CNAM Paris - France
This study concerns linear sloshing problems of liquids in moving containers [1] and parameterized reduced-order modeling (ROM) [2] using Isogeometric Analysis (IGA) [3]. The challenge consists in computing a ROM that incorporates a geometrical parameterization of the liquid domain inside a rigid tank as a function of liquid height. IGA enables the geometric parameterization and the mapping on a reference configuration. In ROM approaches, geometrical parameters often lead to non-affine operators, and the precomputation of reduced operators is no more possible. Hyper-reduction techniques are thus necessary (e.g., energy conservation sample weights [4]). The originality of this work lies in the development of a parameterized ROM for fast and accurate linear sloshing analyses. The ROM can then be used in fluid-structure simulations, accounting for the elasticity of the container. The methodology is as follows. First, a 3D geometrical parameterization of the liquid domain is established based on the positions of control points and associated weights. The mapping between a reference configuration and various current geometrical domains is directly obtained using NURBS discretization. Parameterized operators are then computed onto a unique fluid domain for integration. The ROM approach consists of two steps: (i) generating a basis either from snapshots of the high-dimensional model (HDM) time-domain integration and (ii) constructing the ROM using a projection-based approach and hyper-reduction techniques. A comparison of quantities of interest between HDM and ROM will be conducted, considering both the speed-up factor and accuracy [5].
[1] Dodge F. T., The new “dynamic behavior of liquids in moving containers”. San Antonio, TX: Southwest Research Inst., 2000.
[2] Morand H. J-P., and Ohayon R. Fluid-structure interaction: Applied numerical methods. 1995.
[3] Cottrell J. A., Hughes T. J. R, and Bazilevs Y., Isogeometric analysis: toward integration of CAD and FEA. John Wiley & Sons, 2009.
[4] Farhat C., et al. “Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy‐based mesh sampling and weighting for computational efficiency.” International Journal for Numerical Methods in Engineering 98.9 (2014): 625-662.
[5] Hoareau C., Deü, J.-F., and Ohayon R., Projection-based reduced order model and hyper-reduction of linear sloshing with geometric parameters using isogeometric analysis. Advanced Modeling and Simulation in Engineering Sciences (2025), 12(1), 1-32.