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Conservative load transfer along curved fluid–solid interface with non-matching meshes. (English) Zbl 1158.76405
Summary: We investigate the effect of curvature on the accuracy of schemes used to transfer loads along the interface in coupled fluid–solid simulations involving non-matching meshes. We analyze two types of load transfer schemes for the coupled system: (a) point-to-element projection schemes and (b) common-refinement schemes. The accuracy of these schemes over the curved interface is assessed with the aid of static and transient problems. We show that the point-to-element projection schemes may yield inaccurate load transfer from the source fluid mesh to the target solid mesh, leading to a weak instability in the form of spurious oscillations and overshoots in the interface solution. The common-refinement scheme resolves this problem by providing an accurate transfer of discrete interface conditions across non-matching meshes. We show theoretically that the accurate transfer preserves the stability of the coupled system while maintaining the energy conservation over a reference interface. Finally, we introduce simple analytical error functions which correlate well with the numerical errors of the load transfer schemes.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76T99 Multiphase and multicomponent flows
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[1] Simo, J.C.; Wriggers, P.; Taylor, R.L., A perturbed Lagrangian formulation for the finite element solution of contact problems, Comput. methods appl. mech. engrg., 50, 163-180, (1985) · Zbl 0552.73097
[2] El-Abbasi, N.; Bathe, K.-J., Stability and patch test performance of contact discretizations and a new solution algorithm, Comput. struct., 79, 1473-1486, (2001)
[3] Flemisch, B.; Puso, M.A.; Wohlmuth, B.I., A new dual mortar method for curved interfaces: 2D elasticity, Int. J. numer. methods engrg., 63, 813-832, (2005) · Zbl 1084.74050
[4] C. Bernardi, Y. Maday, A.T. Patera, A new nonconforming approach to domain decomposition: The mortar element method, in: H. Brezis, J.L. Lions (Eds.), Nonlinear Partial Differential Equations and their applications College de France Seminar Volume XI, 1994, pp. 13-51. · Zbl 0797.65094
[5] Cai, X.C.; Dryja, M.; Sarkis, M., Overlapping nonmatching grid mortar element methods for elliptic problems, SIAM J. numer. anal., 36, 581-606, (1999) · Zbl 0927.65131
[6] Lee, S.-C.; Vouvakis, M.N.; Lee, J.-F., A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays, J. comput. phys., 203, 1-21, (2005) · Zbl 1059.78042
[7] Felippa, C.A.; Park, K.C., Staggered transient analysis procedures for coupled mechanical systems: formulation, Comput. methods appl. mech. engrg., 24, 61-111, (1980) · Zbl 0453.73091
[8] Smith, M.J.; Hodges, D.H.; Cesnik, C.E.S., Evaluation of computational algorithms suitable for fluid-structure interactions, J. aircraft, 37, 282-294, (2000)
[9] Guruswamy, G.P., A review of numerical fluids/structures interface methods for computations using high-fidelity equations, Comput. struct., 80, 31-41, (2002)
[10] Farhat, C.; Lesoinne, M.; LeTallec, P., Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity, Comput. methods appl. mech. engrg., 157, 95-114, (1998) · Zbl 0951.74015
[11] Cebral, J.R.; Lohner, R., Conservative load projection and tracking for fluid-structure problems, Aiaa j., 35, 687-692, (1997) · Zbl 0895.73077
[12] S.A. Brown, Displacement extrapolations for CFD+CSM aeroelastic analysis, in: AIAA 97-1090 CP, 1997.
[13] Jaiman, R.; Jiao, X.; Geubelle, X.; Loth, E., Assessment of conservative load transfer on fluid-solid interface with nonmatching meshes, Int. J. numer. methods engrg., 64, 2014-2038, (2005) · Zbl 1122.74544
[14] Jiao, X.; Heath, M.T., Common-refinement based data transfer between nonmatching meshes in multiphysics simulations, Int. J. numer. methods engrg., 61, 2402-2427, (2004) · Zbl 1075.74711
[15] Farhat, C.; Geuzaine, P.; Grandmont, C., The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids, J. comput. phys., 174, 669-694, (2001) · Zbl 1157.76372
[16] Zienkiewicz, O.C.; Morgan, K., Finite elements and approximations, (1983), Wiley and Sons
[17] Jiao, X.; Heath, M.T., Overlaying surface meshes, (part 1): algorithms, Int. J. comput. geom. appl., 14, 379-402, (2004) · Zbl 1080.65015
[18] Farhat, C.; Lesoinne, M., Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems, Comput. methods appl. mech. engrg., 182, 499-515, (2000) · Zbl 0991.74069
[19] Boujot, J., Mathematical formulation of fluid-structure interaction problems, Math. model. numer. anal., 21, 239-260, (1987) · Zbl 0617.73052
[20] Feng, X., Analysis of finite element methods and domain decomposition algorithms for a fluid-solid interaction problem, SIAM J. numer. anal., 38, 1312-1336, (2000) · Zbl 0984.76046
[21] Heath, M.T., Scientific computing: an introduction survey, (2002), MacGraw-Hill New York
[22] Ofengeim, D.K.; Drikakis, D., Simulation of blast wave propagation over a cylinder, Shock waves, 7, 305-317, (1997) · Zbl 0896.76030
[23] Liepmann, H.W.; Roshko, A., Elements of gas dynamics, (1957), Wiley New York · Zbl 0078.39901
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