Goal-Oriented Mesh Adaptation for High-Fidelity Aeroelastic Simulations

Abstract

This work demonstrates a solution-adaptive approach for solving fluid-structure interaction problems using high-fidelity numerical methods along with a detailed analysis of mesh-motion errors. A high-order partitioned approach is applied to couple the fluid and the structural subsystems, where the fluid subsystem is discretized using a discontinuous Galerkin finite-element method, while the structural solver uses a continuous Galerkin discretization. High-order time integration schemes are used by the coupled solver to march forward in time, and the spatial meshes of the fluid and the structural subsystems are adapted using output-based methods. The error estimates for the unsteady outputs are evaluated by calculating the unsteady adjoint of the coupled problem. Adaptive meshing is used to demonstrate the importance of mesh-motion errors on output convergence and a comprehensive analysis is conducted to control such errors arising from the mesh deformation algorithm. The adapted meshes converge at a faster rate with fewer degrees of freedom, thereby increasing accuracy and reducing computational cost. The benefits of adaptive meshing are demonstrated on two-dimensional and three-dimensional aeroelastic problems for a variety of coupled outputs. As an alternative to the adjoint-based mesh adaptation process, a data-driven method is also developed to improve the efficiency of non-uniform anisotropic mesh generation.