A comparative study of interpolation algorithms on non-matching meshes for PFEM-FEM fluid-structure interactions

Non-matching meshes; Radial basis functions; k-nearest neighbours; Fluid-structure interaction; Particle finite element method; Computational fluid dynamics

Abstract :

[en] In simulations involving fluid-structure interactions, the partitioned coupling approach allows calculating the fluid flow and the structural displacement using different solvers, which are coupled by a structure-to-fluid algorithm. This partitioned scheme can result in non-conforming meshes at the solid-fluid interface, especially when the fluid and the structure meshes contain elements of different characteristic sizes. In this context, a mesh-interpolation technique is required to transmit the nodal information from one mesh to the other. This paper focuses on comparing radial basis functions and k-nearest neighbours interpolations on fluid-structure interaction test cases. Indeed, those are fast and flexible techniques requiring no topological information other than relative distances between nodes, allowing a straightforward transfer of nodal data between non-conforming meshes. This feature is particularly favourable in the Particle Finite Element Method (PFEM), where remeshing procedures result in significant changes of the finite element discretisation at the fluid-structure interface. Accordingly, our contribution compares the interpolations in a PFEM/FEM partitioned scheme, using 2D and 3D benchmark problems.

Research center :

A&M - Aérospatiale et Mécanique - ULiège [BE]

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Lacroix, Martin ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)

Février, Simon ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire

Fernandez Sanchez, Eduardo Felipe ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)

Papeleux, Luc ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire

Boman, Romain ; Université de Liège - ULiège > Département d'aérospatiale et mécanique

Ponthot, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire

Language :

English

Title :

A comparative study of interpolation algorithms on non-matching meshes for PFEM-FEM fluid-structure interactions

Publication date :

February 2024

Journal title :

Computers and Mathematics with Applications

ISSN :

0898-1221

Publisher :

Elsevier BV

Volume :

155

Pages :

51-65

Peer reviewed :

Peer reviewed

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Funding number :

T.0183.21

Available on ORBi :

since 11 December 2023

Statistics

Number of views

47 (25 by ULiège)

