UNSTRUCTURED ADAPTIVE-MESH MODEL FOR STRATIFIED TURBULENCE IN ATMOSPHERIC FLOWS

这项研究的重点是新技术的开发。NERC的技术主题行动计划已经确定了新的数值模型开发领域，作为英国技能和专业知识应该发展的关键领域。nerc资助的研究的一个重要目标是“解决气候变化的关键问题”，因此“确定特定模型的局限性是促进进一步改进和推进我们的理解的重要组成部分”（http://www.nerc.ac.uk/research/issues/climatechange/predict.asp）。拟议的研究侧重于这一目标与大气流动的关系。当前用于分层旋转大气流动模拟的数值模型主要基于结构化计算网格，具有笛卡尔网格的刚性连接。对于某些问题（例如，飓风和长蜿蜒山谷中的流动），网格自适应具有实现其他方法无法获得的解决方案的潜力。然而，与已建立的结构化网格代码和最先进的非结构化网格工程进展相比，现有的非结构化网格模型仍处于起步阶段。此外，它们的实现倾向于强调小尺度对流现象和应急响应，由于噪声与信号比大，并且事件接近激励区域，因此相对容易建模。就波浪动力学的全范围而言，包括波-波和波-平均流相互作用等微妙之处，以及远离激励区域发生的大振幅事件，非结构网格技术的潜力仍然未知。为了证明非结构网格技术在模拟大气和海洋中全尺度流动方面的能力和竞争力，迫切需要开发一种先进的、完全非流体静力模型，用于在广泛的罗斯比、弗劳德和雷诺数制度下精确模拟旋转分层流动。在这项工作中，我们提出开发一种新的代码，用于在混合（任意多面体）网格上运行，用于求解具有柔性网格自适应能力的大气流体动力学非流体静力方程的许多可选形式。所提出的模型将反映结构网格模型EULAG（欧拉/拉格朗日）的分层、旋转湍流模拟能力，该模型已被证实的记录包括从实验室到中尺度，再到行星尺度的复杂流体问题的直接和大涡模拟。此外，我们将进行严格的研究和比较，将新模型和EULAG应用于复杂的基准和研究问题，结合与天气、气候和极端事件相关的尺度上的波动动力学和湍流产生。据我们所知，该提案首次深入研究了分层湍流中涉及惯性-重力波动力学实际计算的结构化和非结构化/自适应网格的相对性能。成果：1)新技术——高分辨率非流体静力非结构化网格模型。2)方法验证和非结构化网格在高级测试用例上的首次演示，这将提供有关此类网格对现实大气问题适用性的信息。3)定量研究网格自适应技术的性能特性。

This research is focused on new technology development. The NERC's Technologies Theme Action Plan, has identified the area of new numerical model development as a critical area where UK skills and expertise should be developed. An important goal of NERC-funded research is 'tackling the key issue of climate change', and as such 'identifying the limitations of a particular model is an important part of stimulating further improvements, and advancing our understanding' (http://www.nerc.ac.uk/research/issues/climatechange/predict.asp). The proposed research focuses on this goal in relation to atmospheric flows. Contemporary numerical models used in the simulation of stratified rotating atmospheric flows are predominantly based on structured computational meshes, with rigid connectivity of a Cartesian grid. For some problems (e.g., hurricanes and flows in long winding valleys), mesh adaptivity has a potential to achieve solutions not obtainable by other methods. However, existing unstructured mesh models are still in their infancy compared to both established structured-grid codes and state-of-the-art engineering advancements with unstructured meshes. Furthermore, their implementation tends to emphasize small-scale convective phenomena and emergency responses, which are relatively easy to model because of the large noise-to-signal ratio, and because of the proximity of events to the excitation region. Insofar as the full-range of wave dynamics are concerned -- including such subtleties as wave-wave and wave-mean-flow interactions, as well as large-amplitude events occurring far from the excitation region -- the potential of unstructured-mesh technology remains unknown. In order to prove the competence and competitiveness of unstructured-mesh technology for simulating all-scale flows in the atmosphere and oceans, there is a pressing need for developing an advanced, fully non-hydrostatic model for simulating accurately rotating stratified flows in a broad range of Rossby-, Froude-, and Reynolds-number regimes. In this work we propose to develop a novel code operating on hybrid (arbitrary polyhedra) meshes, for solving a number of optional forms of non-hydrostatic equations of atmospheric fluid dynamics with flexible mesh-adaptivity capabilities. The proposed model will mirror stratified, rotating turbulence-simulation capabilities of the structured-grid model EULAG (EUlerian/LAGrangian), the proven record of which includes direct and large-eddy simulations of complex fluid problems from laboratory-, to meso-, up to the planetary scale. Additionally, we shall perform rigorous studies and comparisons, by applying both the new model and EULAG to complex benchmarks and research problems combining wave dynamics and turbulence generation on scales relevant to weather, climate and extreme events. To the best of our knowledge, the proposal offers the first ever in-depth study of the relative performance of structured and unstructured/adapted meshes for stratified turbulent flows which involve practical computations of inertia-gravity-wave dynamics. Deliverables: 1) Novel technology --- a high-resolution non-hydrostatic unstructured mesh based model. 2) Method validation and first ever demonstrations of unstructured meshes on advanced test cases, which will deliver information about the applicability of such meshes to realistic atmospheric problems. 3) Quantitative study identifying performance properties of the mesh adaptivity technologies.