High-Order Adaptive Space-Time Flow Analysis

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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.