Goal-oriented error estimation in the analysis of fluid flows with structural interactions

Abstract

We present some developments for the extension of goal-oriented error estimation procedures to the analysis of Navier-Stokes incompressible fluid flows with structural interactions. Particular focus is given on error assessment of specific quantities of interest defined on the structural part. The goal is to establish relatively coarse meshes to model the fluid flow but achieve acceptable accuracy in the quantities of interest. A nonlinear goal-oriented error estimation procedure is presented which is applicable to general nonlinear analyses. Some illustrative solutions using ADINA are given.

A posteriori error estimation techniques in practical finite element analysis

“…Here the premise is that an integrated quantity might be calculated with sufficient accuracy using a well-chosen coarse mesh in part of the domain. For example, considering a fluid flow structural interaction analysis, a coarse mesh representing the fluid might be sufficient to calculate the total force and moment on the structure [81]. And the computational expense to establish and use the coarse mesh of the fluid might be much less than the expense to use a very fine fluid mesh, in particular, if a structural optimization is required.…”

Goal-oriented error estimation for fluid–structure interaction problems

“…Grätsch and Bathe [GB95] first applied goal-oriented error estimation to fluidstructure interaction problems. Sensitivity based adaptation for fsi-problems however are not well understood so far.…”

An unstructured finite volume approach for structural dynamics in response to fluid motions

“…(5) to the dynamic equilibrium Eq. (2) yields (6) which is subject to the boundary conditions: (7) Here the structural boundary is the union of the prescribed displacement boundary d p and the prescribed traction boundary t p which includes the external force f. T is the matrix of outward normal operators. (8) where n = (n x , n y ) is the unit vector outward normal to the domain boundary.…”

“…In particular, Bathe et al [2][3][4][5] proposed a flow-condition-based interpolation (FCBI) finite element scheme for incompressible fluid flows to achieve local mass and momentum conservation which was considered the unique property of the FV method. The FCBI finite element procedure was applied to solve multi-physics problems in a consistent FE framework and its accuracy was assessed by the goal-oriented error estimation technique [6,7]. The current effort also attempts to bridge the gap between FE and FV by developing an unstructured-grid FV structural dynamic solver and by integrating the structural solver with a baseline fluid solver for fluid-structure interaction (FSI) simulation.…”