Solution of physically-complex flows using parallel high-order finite-volume methods and hydrid solution-adaptive meshes

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使能技术。尽管CFD已经相对成熟并取得了广泛的成功，但仍然存在各种物理上复杂的流动，这些流动仍然没有被很好地理解，并且被证明是非常具有挑战性的数值方法(例如，湍流和反应流以及非平衡微尺度流动)。随着CFD算法的发展，在过去的10-15年里，高性能计算系统的快速增长导致了千万亿级的并行系统，最近又出现了千万亿级的并行系统，其大小从几千到数十万个核心不等。计算硬件的这些进步反过来又为物理上复杂的流动的CFD创造了重要的机会。然而，需要在数值方法方面取得重大进展，以充分利用当前和未来的计算平台，从而使物理上复杂的流动的更常规的解决方案能够用于实际的工程应用。这项研究将致力于开发新的并行高阶有限体积和混合自适应网格加密(AMR)格式，用于使用并行和新兴的计算体系结构来预测物理复杂的流动。研究的主要内容将包括：(I)开发AMR和嵌入网格策略，用于使用混合(结构和非结构)多块网格处理复杂几何形状和界面；(Ii)开发基于双重加权重建和残差估计的各向异性网格精化技术；(Iii)设计高效和可扩展的、两级、粗-细粒度并行方法，以有效利用多核系统和浮点加速器；(Iv)开发改进的并行隐式时间推进方法；以及(V)增强高阶有限体积空间离散程序，以提高求解精度。所提出的方法的潜力和性能将通过应用于湍流反应流和非平衡微通道流动的预测而得到验证。

Computational fluid dynamics (CFD) has proven to be an important enabling technology in many areas of science and engineering. In spite of the relative maturity and widespread successes of CFD, there remain a variety of physically-complex flows, which are still not well understood and have proven to be very challenging to predict by numerical methods (e.g., turbulent and reactive flows and non-equilibrium micro-scale flows). Along with CFD algorithm development, the rapid increase in high-performance computing systems in the last 10-15 years has lead to terascale and, very recently, petascale parallel systems, ranging in size from a few thousand to hundreds of thousands of cores. These advances in computing hardware are, in turn, creating significant opportunities for CFD of physically-complex flows. Nevertheless, significant advances in numerical methods are required to fully exploit current and future computing platforms and thereby enable the more routine solution of physically-complex flows for practical engineering applications. The proposed research will focus on the development of novel parallel high-order finite-volume and hybrid adaptive mesh refinement (AMR) schemes for predicting physically-complex flows using parallel and new emerging computational architectures. Key elements of the research will include: (i) development of AMR and embedded mesh strategies for treatment of complex geometries and interfaces using hybrid (structure and unstructured) multi-block meshes; (ii) development of anisotropic mesh refinement techniques based on dual-weighted reconstruction and residual error estimates; (iii) design of efficient and scalable, two-level, coarse-fine-grain parallel methods for effective use of multi-core systems and floating-point accelerators; (iv) development of improved parallel implicit time-marching methods; and (v) enhancements of high-order finite-volume spatial discretization procedures for improved solution accuracy. The potential and performance of the proposed methodology will be demonstrated through application to the prediction of turbulent reactive flows, as well as non-equilibrium micro-channel flows.