Elasto–acoustic and acoustic–acoustic coupling on non‐matching grids

Flexible discretization techniques for the approximative solution of coupled wave propagation problems are investigated, focussing on aero–acoustic and elasto–acoustic coupling. In particular, the advantages of using non-matching grids are presented, when one subregion has to be resolved by a substantially finer grid than the other subregion. For the elasto–acoustic coupling, the problem formulation remains essentially the same as for the matching situation, while for the aero–acoustic coupling, the formulation is enhanced with Lagrange multipliers within the framework of mortar finite element methods. Several numerical examples are presented to demonstrate the flexibility and applicability of the approach. Copyright © 2006 John Wiley & Sons, Ltd.

[1]  Barbara Wohlmuth A COMPARISON OF DUAL LAGRANGE MULTIPLIER SPACES FOR MORTAR FINITE ELEMENT DISCRETIZATIONS , 2002 .

[2]  A. Majda,et al.  Absorbing boundary conditions for the numerical simulation of waves , 1977 .

[3]  Michael A. Puso,et al.  A 3D mortar method for solid mechanics , 2004 .

[4]  Barbara I. Wohlmuth,et al.  A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier , 2000, SIAM J. Numer. Anal..

[5]  B. Engquist,et al.  Absorbing boundary conditions for acoustic and elastic wave equations , 1977, Bulletin of the Seismological Society of America.

[6]  Patrick Le Tallec,et al.  Numerical analysis of a linearised fluid-structure interaction problem , 2000, Numerische Mathematik.

[7]  J. Z. Zhu,et al.  The finite element method , 1977 .

[8]  Alfredo Bermúdez,et al.  Finite element approximation of a displacement formulation for time-domain elastoacoustic vibrations , 2003 .

[9]  Manfred Kaltenbacher,et al.  Numerical Simulation of Mechatronic Sensors and Actuators , 2004 .

[10]  Alfio Quarteroni 2. Domain Decomposition Methods for Wave Propagation Problems , 1995, Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering.

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

[12]  Roland Glowinski,et al.  A Domain Decomposition Method for the Acoustic Wave Equation with Discontinuous Coefficients and Grid Change , 1997 .

[13]  Claus-Dieter Munz,et al.  Direct Simulation of Aeroacoustics , 2003 .

[14]  L. Gaul,et al.  APPLICATION OF THE FAST MULTIPOLE BEM FOR STRUCTURAL–ACOUSTIC SIMULATIONS , 2005 .

[15]  P. Hansbo,et al.  Nitsche's method combined with space–time finite elements for ALE fluid–structure interaction problems☆ , 2004 .