Number of downloads

3 (3 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

Bibliography

Antoci, C., Gallati, M., Sibilla, S., Numerical simulation of fluid-structure interaction by SPH. Comput. Struct. 85 (2007), 879–890, 10.1016/j.compstruc.2007.01.002.
Bano, T., Hegner, F., Heinrich, M., Schwarze, R., Investigation of fluid-structure interaction induced bending for elastic flaps in a cross flow. Appl. Sci., 10, 2020, 6177, 10.3390/app10186177.
Becker, P., Idelsohn, S.R., Oñate, E., A unified monolithic approach for multi-fluid flows and fluid-structure interaction using the particle finite element method with fixed mesh. Comput. Mech. 55 (2015), 1091–1104, 10.1007/s00466-014-1107-0.
Beckert, A., Wendland, H., Multivariate interpolation for fluid-structure-interaction problems using radial basis functions. Aerosp. Sci. Technol. 5 (2001), 125–134, 10.1016/S1270-9638(00)01087-7.
Belytschko, T., Liu, W.K., Moran, B., Elkhodary, K., Nonlinear Finite Elements for Continua and Structures. 2014, John Wiley & Sons.
Bussetta, P., Boman, R., Ponthot, J.-P., Efficient 3D data transfer operators based on numerical integration. Int. J. Numer. Methods Eng. 102 (2015), 892–929, 10.1002/nme.4821.
Cerquaglia, M.L., Deliège, G., Boman, R., Papeleux, L., Ponthot, J.-P., The particle finite element method for the numerical simulation of bird strike. Int. J. Impact Eng. 109 (2017), 1–13, 10.1016/j.ijimpeng.2017.05.014.
Cerquaglia, M.L., Thomas, D., Boman, R., Terrapon, V., Ponthot, J.-P., A fully partitioned Lagrangian framework for FSI problems characterized by free surfaces, large solid deformations and displacements, and strong added-mass effects. Comput. Methods Appl. Mech. Eng. 348 (2019), 409–442, 10.1016/j.cma.2019.01.021.
Chorin, A.J., Numerical solution of the Navier-Stokes equations. Math. Comput. 22 (1968), 745–762.
Codina, R., Pressure stability in fractional step finite element methods for incompressible flows. J. Comput. Phys. 1 (2001), 112–140, 10.1006/jcph.2001.6725.
de Boer, A., van Zuijlen, A.H., Bijl, H., Comparison of conservative and consistent approaches for the coupling of non-matching meshes. Comput. Methods Appl. Mech. Eng. 197 (2008), 4284–4297, 10.1016/j.cma.2008.05.001.
de Boer, A., van Zuijlen, A.H., Bijl, H., Radial basis function interpolation for computational fluid-structure interaction. Barry, K., Kees, V., (eds.) Advanced Computational Methods in Science and Engineering, 2010, Springer Berlin Heidelberg, Germany, 143–178.
Degroote, J., Haelterman, R., Annerel, S., Vierendeels, J., Coupling techniques for partitioned fluid-structure interaction simulations with black-box solvers. 10th MPCCI User Forum, 2009, 82–91.
Degroote, J., Souto-Iglesias, A., Paepegem, W.V., Annerel, S., Bruggeman, P., Vierendeels, J., Partitioned simulation of the interaction between an elastic structure and free surface flow. Comput. Methods Appl. Mech. Eng. 199 (2010), 2085–2098, 10.1016/j.cma.2010.02.019.
Delaissé, N., Demeester, T., Fauconnier, D., Degroote, J., Comparison of different quasi-Newton techniques for coupling of black-box solvers. ECCOMAS 2020, Proceedings, France, 2021, 12 https://doi.org/10.23967/wccm-eccomas.2020.088.
du Toit, W., Radial Basis Function Interpolation. Master's thesis, 2008, University of Stellenbosch, South Africa http://hdl.handle.net/10019.1/2002.
Falla, R., Bobach, B.-J., Boman, R., Ponthot, J.-P., Terrapon, V.E., Mesh adaption for two-dimensional bounded and free-surface flows with the particle finite element method. Comput. Part. Mech. 10 (2023), 1049–1076, 10.1007/s40571-022-00541-2.
Fernández, E., Février, S., Lacroix, M., Boman, R., Ponthot, J.-P., Generalized-α scheme in the PFEM for velocity-pressure and displacement-pressure formulations of the incompressible Navier-Stokes equations. Int. J. Numer. Methods Eng. 124 (2022), 1–40, 10.1002/nme.7101.
Franci, A., Cremonesi, M., On the effect of standard PFEM remeshing on volume conservation in free-surface fluid flow problems. Comput. Part. Mech. 4 (2016), 331–343, 10.1007/s40571-016-0124-5.
Franci, A., Oñate, E., Carbonell, J.M., Unified Lagrangian formulation for solid and fluid mechanics and FSI problems. Comput. Methods Appl. Mech. Eng. 298 (2016), 520–547, 10.1016/j.cma.2015.09.023.
Fuchs, S.L., Meier, C., Wall, W.A., Cyron, C.J., A novel smoothed particle hydrodynamics and finite element coupling scheme for fluid-structure interaction: the sliding boundary particle approach. Comput. Methods Appl. Mech. Eng., 383, 2021, 113922, 10.48550/arXiv.2010.09526.
Février, S., Development of a 3D Compressible Flow Solver for PFEM Fluid Simulations. Master's thesis, 2020, The University of Liège, Belgium http://hdl.handle.net/2268.2/9010.
