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

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.

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。

准确且高效地模拟各种流体的运动在计算机图形学中是一大重要方向。传统基于宏观不可压缩纳维-斯托克斯方程的求解方法由于方程本身的复杂性，需要非常复杂的数学建模与程序实现优化才做到高效和精确的计算。在该项目中，我们研究了基于格子玻尔兹曼模型的流体计算方法，该方法具有一系列优点，如高并行性，物理量守恒，低数值粘度等。但是其精度和稳定性较差一直限制了它在计算机图形学及流体仿真的相关领域的大规模应用。通过该项目的研究，我们对基于格子玻尔兹曼模型的流体模拟做了较为深入的研究与探索，主要针对碰撞建模，数值离散与逼近，无网格计算模型，湍流的代数化建模，流体场的连续尺度与涡旋结构可视化，以及真实感流体的渲染进行了研究。这些研究让我们对格子玻尔兹曼方法的理论有了较为深入的理解，在模拟方法上得出了一些重要的结论，如参数自适应调节非正交中心矩弛豫时间碰撞模型及连续尺度建模的重要性。同时该项目研究也让我们能成功模拟真实感烟雾及水流，并建立了一套程序库，且实现在多节点多GPU的系统上运行，推动了格子玻尔兹曼模型在计算机图形学领域的发展。作为应用，该项目研究的技术可以首先服务于对流体模拟有需求的电影特效及广告行业，这也是计算机图形学重要应用领域之一。另外，该项目研究的技术还可以做进一步扩展与改进，在未来应用于血流仿真及基于计算机辅助设计的工业制造等领域。