Robust sub-cycling approach for strongly coupled fluid structure interaction problems with supersonic flows
Abstract
This paper presents a strongly coupled approach for Fluid-Structure Interaction (FSI) problems based on the introduction of Lagrange Multipliers (LM) at the fluid-structure interface. The coupling is built upon the compressible fluid equations interacting with an elastic structure, which involve markedly different time and space scales. This coupling strategy enables a separate solving of the fluid and structure subdomains while strongly enforcing the continuity of the normal velocity across the interface. Each subdomain is treated with space and time discretizations suited to its own physics: the fluid is discretized using a vertex-centered Arbitrary Lagrangian-Eulerian (ALE) Finite Volume Method (FVM) on triangular meshes, whereas the structure relies on the Finite Element Method (FEM) with quadratic quadrilateral elements. The non-conforming meshes at the interface are handled by the Mortar method. Each subdomain is advanced in time using only implicit time integrators: a second-order Backward Differentiation Formula (BDF2) solved with a Newton method for the fluid and the Newmark Constant Average Acceleration (CAA) scheme for the structure. A key feature of the proposed approach is a multi-time step strategy, based on the Gravouil-Combescure (GC) method, that allows for heterogeneous time steps and fluid sub-cycling. A variant of the GC method relying on a cubic Hermite (C 1 ) interpolation is also investigated. The proposed approach is validated on several classical benchmarks: the one-dimensional piston problem with a rod; the two-dimensional deformable panel subjected to a shock wave, for which the numerical results match the experimental data despite a highly non-conforming interface and a large time step ratio (up to 20); and the supersonic flutter of a flat panel, where the aeroelastic instability is accurately captured.
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BibTeX
@misc{pulicani2026robust,
title = {{Robust sub-cycling approach for strongly coupled fluid structure interaction problems with supersonic flows}},
author = {Roxan Pulicani and Michael Brun and Olivier Allain and Anthony Gravouil},
howpublished = {HAL},
year = {2026},
month = nov,
url = {https://hal.science/hal-05847096v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Robust sub-cycling approach for strongly coupled fluid structure interaction problems with supersonic flows
AU - Roxan Pulicani
AU - Michael Brun
AU - Olivier Allain
AU - Anthony Gravouil
PY - 2026
DA - 2026/11/01
PB - HAL
UR - https://hal.science/hal-05847096v1
AB - This paper presents a strongly coupled approach for Fluid-Structure Interaction (FSI) problems based on the introduction of Lagrange Multipliers (LM) at the fluid-structure interface. The coupling is built upon the compressible fluid equations interacting with an elastic structure, which involve markedly different time and space scales. This coupling strategy enables a separate solving of the fluid and structure subdomains while strongly enforcing the continuity of the normal velocity across the interface. Each subdomain is treated with space and time discretizations suited to its own physics: the fluid is discretized using a vertex-centered Arbitrary Lagrangian-Eulerian (ALE) Finite Volume Method (FVM) on triangular meshes, whereas the structure relies on the Finite Element Method (FEM) with quadratic quadrilateral elements. The non-conforming meshes at the interface are handled by the Mortar method. Each subdomain is advanced in time using only implicit time integrators: a second-order Backward Differentiation Formula (BDF2) solved with a Newton method for the fluid and the Newmark Constant Average Acceleration (CAA) scheme for the structure. A key feature of the proposed approach is a multi-time step strategy, based on the Gravouil-Combescure (GC) method, that allows for heterogeneous time steps and fluid sub-cycling. A variant of the GC method relying on a cubic Hermite (C 1 ) interpolation is also investigated. The proposed approach is validated on several classical benchmarks: the one-dimensional piston problem with a rod; the two-dimensional deformable panel subjected to a shock wave, for which the numerical results match the experimental data despite a highly non-conforming interface and a large time step ratio (up to 20); and the supersonic flutter of a flat panel, where the aeroelastic instability is accurately captured.
ER -