An Aeroelastic Solver Integrating Reformulated-Vortex-Particle and Finite-Element Methods across Non-Conforming Interfaces

Abstract

We present $\texttt{VarFlExI}$ (Variable Fidelity Unsteady Flow-FEniCS Exchange Interface), a modular aeroelastic solver for modeling two-way fluid-structure interaction (FSI) of flexible lifting surfaces. The framework employs a reformulated Vortex Particle Method (rVPM) to solve the incompressible Navier-Stokes equations without the need for computationally expensive volumetric meshing, while supporting variable-fidelity aerodynamic modeling using the $\texttt{FLOWUnsteady}$ framework. On the structural side, a Reissner-Mindlin plate formulation is discretized using the finite element method and integrated in time through the generalized-$α$ method, with the nonlinear equilibrium equations solved using a Gauss-Newton procedure within the $\texttt{FEniCS}$ framework. Fluid and structural solvers are coupled through an explicit staggered partitioned scheme, ensuring conservation of virtual work for load and displacement transfer across the non-matching interface. To accommodate the multi-representative nature of the aerodynamic loads and geometry, the interface coupling employs separate work-conservative force and reverse-geometry transfer operators via a common intermediate interface. The framework is validated against water-tunnel experiments, demonstrating accurate prediction of the coupled aeroelastic response rather than independent validation of the constituent solvers. The computational efficiency of the meshless aerodynamic solver enables simulations at significantly lower computational cost while maintaining accuracy. The solver is further evaluated through sensitivity analyses and parameter studies spanning different flow conditions, structural properties, and coupling parameters.