Output-Based Error Estimation and Mesh Adaptation for High-Fidelity Fluid-Structure Interaction

Abstract

Complex multidisciplinary systems require high-fidelity analysis techniques to accurately capture the mutual interactions and coupling of the participating disciplines. However, high costs associated with preparing, running, and verifying these models can limit their use. Numerical methods like error estimation and adaptive mesh refinement have been shown to significantly reduce some of the cost burden associated with high-fidelity analysis approaches. Therefore, their adoption can potentially allow for improvements in the design process of multidisciplinary systems. This dissertation aims to develop output-based error estimation and mesh adaptation methods in a high-fidelity framework for fluid-structure interaction and to demonstrate the computational and operational benefits when applied to fluid-structure interaction simulations.

A partitioned framework for high-fidelity, steady, aeroelastic analysis is presented. The fluid system models the compressible Euler and Navier-Stokes equations using a high-order discontinuous Galerkin finite element method, whereas the structural system models a built-up shell formulation using a high-order continuous Galerkin finite element method. Spatial coupling between the fluid and structural domains is accomplished using a least-squares technique and the principle of virtual work to transfer sets of displacements and loads across the non-matching discretizations of the fluid-structure interface. Mesh motion in the fluid domain is done with a multiscale radial basis function interpolation technique to complete the coupling cycle. These components are assembled together in a single computing environment that executes the four main components of the proposed analysis procedure: the primal state solution, adjoint solution, error estimation, and mesh adaptation.

Details of the coupled primal and adjoint systems are presented, including the development of the coupled adjoint and related derivative evaluations. Both primal and adjoint solutions are made with block Gauss-Seidel fixed-point iterations. The output-based error estimate is determined using nested approximation spaces and evaluated with an adjoint-weighted residual. The error estimates are localized to the elements of each domain and are used to form adaptive indicators for mesh refinement. Mesh refinement is carried out on either the element size or order of approximation. Error estimation and mesh adaptation are applied concurrently in both domains until an error tolerance in the output of interest is achieved. The various components of the complete framework are demonstrated and verified independently on geometries including half-vehicle and isolated wing models of conventional transonic transport aircraft. The coupled adaptive analysis is applied to a sample test case considering various outputs of interest for both the fluid and structural domains. The adaptive approach was able to achieve approximately an order of magnitude reduction in the number of degrees of freedom required for a converged output compared to uniform refinement. Likewise, the adaptive analysis saw computational times as low as 23% of what was required by the conventional approach. These results indicate significant time, computational resource, and user interaction cost savings from the proposed approach.