Flux Reconstruction for Future High Accuracy Aerospace Design Tools

在计算流体动力学中，高阶精度方法已经被证明至少与标准二阶精度方案一样精确，如果不是显著更精确的话，同时使用显著更少的计算能力。因此，这些方法可以提供机会，以更好地模拟高度复杂的流体流动，如在原动机或发电设备，例如，通过利用快速的计算机速度目前可用然而，个别处理器的速度并没有大幅增加，在最近几年和更快的计算机是由于制造商简单地增加处理器的数量。这对评估流体流动造成了重大问题，因为分析必须在许多处理器上进行，并且大部分计算时间仅用于在不同处理器之间传输数据，而不是进行计算。高阶方法特别容易受到这种影响，并且当使用多个核心时，它们的性能要差得多。对于非常大的工作，这是一个巨大的问题，可能只有5%的计算机的处理能力实际上被用于计算，所以在使用当前的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的限制。通量重建（FR）试图保持使用高阶方法的好处，但使他们能够利用当今可用的计算机硬件。流体域被划分成单元，并且高阶方程用于求解每个单元内的感兴趣的参数及其通量（运动速率）。然而，由于每个元素是单独求解的，与相邻元素没有关系，因此该解在整个域中是不连续的。它是使用在每个元素的接口，这是用来'重建'一个连续的解决方案在整个domain.Modern流体分析软件包中使用的计算通量值进行校正主要是基于前面提到的二阶方程，这需要显着更多的计算能力，以达到相同的精度水平作为高阶方程。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，而没有与在许多处理器之间传输数据相关的问题。因此，这是一个新的解决方案，如果它可以成功地应用于实际的流体分析，虽然一些努力已经进入目前的理解FR方法，有一些限制周围的复杂性，鲁棒性和适用性的商业软件包。进行进一步的研究并尝试解决这些问题中的一些并提高该方法的效率。然后可以确定是否有潜力将其发展成为工业应用的有用的计算流体动力学工具。该项目是基础研究，因此其方向将由结果主导，但可能的探索领域包括开发方法，并将其应用于真实的问题，如Navier-Stokes方程。与计算流体动力学相关的典型问题也需要在整个项目过程中得到解决，例如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，这些公司需要高度准确的动态知识，高度复杂的流体流动。目前最先进的技术被用来模拟这些流场，但它是非常昂贵的计算和金钱方面。如果它被证明是可行的，FR可以大大降低运行模拟的成本，例如燃气涡轮机发动机。它还将使实施湍流建模技术变得更容易，这些技术可能导致革命性的新设计，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.