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A High-Order Computational Framework for Simulating Flows around Rotating and Moving Objects Open Access

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Fluid flows around rotating and moving objects are ubiquitous in engineering applications. For example, the bubbly flow around a marine propeller, the high-speed airflow in a turbojet engine. To simulate these flows, there are two major challenges: accurate capturing of vortical flow structures that are sensitive to numerical dissipation; accurate and efficient incorporation of moving geometries into a flow solver. The present work tackles these challenges by developing a high-order computational framework for both 2D and 3D flows. The spectral difference (SD) method, which is a high-order accurate and low-dissipative method, is employed to deal with the first challenge. To handle the second challenge, a sliding-mesh approach has been designed for the SD method for the first time. In this approach, a computational domain is decomposed into multiple non-overlapping subdomains that may enclose moving objects. A subdomain is allowed to freely rotate relative to its neighbors, resulting in one or multiple nonconforming sliding interfaces in between. A novel curved dynamic mortar method is developed for communication on the nonconforming sliding interfaces to ensure continuity of solution and conservation of fluxes. The resulting framework consists several unstructured-mesh flow solvers and is further extensible. A 2D sliding-mesh SD (SSD) solver for rotating objects is developed at first to verify the numerical methods. It is shown that the new sliding-mesh method maintains the high-order accuracy of the SD method. Meanwhile, this method is found to be highly efficient by introducing negligible computational cost to the overall computation. A 2D sliding and deforming-mesh SD (SD^2) solver is subsequently developed for moving objects with combined rotational and translational motions. In this solver, the integration of the sliding-mesh method and the arbitrary-Lagrangian-Eulerian (ALE) method greatly improves the mesh and solution qualities compared to traditional conforming ALE methods that are limited to small rotational motions to avoid large mesh skewness. A 3D SD^2 solver is finally developed for more realistic flows. This solver is able to handle multiple sliding interfaces with different orientations, which makes simulation of complex geometries very flexible. From parallelization studies, it is also confirmed that this framework is efficient for parallel computing on distributed memory clusters. This framework is applicable to a wide range of engineering problems. For example, the energy-extraction by oscillating foils and wind turbines, the flow mixing in stirred vessels, the propulsion performances of propellers.

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