A spectrally accurate hybrid moment-of-fluid and level set method for multiphase flows

为模拟具有工程和技术重要性的多物理场和多相流，将开发最先进的、高精度和高效率的数值算法。这些新的数值方法也被设计为可扩展的相对于一个非常增加的计算机处理器的数量，因此很容易实现在当前和即将到来的高性能计算平台。它们将成为科学、工程、医学、工业和军事从业人员使用的一种赋能技术。该技术的主要应用将是柴油发动机的燃料喷射器的设计，现代飞机燃气涡轮机发动机中的旋流喷射器的设计，用于燃烧、喷漆、喷雾冷却、农业灌溉应用的扁平扇形喷嘴的设计，用于将天然气转化为液态的离岸设施的设计，患者特定药物输送，以及机翼防冻装置的设计。这些方法的高精度和高效率将允许参数研究和设计优化程序，更复杂的几何形状和模型，到目前为止，已被证明是昂贵的。一个混合的方法耦合自适应网格细化，易于并行化，谱元方法与流体的动量方法将被开发用于数值模拟多相流。主要研究人员已经开发了一个自适应的，并行的，不可压缩和可压缩的多相流的流体矩算法。 该提案的主要目标是将主要研究人员以前的工作提升到更高的水平，其中每种材料都有自己的光谱元素表示，包含多种材料的网格单元将包含每种材料的独立解展开。将实施稳健的单元集成半拉格朗日方法，使得每个矩形网格单元中的每种材料具有从出发区域到目标区域的单独映射，使得所有映射的组合镶嵌计算域。 将开发一种切割单元谱元算法，用于数值求解压力投影方程（Helmholtz方程）和数值求解多物质流中的粘性力。 新算法的好处将是在预测变形材料边界的形状时大大提高精度（而不损失鲁棒性），其中存在薄剪切层和/或薄热边界层。

State-of-the-art, highly accurate and efficient numerical algorithms will be developed for simulating multi physics and multi-phase flows of engineering and technological importance. These new numerical methods are also designed to be scalable with respect to an exceedingly increasing number of computer processors, and thus easily implemented on the current and immediately future high-performance computing platforms. They will constitute an enabling technology for use by practitioners in science, engineering, medicine, industry and military. The primary applications of this technology will be to the design of fuel injectors for diesel engines, the design of swirling flow injectors in modern aircraft gas turbine engines, the design of flat fan nozzles employed in combustion, painting, spray cooling, agriculture irrigating applications, the design of off-shore facilities for the conversion of natural gas into liquid state, patient specific drug delivery, and the design of aircraft wing anti-freezing devices. The high accuracy and efficiency of these methodologies will allow parameter studies and design optimization procedures, more sophisticated geometries and models, which have proved until now to be prohibitively expensive.A hybrid methodology coupling an adaptive mesh refinement, easily parallelizable, spectral-element method with the moment-of-fluid method will be developed for numerically simulating multi-phase flows. The principal investigators have already developed an adaptive, parallel, moment-of-fluid algorithm for incompressible and compressible multiphase flows. The primary objective of this proposal is to take the previous work of the principal investigators to a higher level, where each material has its own spectral-element representation, and a grid cell containing multiple materials will contain independent solution expansions for each material. A robust cell integrated semi-Lagrangian method will be implemented so that each material in each rectangular grid cell has a separate mapping from the departure region to the target region in such a way that the combination of all mappings tessellate the computational domain. A cut-cell spectral-element algorithm will be developed for numerically solving the pressure projection equation (a Helmholtz equation) and for numerically solving for the viscous forces in multi-material flows. The benefits of the new algorithm will be the greatly improved accuracy (without loss of robustness) in predicting the shape of deforming material boundaries where there are thin shear layers and/or thin thermal boundary layers.