Goal-oriented error estimation for fluid–structure interaction problems

Abstract

In this work, we present an adaptive finite element method for the numerical simulation of fluid-structure interaction problems. The coupled system is formulated in a variational monolithic Arbitrary Lagrangian Eulerian framework. We derive methods for goal-oriented error estimation and mesh adaptation with the dual weighted residual method. Key to this error estimator is a Petrov-Galerkin approach for deriving the variational formulation of the coupled system. The developed method is applied to two and three dimensional stationary benchmark problems to demonstrate its efficiency.

The Numerical Simulation of Large-Scale Fluid-Structure Interaction Problems in a Fully Coupled Form

“…The computed u−velocity vector component isosurfaces are shown in Figure 6 with the streamtraces at Re = 40. The computed deformation vector components at the point A(0.45, 0.15, 0.15) are given in Table 5 and the values are compared with the results of Richter [30]. The results are relatively in good agreement.…”

A Parallel Fully Coupled Approach for Large-Scale Fluid-Structure Interaction Problems

“…In addition, the streamtraces computed on the solid walls are shown in Figure 8 on the front and on the back side of the solid body. The computed deformation vector components at the point A(0.45, 0.15, 0.15) are given in Table 5 for more precise comparison and the values are compared with the results of Richter [56]. The results are relatively in good agreement.…”

Partitioned Simulation of Fluid-Structure Interaction

“…In that case, a new grid has to be generated for at least part of the domain. Richter [161] uses local grid adaptivity driven by goal-oriented error estimation. The interpolation from the old to the new grid inevitably causes errors.…”