Ganzenmüller, G.C., Hiermaier, S., May, M., On the similarity of meshless discretizations of peridynamics and smooth-particle hydrodynamics. Comput. Struct. 150 (2015), 71–78, 10.1016/j.compstruc.2014.12.011.
Groth, C., Porziani, S., Biancolini, M.E., Radial basis functions vector fields interpolation for complex fluid structure interaction problems. Fluids, 6, 2021, 314, 10.3390/fluids6090314.
Idelsohn, S.R., Oñate, E., del Pin, F., The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int. J. Numer. Methods Eng. 61 (2004), 964–989, 10.1002/nme.1096.
Janett, W., Yan, L., Comparative study of distance functions for nearest neighbors. Advanced Techniques in Computing Sciences and Software Engineering, 2008, 79–84, 10.1007/978-90-481-3660-5_14.
Jeunechamps, P.-P., Ponthot, J.-P., An efficient 3D implicit approach for the thermomechanical simulation of elastic-viscoplastic materials submitted to high strain rate and damage. Int. J. Numer. Methods Eng. 94 (2013), 920–960, 10.1002/nme.4489.
Kaneko, S., Hong, G., Mitsume, N., Yamada, T., Yoshimura, S., Partitioned-coupling FSI analysis with active control. Comput. Mech. 60 (2017), 549–558, 10.1007/s00466-017-1422-3.
Kedward, L., Allen, C.B., Rendall, T.C.S., Efficient and exact mesh deformation using multiscale RBF interpolation. J. Comput. Phys. 345 (2017), 732–751, 10.1016/j.jcp.2017.05.042.
Küttler, U., Wall, W.A., Fixed-point fluid-structure interaction solvers with dynamic relaxation. Comput. Mech. 43 (2008), 61–72, 10.1007/s00466-008-0255-5.
Lindner, F., Mehl, M., Uekermann, B., Radial basis function interpolation for black-box multi-physics simulations. International Conference on Computational Methods for Coupled Problems in Science and Engineering, Institute for Parallel and Distributed Systemes, Greece, 2017, 50–61.
Morris, J.P., A study of the stability properties of smooth particle hydrodynamics. Publ. Astron. Soc. Aust. 13 (1995), 97–102, 10.1017/S1323358000020610.
Ponthot, J.-P., Unified stress update algorithms for the numerical simulation of large deformation elasto-plastic and elasto-viscoplastic processes. Int. J. Plast. 18 (2002), 91–126, 10.1016/S0749-6419(00)00097-8.
Ponthot, J.-P., Boman, R., Papeleux, L., Metafor. http://metafor.ltas.ulg.ac.be/dokuwiki/, 2022. (Accessed 6 February 2023)
Rugonyi, S., Bathe, K.J., On finite element analysis of fluid flows coupled with structural interaction. Comput. Model. Eng. Sci. 2 (2001), 195–212, 10.3970/cmes.2001.002.195.
Scheufele, K., Mehl, M., Robust multisecant quasi-Newton variants for parallel fluid-structure simulations and other multiphysics applications. SIAM J. Sci. Comput. 39 (2017), 404–433, 10.1137/16M1082020.
Temam, R., Remark on the pressure boundary condition for the projection method. Theor. Comput. Fluid Dyn. 3 (1991), 181–184, 10.1007/BF00271801.
The CGAL Project, User and reference manual. https://doc.cgal.org/latest/Manual/index.html, 2022. (Accessed 6 February 2023)
Thomas, D., Cerquaglia, M.L., Boman, R., Economon, T.D., Alonso, J., Dimitriadis, G., Terrapon, V.E., CUPyDO – an integrated python environment for coupled fluid-structure simulations. Comput. Mech. 128 (2019), 69–85, 10.1016/j.advengsoft.2018.05.007.
Témam, R., Sur l'Approximation de la Solution des Équations de Navier-Stokes par la Méthode des Pas Fractionnaires. Arch. Ration. Mech. Anal. 33 (1969), 377–385, 10.1007/BF00247678.
Vincent, S., Sarthou, A., Caltagirone, J.P., Sonilhac, F., Février, P., Mignot, C., Pianet, G., Augmented Lagrangian and penalty methods for the simulation of two-phase flows interacting with moving solids. Application to hydroplaning flows interacting with real tire tread patterns. J. Comput. Phys. 4 (2011), 956–983, 10.1016/j.jcp.2010.10.006.
Wu, K., Yang, D., Wright, N., A coupled SPH-DEM model for fluid-structure interaction problems with free-surface flow and structural failure. Comput. Struct. 177 (2016), 141–161, 10.1016/j.compstruc.2016.08.012.
Xin, S.-Q., Wang, G.-J., Improving Chen and Han's algorithm on the discrete geodesic problem. ACM Trans. Graph. 28 (2009), 1–8, 10.1145/1559755.1559761.
Yaman, H., A'Fza, S., Zahiraniza, M., Naila, I., An application of K-nearest neighbor interpolation on calibrating corrosion measurements collected by two non-destructive techniques. Proceedings of the IEEE 3rd International Conference on Smart Instrumentation, Measurement and Applications, Malaysia Institute of Electrical and Electronics Engineers, 2015, 1–5, 10.1109/icsima.2015.7559030.
Zhu, M., Scott, M.H., Improved fractional step method for simulating fluid-structure interaction using the PFEM. Numer. Methods Eng. 99 (2014), 925–944, 10.1002/nme.4727.