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支持技术。尽管CFD相对成熟并取得了广泛的成功，但仍然存在各种物理复杂的流动，这些流动仍然没有得到很好的理解，并且已被证明是非常具有挑战性的数值方法预测（例如，湍流和反应性流动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万亿级和最近的千万亿级并行系统的出现，其规模从几千到几十万核不等。计算硬件的这些进步反过来又为物理复杂流动的CFD创造了重要的机会。然而，数值方法的重大进步需要充分利用当前和未来的计算平台，从而使实际工程应用中物理复杂流的更常规解决方案成为可能。提出的研究将侧重于开发新的并行高阶有限体积和混合自适应网格细化（AMR）方案，用于使用并行和新兴的计算架构预测物理复杂的流动。研究的关键要素将包括：(i)开发AMR和嵌入式网格策略，用于使用混合（结构和非结构）多块网格处理复杂的几何形状和界面；（ii）基于双加权重建和残差估计的各向异性网格细化技术的发展；（iii）设计高效、可扩展、两级、粗-细粒度并行方法，以便有效地使用多核系统和浮点加速器；（iv）发展改进的并行隐式时间推进方法；(v)提高求解精度的高阶有限体积空间离散化程序。所提出的方法的潜力和性能将通过应用于预测湍流反应流动以及非平衡微通道流动来证明。

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.