Adaptive High-Order Fluid-Structure Interaction Simulations with Reduced Mesh-Motion Errors

Abstract

This paper demonstrates an 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 structures solver uses a continuous Galerkin discretization. An explicit mapping is used as the primary mesh deformation algorithm. High-order time-integration schemes are used by the coupled solver to march forward in time, and the space-time mesh of the fluid subsystem is adapted using output-based methods. The error estimates for the unsteady outputs are evaluated by calculating the uncoupled, unsteady adjoint of the fluid subsystem. 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 benefits of adaptive meshing are demonstrated on a cantilevered Euler–Bernoulli beam placed in a low-Reynolds number flow and on a two-dimensional pitching–plunging airfoil in a high-Reynolds number flow.