An Eulerian-ALE Embedded Boundary Method for Turbulent Fluid-Structure Interaction Problems

The FInite Volume method with Exact two-phase Riemann problems (FIVER) is a robust Eulerian semi-discretization method for compressible multi-material (fluid-fluid, fluid-structure, or multi-fluid-structure) problems characterized by large density jumps and highly nonlinear structural motions and deformations. Its key components include an embedded boundary method for Computational Fluid Dynamics (CFD), the construction and solution of local, exact, two-phase Riemann problems at the material interfaces, and a conservative algorithm for computing the finite element representation of flow-induced loads on the structure. Originally developed for inviscid multi-material problems, FIVER is extended in this paper to turbulent viscous fluid-structure interaction problems. To this effect, it is equipped with a carefully designed extrapolation scheme for populating the ghost fluid values required for the construction of a second-order spatial approximation of the viscous and source terms of the governing flow equations. Its load distribution algorithm is also extended to account for the contribution of the viscous stress tensor. To maintain the boundary layers resolved during large displacements, rotations, and/or deformations of the structure, the governing flow equations are formulated in a rigid instance of the Arbitrary Lagrangian Eulerian (ALE) framework, and FIVER is further equipped with the corotational method for updating the rigid body motion of the CFD mesh. This non deformable mesh motion enables the original non body-fitted CFD mesh to follow the boundary layers, and therefore minimize the need for complex adaptive mesh refinement. To achieve nonlinear stability, temporal discretization is performed using an extension of the second-order three point backward difference implicit scheme that satisfies its discrete geometric conservation law. Finally, the resulting Eulerian-ALE FIVER method is verified with the Large Eddy Simulation (LES) of turbulent flows past two counter-rotating cylinders and a heaving airfoil. Its potential for the solution of challenging viscous fluidstructure interaction problems characterized by large structural motions is demonstrated with the simulation, using the Spalart-Allmaras and Detached Eddy Simulation (DES) turbulence models, of pitch-up and roll maneuvers of an aeroelastic F/A-18 configuration driven by suitable deployments of its control surfaces.