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得到发展的关键领域。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促进我们理解的重要组成部分”（http：//www.nerc.ac.uk/research/issues/climatechange/predict.asp）。拟议的研究侧重于与大气流动有关的这一目标。用于分层旋转大气流模拟的现代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，飓风和蜿蜒山谷中的水流），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，现有的非结构网格模型仍然处于起步阶段相比，既建立结构网格代码和国家的最先进的工程进展与非结构网格。此外，它们的实施往往强调小规模的对流现象和应急反应，这是相对容易建模，因为大的噪声信号比，因为事件的激发区域的接近。尽管涉及到全方位的波浪动力学-包括诸如波-波和波-平均流相互作用等微妙问题，以及发生在远离激发区的大幅度事件-非结构网格技术的潜力仍然是未知的。为了证明非结构网格技术在模拟大气和海洋中的所有尺度流动方面的能力和竞争力，迫切需要开发一种先进的、完全非流体静力学的模型，用于在广泛的Rossby数、Froude数和Molds数范围内精确地模拟旋转分层流动。在这项工作中，我们建议开发一种新的代码操作混合（任意多面体）网格，用于解决一些可选形式的非流体静力学方程的大气流体动力学与灵活的网格自适应能力。拟议的模型将反映分层，旋转的连续性模拟能力的结构网格模型EULAG（欧拉/拉格朗日），其中已被证明的记录，包括直接和大涡模拟复杂的流体问题，从实验室，中，到行星尺度。此外，我们将通过将新模型和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浪动力学和湍流生成，进行严格的研究和比较。据我们所知，该提案提供了有史以来第一次深入研究的相对性能的结构化和非结构化/适应网格分层湍流，其中涉及实际计算的惯性重力波动力学。优点：1）新技术-高分辨率非静力非结构网格模型。2)在先进的测试案例中进行方法验证和首次非结构化网格演示，这将提供有关此类网格适用于现实大气问题的信息。3)确定网格自适应技术性能特性的定量研究。

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.