Review of coupling methods for non-matching meshes

Abstract Domain decomposition is nowadays a common way to speed up complex computations. However, the discrete meshes used in the different domains do not have to match at their common interface, especially when different physical fields are involved such as in fluid–structure interaction computations. Exchange of information over this interface is therefore no longer trivial. In this paper six methods that can deal with the information transfer between non-matching meshes in fluid–structure interaction computations are compared for different criteria. This is done for analytical test cases as well as a quasi-1D fluid–structure interaction problem. Two methods based on radial basis functions, one with compact support and one using thin plate splines, are favoured over the other methods because of their high accuracy and efficiency.

[1]  Andrea Toselli,et al.  Domain decomposition methods : algorithms and theory , 2005 .

[2]  M. G. Salvadori,et al.  Numerical methods in engineering , 1955 .

[3]  Martin W. Heinstein,et al.  Consistent mesh tying methods for topologically distinct discretized surfaces in non‐linear solid mechanics , 2003 .

[4]  J. C. Simo,et al.  A perturbed Lagrangian formulation for the finite element solution of contact problems , 1985 .

[5]  M. Hafez,et al.  Computational fluid dynamics review 1995 , 1995 .

[6]  C. Felippa,et al.  A simple algorithm for localized construction of non‐matching structural interfaces , 2002 .

[7]  C. Bernardi,et al.  A New Nonconforming Approach to Domain Decomposition : The Mortar Element Method , 1994 .

[8]  Carlos E. S. Cesnik,et al.  EVALUATION OF SOME DATA TRANSFER ALGORITHMS FOR NONCONTIGUOUS MESHES , 2000 .

[9]  Charles Hirsch,et al.  Numerical computation of internal & external flows: fundamentals of numerical discretization , 1988 .

[10]  Rainald Löhner,et al.  Conservative load projection and tracking for fluid-structure problems , 1996 .

[11]  C. Farhat,et al.  Partitioned procedures for the transient solution of coupled aroelastic problems Part I: Model problem, theory and two-dimensional application , 1995 .

[12]  H. Wendland,et al.  Multivariate interpolation for fluid-structure-interaction problems using radial basis functions , 2001 .

[13]  F. Baaijens A fictitious domain/mortar element method for fluid-structure interaction , 2001 .

[14]  M. Unser,et al.  Interpolation revisited [medical images application] , 2000, IEEE Transactions on Medical Imaging.

[15]  Charbel Farhat,et al.  Matching fluid and structure meshes for aeroelastic computations : a parallel approach , 1995 .

[16]  J. Ransom A Multifunctional Interface Method for Coupling Finite Element and Finite Difference Methods: Two-Dimensional Scalar-Field Problems , 2002 .

[17]  Carlos A. Felippa,et al.  Partitioned formulation of internal fluid–structure interaction problems by localized Lagrange multipliers , 2001 .

[18]  P. Tallec,et al.  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 , 1998 .

[19]  J. Barlow,et al.  Constraint relationships in linear and nonlinear finite element analyses , 1982 .

[20]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[21]  Carlos E. S. Cesnik,et al.  Evaluation of computational algorithms suitable for fluid-structure interactions , 2000 .