An error estimator for transmitting boundary conditions in fluid-structure interaction problems

Abstract

This paper proposes error estimators to validate Transmitting Boundary Conditions (TBCs) in fluid-structure interaction problems. The error estimators are based on a new formulation of the dynamic response of fluid-structure systems including TBCs. The mathematical background is briefly discussed and the obtained equations are solved numerically to assess the accuracy of a given TBC and determine the associated error independently of FEM or BEM modeling of the fluid domain. The error estimators take account of : (i) structure's flexibility, (ii) fluid compressibility, (iii) energy dissipation at fluid boundaries, (iv) fluid domain truncation length, and (v) excitation frequency. An illustrative example consisting of a dam-reservoir system is presented where an error estimator is used to evaluate the effects of various TBCs on the hydrodynamic pressure acting on the dam upstream face. The proposed formulation can be programmed easily and used efficiently for rigorous assessment of classical or newly-developed TBCs for vibrating fluid-structure systems.

An Efficient Dynamic Coupling Calculation Method for Dam–Reservoir Systems Based on FEM-SBFEM

“…In the dynamic response analysis of dams under earthquake conditions, hydrodynamic pressure is one of the important factors that must be considered in order to reasonably evaluate the seismic safety of dams, so many researchers have done a lot of research work in this area. At present, the FEM [26][27][28][29][30][31][32][33][34][35][36][37], the boundary element method (BEM) [38][39][40][41][42][43], and the SBFEM [2,[19][20][21][22][23] are the three commonly used methods to calculate the hydrodynamic pressure of reservoir water in front of a dam. In the BEM and SBFEM, the reservoir model is established based on the Eulerian approach [21,31], while both Eulerian and Lagrangian [31,33,35] approaches could be used to model the reservoir with the FEM.…”