Abstract
This work aims to develop a FVM-based structural solver that can seamlessly be integrated with Computational Fluid Dynamics (CFD) solvers for fluid-structure interaction (FSI) problems. For flexibility in gridding and efficient computation, hexahedral multi-block grids are adopted which are locally structured, but globally unstructured. Besides, ghost cells are introduced to solve the partial derivatives and displacements at the boundaries of the computational domain. Time-accurate solutions are obtained by employing a matrix-free, dual time stepping approach, and the implicit residual value smoothing method is used to increase the convergence rate. Stresses are evaluated using Green's theorem based on the gradients of the displacement of the cells. The proposed method is applied to static and dynamic response of 3D cantilevers. Results are found to agree well with analytical solutions, and the amplitude error of the dynamic response is less than 1.5%. Besides, resonance and beating phenomena were clearly observed and compared to Finite Element approaches in accuracy and efficiency. Finally, the dynamic response of a cantilever beam with NACA0012 airfoil is analyzed preliminarily.
Highlights
Fluid-structure interaction (FSI) is one of the most important problems in aeronautical engineering design and analysis
Unlike the finite element method (FEM) that only satisfies the relevant conservation principles and equilibrium of forces in a global sense, the finite volume method (FVM) is conservative from the whole domain scale to the element or control volume level
Results agree well with analytical solutions, and the amplitude error of dynamic response is less than 1.5%
Summary
Fluid-structure interaction (FSI) is one of the most important problems in aeronautical engineering design and analysis. No detailed grid independence analysis, convergence and efficiency analysis have been carried out for 3D dynamics It is not clear whether the matrix-free finite volume method has the same accuracy in simulating forced vibration under higher harmonic loads like FEM. In the development of the matrix-free finite volume method, the structured grid has not been adopted to calculate and analyze the CSD problems. The hexahedral structural grids are introduced to a matrix-free finite volume method of cell-centred scheme for 3D linear elasticity problems. Results agree well with analytical solutions, and the amplitude error of dynamic response is less than 1.5% This is a first step towards the development of a finite volume FSI methods for aeroelastic studies
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