开发高效的基于分散采样点的渲染与可视化方法。该研究成果将被用于灵活边界的流体仿真计算领域。我们着重考虑电影特效的应用，并生成烟和火的仿真与真实感渲染。

中文关键词： 流体模拟；时变现象模拟；基于物理的建模

英文摘要： In computer graphics, physically-based flow simulation and rendering give sufficient visual realism to generate believable flow animations that could be largely used in flow-centered industries/researches, with particular novel applications in special effects of movie industry. Existing flow solvers usually reply on meshes that could meet a lot of challenges under complex boundaries. Particle (meshless) solvers can be more flexible, but at the sacrifice of accuracy. This project aims to provide a meshless kinetic solver for flow simulations which is easier to solve with ensured accuracy under complex boundaries based on the lattice Boltzmann modeling. Traditional lattice Boltzmann approach is advantageous for much easier and naturally parallel solution, but with the drawback of extending to complex boundaries with sufficient accuracy. By developing a new weighted least-square radial basis function scheme, we will transform the traditional lattice Boltzmann method into a meshless kinetic solver with sufficient accuracy and stability. Appropriate turbulence models will also be developed to preserve flow details with less demand of computing resources. In addition, we will develop a completely new adaptive grid indexing scheme, which will make the searching based on scattered points much faster with high parallelism. This will significantly increase the system efficiency. Meanwhile, we will develop efficient rendering and visualization method based on scattered points. The final results of such research study can be used in any fields requiring flow simulations with boundary flexibility, and in particular, we will emphasize our application to generate realistic flows in nature that could be used as special effects in movie industries, such as the motion of smokes and fires.

英文关键词： Fluid Simulation;Time-Varying Phenomena Simulation;Physically-based Modeling