Numerical Investigation of Elastically-Mounted tandem Cylinders using an ALE Runge-Kutta Discontinuous Galerkin method

TL;DR

This paper develops a high-order ALE Discontinuous Galerkin framework for simulating vortex-induced vibrations of elastically-mounted tandem cylinders, demonstrating its efficiency and accuracy in capturing complex wake interactions.

Contribution

It introduces a high-order ALE DG method with minimal overhead, incorporating GCL enforcement and RBF mesh deformation for accurate CFD-FSI simulations of multi-body vortex-induced vibrations.

Findings

High-order methods better capture wake dynamics on coarse meshes.

Irregular trajectories driven by wake interference observed in three-cylinder case.

hp-refinement outperforms mesh refinement in efficiency and accuracy.

Abstract

This work presents a high-order Arbitrary-Lagrangian-Eulerian (ALE) Discontinuous Galerkin framework for simulating multi-body Vortex-Induced Vibrations. The ALE formulation extends a Runge-Kutta Interior-Penalty nodal DG solver with minimal additional computational overhead, incorporating discrete enforcement of the Geometric Conservation Law (GCL) to ensure free-stream preservation and Radial Basis Function (RBF) mesh deformation to handle large structural displacements. The framework is applied to elastically-mounted tandem cylinder configurations: a two-cylinder arrangement with cross-flow oscillations at Re=200, and a three-cylinder arrangement with two degrees of freedom at Re=150. In the three-cylinder case, the trajectories exhibit highly irregular behavior driven by complex wake interference, including a periodic attract-and-release mechanism governing the trailing cylinder's stream-wise response. Results are verified against established benchmarks through Lissajous curves, Poincar\'{e} phase maps, power spectra, and vortex shedding mode classification. An hp-refinement comparison demonstrates that increasing the polynomial order is more effective and computationally efficient than mesh refinement for capturing multi-body wake dynamics, as the low numerical diffusion of the high-order method preserves vortical structures over long distances on relatively coarse meshes. These findings highlight the importance of high-order methods for CFD-FSI applications where wake interactions drive the structural response.