Parallel High-Order Adaptive Mesh Refinement Finite-Volume Schemes for Multi-Scale Physically-Complex Flows

计算流体动力学 (CFD) 已被证明是许多科学和工程领域的重要支持技术。尽管取得了许多进展，但仍然存在各种各样的多尺度、物理复杂的流动，人们对这些流动仍然知之甚少，而且事实证明通过计算手段预测这些流动非常具有挑战性。此类流动包括但不限于： (i) 先进航空航天推进、更一般的运输以及固定发电系统中遇到的湍流和反作用流； (ii) 气体、导电流体和等离子体的高速可压缩流； (iii) 微观尺度和/或稀薄的非平衡流动等。 与所有多尺度过程一样，小尺度物理直接影响观察到的大尺度行为。 为了能够为实际工程应用提供更常规的多尺度、物理复杂的流动解决方案，需要在数值方法和 CFD 算法设计方面取得进一步的重大进展。 因此，拟议的研究将集中于进一步开发一类或一系列高度可扩展、并行、自适应网格细化（AMR）、高阶、有限体积方案，以使用新兴的 HPC 架构来预测多块、贴体、非结构化和混合计算网格上的多尺度、物理复杂流。 申请人在过去 4-6 年期间在高阶空间离散化程序、具有局部解相关细化的各向异性和混合 AMR 网格划分策略以及高效并行算法设计方面的最新进展将为今后的研究奠定基础。 研究的关键要素将包括：（i）进一步开发各向同性和各向异性 AMR 技术，用于使用混合（结构化和非结构化）多块网格处理复杂的几何形状和界面，其中网格细化是通过基于伴随的解误差估计来指导的； (ii) 与高阶时间离散化方案相结合的高阶有限体积空间的增强和扩展，以提高各向异性和混合 AMR 网格的求解精度； (iii) 使用多级预处理技术开发改进的并行隐式时间推进方法； (iv) 设计高效且可扩展的并行方法，以有效利用具有浮点加速器的异构多核系统。所提出的计算工具针对多尺度、物理复杂问题的潜力、能力和性能将通过应用于层流和湍流反应流、非平衡微通道流以及高速空间等离子体流的预测来评估。 预计与当前使用的 CFD 算法相比，该研究的结果将在计算性能和分辨率能力方面将效率提高一个数量级以上。 这将使我们能够对更广泛的物理复杂流进行更常规的预测，以解决更多的实际问题。 对于航空航天推进和其他运输系统应用，改进对燃气轮机燃烧器中湍流燃烧流的预测将改进飞机发动机，降低排放、降低噪音输出、降低燃料消耗和减少对环境的影响。 特别是，拟议的研究将极大地增强申请人与两家领先的燃气涡轮发动机制造商（加拿大普拉特惠特尼公司和加拿大劳斯莱斯公司）正在进行的研究伙伴关系和合作，并在其中找到应用。

Computational fluid dynamics (CFD) has proven to be an important enabling technology in many areas of science and engineering. Despite the numerous advances, there is still a wide variety of multi-scale, physically-complex flows that remain both poorly understood and which have proven to be very challenging to predict by computational means. Such flows would include but are not limited to: (i) turbulent and reactive flows encountered in advanced aerospace propulsion, more general transportation, as well as stationary power generation systems; (ii) high-speed compressible flows of gases and conducting fluids and plasmas; and (iii) micro-scale and/or rarefied non-equilibrium flows among others. As with all multi-scale processes, the small-scale physics directly impacts the observed large-scale behaviour. In order to enable the more routine solution of multi-scale, physically-complex flows for practical engineering applications, further and rather significant advances in numerical methods and CFD algorithm design are required. The proposed research will therefore focus on the further development of a novel class or family of highly-scalable, parallel, adaptive mesh refinement (AMR), high-order, finite-volume schemes for the prediction of multi-scale, physically-complex flows on multi-block, body-fitted, unstructured, and hybrid computational meshes using new and emerging HPC architectures. The applicant's recent advances in high-order spatial discreatization procedures, anisotropic and hybrid AMR meshing strategies with local solution-dependent refinement, and efficient parallel algorithm design in the last 4-6 year period will provide the basis for the research moving forward. Key elements of the research will include: (i) the further development of isotropic and anisotropic AMR techniques for the treatment of complex geometries and interfaces using hybrid (structured and unstructured) multi-block grids where the mesh refinement is directed by adjoint-based estimates of the solution error; (ii) the enhancement and extension of high-order finite-volume spatial coupled with high-order temporal discretization schemes for improved solution accuracy on both anisotropic and hybrid AMR meshes; (iii) the development of improved parallel implicit time-marching methods using multi-level preconditioning techniques; and (iv) the design of efficient and scalable parallel methods for effective use of heterogeneous multi-core systems with floating-point accelerators. The potential, capabilities, and performance of the proposed computational tools for multi-scale, physically-complex problems will be assessed through application to the prediction of laminar and turbulent reactive flows, non-equilibrium micro-channel flows, as well as high-speed space plasma flows. It is anticipated that the results arising from the research will lead to a more than one order of magnitude improvement in efficiency when compared to CFD algorithms in current use, both in terms of computational performance and resolution capabilities. This will enable the more routine prediction of a far wider range of physically complex flows for many more practical problems. For aerospace propulsion and other transportation system applications, improved prediction of turbulent combusting flows in gas-turbine combustors would lead to improved aircraft engines with lower emissions, reduced noise output, lower fuel consumption, and less environmental impact. In particular, the proposed research will greatly enhance and find application in the applicant's on-going research partnerships and collaborations with two leading manufacturers of gas turbine engines: Pratt & Whitney Canada and Rolls-Royce Canada.