High-Order Adaptive Space-Time Flow Analysis

这项研究是我们以前工作的自然延伸。我们的研究计划针对的基本问题，如高度非线性的流体-结构相互作用（FSI）和强烈的流致振动（FIV）在低质量比是常见的各种工程应用。例如，在更深的沃茨进行海上钻探就提出了新的安全、污染和设计问题。越来越柔性和细长的翼片从根本上改变了非定常流动分离和旋涡脱落模式。在这样的极端条件下，浮力罐和浮力罐的动态行为是低质量比下强FIV的结果。该提案的理论框架将利用谱有限元（SFEM）实现空间分辨率，后向微分公式BDF自适应时间步进实现时间精度，后验误差估计和自适应网格细化以确保所产生方法的成本效益。我们将扩展我们的非结构化网格有限时间李雅普诺夫指数（FTLE）流分析方法，自适应高阶SFEM驱动的误差估计，以实现成本效益，高精度的评估FTLE领域。FTLE场的脊定义了材料线（LCS），这些材料线有助于隔离材料相干性的根本原因，并揭示严格的独立于帧的设置中流动结构的复杂性和相互作用。我们将把这种方法应用于非定常流，以更好地理解流动分离和旋涡脱落之间的相互作用。将使用分层方法来估计空间离散化误差，并将开发新的度量标准，以自动调整计算网格，从而使解决方案验证过程自动化。我们将开发工具，通过详细的SFEM Navier-Stokes模拟，对旋转，平移和相互作用的刚体进行详细的分析和表征。我们在拉格朗日乘子框架内进行FSI建模，以提供力和力矩的准确预测。对于2D和3D单纯元，我们将构造并研究与Pn-Pn-1 Taylor-Hood速度-压力近似相容的乘子（力）的一组稳定多项式近似。此外，一个更简单的投影稳定套件的多项式逼近的乘数也将被调查。在FSI问题的背景下，这种技术还没有被充分利用。* 这些新近似值的准确性将在一组制造的解决方案上进行测量。有文献记载的问题，如Von Karman涡列、无阻尼自由振荡柱体和拖曳椭圆柱体的混沌旋转，将有助于确认有关几何形状上的力和力矩的准确性。

The proposed research is a natural extension of our previous work. Our research program targets fundamental issues such as highly nonlinear fluid-structure interaction (FSI) and strong flow-induced vibration (FIV) at low mass ratios that are common to a variety of engineering applications. For instance, offshore drilling in deeper waters raises new issues of safety, pollution, and design. Increasingly flexible and slender risers radically alter unsteady flow separation and vortex shedding patterns. In such extreme conditions, the dynamic behaviours of risers and buoyancy cans are the result of strong FIV at low mass ratios.***The theoretical framework for this proposal will leverage spectral finite elements (SFEM) for spatial resolution, backward differentiation formula BDF adaptive time-stepping for temporal accuracy, a posteriori error estimation and adaptive mesh refinement to ensure cost-effectiveness of the resulting approach.***We will extend our unstructured-grid finite-time Lyapunov exponent (FTLE) flow analysis methodology to adaptive high-order SFEM driven by error estimation to achieve cost-effective, highly accurate evaluation of the FTLE field. Ridges of the FTLE field define material lines (LCS) that are useful to isolate the root cause of material coherence and to reveal the complexity and interactions of flow structures in a rigorous frame-independent setting. We will apply the methodology to unsteady flow to better understand the interactions between flow separation and vortex shedding. Hierarchical methods will be used to estimate the space discretization error, and new metrics will be developed for automatically adapting the computational grids so as to automate the solution verification process.****We will develop tools to produce detailed analyses and characterization of rotating, translating, and interacting rigid bodies through detailed SFEM Navier-Stokes simulations. We cast the FSI modeling within the Lagrange multiplier framework to provide accurate prediction of forces and moments. For 2D and 3D simplicial elements, we will construct and investigate a stable suite of polynomial approximations of the multipliers (forces) compatible with the Pn-Pn-1 Taylor-Hood velocity-pressure approximation. Furthermore, a simpler projection stabilized suite of polynomial approximations of the multipliers will also be investigated. This technique has not been exploited to its full potential in the context of FSI problems. ***The accuracy of these new approximations will be measured on a set of manufactured solutions. Well-documented problems such as the Von Karman vortex-street, undamped freely oscillating cylinders and chaotic rotation of a towed elliptical cylinder will be useful to confirm the accuracy of forces and moments on relevant geometries.**