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High-Order Discontinuous Galerkin Fluid-Structure Interaction Methods

We present a high-order accurate scheme for fully coupledfluid-structure interaction problems. The fluid is discretized using adiscontinuous Galerkin method on unstructured tetrahedral meshes, andthe structure uses a high-order volumetric continuous Galerkin finiteelement method. Standard radial basis functions are used for the meshdeformation. The time integration is performed using a partitionedapproach based on implicit-explicit Runge-Kutta methods. Theresulting scheme fully decouples the implicit solution procedures forthe fluid and the solid parts, which we perform using two separateefficient parallel solvers. We demonstrate up to fifth order accuracyin time on a non-trivial test problem, on which we also show thatadditional subiterations are not required. We solve a benchmarkproblem of a cantilever beam in a shedding flow, and show goodagreement with other results in the literature.In addition, we create several simulations which are motivated byreal-world phenomena. First, we investigate flow around a thinmembrane at high-angle of attack, demonstrating the ability of theleading edge of the membrane to align with the incident flow. Examplesare provided in both two and three dimensions. Next, we considerbiologically inspired flight, by investigating wing-like structuresdriven in a flapping motion in both two and three dimensions.Finally, we demonstrate how the method may be used in acousticsproblems, simulating a tuning fork in three dimensions. Here weaccurately capture decay rates purely from the fluid-structureinteraction and without any damping coefficients built into thestructure model.