Parallel numerical methods and data-driven analysis techniques for turbulent fluid-structure interaction

Abstract

This dissertation develops numerical methods and parallel codes to simulate turbulent fluid-structure interaction, and data-driven methods to understand the cause of this interaction. The unsteady pressure and shear-stress fluctuations within a turbulent flow can lead to structural vibration. These vibrations can radiate sound which can cause excessive noise. Large turbulent fluid loads can lead to large structural deformation. Such deformation can cause excessive stresses within the solid, damaging it. The tools developed in this thesis help predict this interaction and analyze the interaction's cause. For accurate simulation of turbulent flows in deforming geometries mappable to a unit cube, a new finite volume method is developed. This method discretizes the domain with quadratic hexahedral control volumes. It yields second-order accurate solution even in the presence of extremely skewed control volumes. Such control volumes can arise when the fluid mesh adapts to the deforming fluid-solid interface. A new cell-centered gradient approximation is developed using the Piola transform. This approximation yields second-order accurate gradients irrespective of the boundary condition. The commonly used Green-Gauss approximation can yield first-order accurate approximation in the presence of Dirichlet or Neumann boundary conditions. To simulate the structural deformation, an in-house parallel finite-element solver, MPCUGLES-SOLID, is developed. This solver can compute the response of compressible linear elastic materials (for e.g., steel and aluminum) and incompressible linear viscoelastic materials (for e.g., synthetic rubber and PDMS). For efficient solution of the spatially discretized problem, the former material requires the continuous Galerkin finite element method, while the latter requires the mixed finite-element method. To simplify code development of both these methods, we develop their unified implementation using specially designed data structures. A new method is developed to couple the finite volume fluid and the finite element solid solvers. This method allows for the concurrent execution of the two solvers. This concurrent execution is essential for the coupled solver's good parallel performance, especially for turbulent FSI problems. A new data-driven method is developed to study the wall-pressure fluctuations' sources in a turbulent channel flow. This method answers the questions -- for each frequency, how do turbulent fluid sources at different distances from the wall contribute to the wall-pressure fluctuation power spectral density (PSD)? To answer this question, the method combines the channel DNS data with the fluid's pressure fluctuation Poisson equation and spectral POD. The previous data-driven method is extended to study the fluid sources that contribute to the excitation of a plate in turbulent channel flow. This extended method answers the question -- for each frequency, how do turbulent fluid sources situated at different distances from the wall contribute to the plate-averaged displacement PSD? To answer this, the method combines the plate's modal decomposition with the channel DNS data, the fluid pressure fluctuation's Poisson equation and spectral POD. Finally, a new DMD algorithm, FOA based DMD, is developed to extract features from a general time-evolving large data. This method is streaming and can process extremely large data sets in parallel. Our algorithm can perform DMD of 201 snapshots of 240 million size in 3 seconds on 16,000 processors. The algorithm shows ideal strong scaling. Our new DMD algorithm's and a few existing DMD algorithm's finite-precision arithmetic error is analyzed. This error is shown to be proportional to (snapshot condition number)^p * O(machine epsilon), where the power ‘p’ depends on the DMD algorithm. For most DMD algorithms, p is one, while for some algorithms, p is two. Therefore, for a given data set, the latter DMD algorithms amplify this error more than the former algorithms.