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

将开发最先进、高精度和高效率的数值算法，用于模拟具有工程和技术重要性的多物理和多相流动。这些新的数值方法也被设计成可针对数量极大地增加的计算机处理器进行扩展，因此很容易在当前和即将到来的高性能计算平台上实现。它们将构成一种使能技术，供科学、工程、医学、工业和军事从业者使用。这项技术的主要应用将是柴油发动机喷油器的设计，现代航空燃气轮机涡流喷射器的设计，用于燃烧、喷漆、喷雾冷却、农业灌溉应用的平板风扇喷嘴的设计，将天然气转化为液体的海上设施的设计，患者特定药物输送的设计，以及飞机机翼防冻装置的设计。这些方法的高精度和高效率将使参数研究和设计优化程序、更复杂的几何和模型成为可能，而这些到目前为止已经被证明是昂贵的。将发展一种结合自适应网格加密、易于并行的谱单元方法和流体矩方法的混合方法来数值模拟多相流。主要研究人员已经开发了一种适用于不可压缩和可压缩多相流的自适应、并行的流体力矩算法。这项提议的主要目标是将主要调查人员以前的工作提高到更高的水平，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。将实现一种健壮的单元集成半拉格朗日方法，以便每个矩形网格单元中的每一种材料都具有从出发区域到目标区域的单独映射，从而所有映射的组合将计算区域划分为网格。本文将发展一种切割单元谱单元算法，用于数值求解压力投影方程(Helmholtz方程)和多物质流动中粘性力的数值求解。新算法的好处将是在预测存在薄剪切层和/或薄热边界层的变形材料边界的形状时，大大提高了精度(而不损失稳健性)。

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.