Flux Reconstruction for Future High Accuracy Aerospace Design Tools

在计算流体力学中，高阶精度方法已被证明至少与标准二阶精度格式的精度相当，如果不是显著高于标准二阶精度格式的话，而使用的计算能力要小得多。这导致了评估流体流动的主要问题，因为分析必须分散在许多处理器上，并且很大一部分计算时间仅用于在不同处理器之间传输数据，而不是用于计算。更高阶的方法特别容易受此影响，当使用多核时，它们的性能要差得多。对于非常大的任务，这是一个巨大的问题，可能只有5%的计算机处理能力实际用于计算，因此在使用当前计算和流体分析技术的实际流体动力学设计中使用高阶方程存在严重限制。通量重建(FR)寻求保持使用高阶方法的好处，但使它们能够利用当今可用的计算机硬件。将流体域划分为单元，并使用高阶方程来求解感兴趣的参数及其在每个单元内的流量(运动速率)。然而，由于每个单元都是单独求解的，与相邻的单元无关，所以整个区域的解是不连续的。FR提供了一种使用这些高阶方程进行流体分析的方法，同时仍然使用当前的计算技术，而不会出现与在许多处理器之间传输数据相关的问题。然后可以确定是否有潜力将其开发为用于工业应用的有用的计算流体力学工具。这个项目是基础研究，所以它的方向将由结果主导，但可能的探索领域包括开发方法，并将它们应用于实际问题，如Navier-Stokes方程。与计算流体力学相关的典型问题也需要在整个项目过程中解决，如FR方法的稳定性和准确性。该项目与航空航天公司直接相关，因为航空航天公司需要高度准确的动态、高度复杂的流体流动知识。目前使用最先进的技术来模拟这些流场，但在计算和金钱方面都非常昂贵。如果它被证明是可行的，FR可以显著降低在例如燃气轮机发动机上运行模拟的成本。它还将使湍流建模技术的实施变得更容易，这些技术可能会导致革命性的新设计，而这些设计目前无法使用，因为结果可能不准确。

In computational fluid dynamics, higher order-of-accuracy methods have been shown to be at least as, if not significantly more accurate than standard second order accuracy schemes while using significantly less computing power. Therefore, these methods could present opportunities to better model highly complex fluid flows, such as in prime movers or power generation equipment for example, through utilising the fast computer speeds available currently.However, individual processor speeds have not increased substantially in recent years and faster computers are as a result of manufacturers simply increasing the number of processors. This causes a major issue for evaluating fluid flows since the analysis must be split over many processors and a large proportion of computing time is devoted solely to transferring data between different processors rather than on calculations. Higher order methods are particularly susceptible to this and their performance is much poorer when multiple cores are used. For very large jobs, it is a huge issue with maybe only 5% of a computer's processing power actually being used for calculations, so there are severe limitations in using higher order equations in practical fluid dynamic design using both current computing and fluid analysis technology. Flux Reconstruction (FR) seeks to maintain the benefits of using higher order methods but enable them to make use of computer hardware that is available today. The fluid domain is divided into elements and high order equations are used to solve for the parameter of interest and its flux (rate of movement) within each element. However, because each element is solved individually with no relation to neighbouring elements, the solution is discontinuous through the domain. It is corrected using the calculated flux values at each element interface which is used to 'reconstruct' a continuous solution throughout the domain.Modern fluid analysis packages used in industry are mainly based on the second order equations mentioned previously, which require significantly more computing power to achieve the same level of accuracy as higher order equations. FR provides a means to conduct fluid analysis using these higher order equations while still using current computing technology without the issues associated with transferring data between many processors. It is therefore a novel solution if it can be successfully applied to practical fluid analysis and though some effort has gone into current understanding of the FR method, there are some limitations surrounding its complexity, robustness and applicability to commercial software packages.The aim of this PhD is to build on the current understanding of FR, conduct further research and attempt to both resolve some of these issues and improve the efficiency of the method. It can then be determined whether there is potential in developing it into a useful computational fluid dynamics tool for industrial applications. This project is fundamental research, so the direction it takes will be led by results, but likely areas of exploration include developing the methods, and applying them to real problems such as the Navier-Stokes Equations. Typical issues associated with computational fluid dynamics would also need to be addressed throughout the course of the project such as stability and accuracy of the FR method.The project is of direct relevance to aerospace companies where highly accurate knowledge of dynamic, highly complex fluid flows is required. Current state-of-the-art technology is used to model these flow fields but it is extremely expensive in both computational and monetary terms. If it proved to be viable, FR could significantly reduce the cost of running simulations on for example gas turbine engines. It would also make it easier to implement turbulence modelling techniques that could lead to revolutionary new designs that cannot currently be used since the results may not be accurate.