Efficient non-linear solid-fluid interaction analysis by an iterative BEM/FEM coupling

Abstract

SUMMARYAn iterative coupling of finite element and boundary element methods for the time domain modelling of coupled fluid-solid systems is presented. While finite elements are used to model the solid, the adjacent fluid is represented by boundary elements. In order to perform the coupling of the two numerical methods, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved. In the case of local non-linearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the non-linear system. In particular a more efficient and a more stable performance of the new coupling procedure is achieved by a special formulation that allows to use different time steps in each subdomain.

An efficient stabilized boundary element formulation for 2D time-domain acoustics and elastodynamics

“…(3b)] convolution operations, an α parameter, which linearly combines three consecutive time-step results, is introduced for the stabilization of the standard boundary element formulation. The combination of consecutives results has been used in several applications (adoption of a relaxation parameter in iterative processes, for instance [16,17]), showing good performance in what concerns the stabilization of an oscillatory tendency. The basic idea here is to smooth the convolution operations, trying to avoid any possible numerical instability.…”

“…The α-δ TDBEM presented here associates stability and efficiency, and it is expected to be also more robust than previously reported TDBEM transmitting boundaries (as for instance in a BEM-FEM coupling context [16,17,24]). …”

Meshless analysis of soil-structure interaction using a MFS-MLPG coupled approach

“…The traction equilibrium conditions are, in turn, established at the MLPG boundary nodes, and are thus considered as additional terms in the MLPG equations established at those nodes. Considering equation (9), and analysing the MLPG nodes along the interface with the MFS domain, one may then write at node NM: (17) in which…”

“…Although many hybrid algorithms correspond to standard direct coupling methodologies, several iterative coupling procedures between different numerical formulations have recently been proposed, allowing the use of independent discretizations while the corresponding sub-domains can be analysed separately [9,10]. For dynamic fluid-structure and soil-structure interaction problems, the specific case of coupling the FEM and the BEM has been extensively documented [11,12].…”

Acoustic modelling by BEM–FEM coupling procedures taking into account explicit and implicit multi‐domain decomposition techniques

“…The work was focused on dynamic two-dimensional elastoplastic models. Later on, the procedure was extended, being applied to model solid-fluid interaction (Soares et al [9]), as well as to simulate three-dimensional and axisymmetric mechanical applications (von Estorff and Hagen [10], Warszawski et al [11]). In all the above-referred publications, a constant pre-selected relaxation parameter was considered in order to ensure and/or to speed up the convergence of the iterative coupling approach.…”