Efficient and Flexible Solution Strategies for Large-Scale, Strongly Coupled Multi-Physics Analysis and Optimization Problems.

摘要

Aerospace problems are characterized by strong coupling of different disciplines, such as fluid-structure interactions. There has been much research over the years on developing numerical solution methods tailored to each of the different disciplines. The classical approach to solving these strongly coupled systems is to stitch together these individual solvers by solving for one discipline and using the solution as boundary conditions for the successive disciplines. In more recent years, research has focused on numerical methods that handle solving coupled disciplines together. These methods offer the potential of better computational efficiency. These coupled solution methods range from monolithic solution strategies to decoupled partitioned strategies. This research develops a flexible finite element analysis tool which is capable of analyzing a range of aerospace problems including highly coupled incompressible fluid-structure interactions and turbulent compressible flows. The goal of this research is to access the viability of streamline-upwind Petrov-Galerkin (SUPG) finite element analysis for compressible turbulent flows. Additionally, this research uses a selection of nonlinear solution methods, linear solvers, iterative preconditioners, varying degrees of coupling, and coupling strategies to provide insight into the computational efficiency of these methods as they apply to turbulent compressible flows and incompressible fluid-structure interaction problems. The results suggest that SUPG finite element analysis for compressible flows may not be robust enough for optimization problems due to ill-conditioned matrices in the linear approximation. This research also shows that it is the degree of coupling and criticality of the coupling that drives the selection of the most efficient nonlinear and linear solution methods.