A high-order in space spectral-element methodology for the solution of a strongly coupled fluid-structure interaction (FSI) problem is developed. A methodology is based on a partitioned solution of incompressible fluid equations on body-fitted grids, and nonlinearly-elastic solid deformation equations coupled via a fixed-point iteration approach with Aitken relaxation. A comprehensive verification strategy of the developed methodology is presented, including h-, p-and temporal refinement studies. An expected order of convergence is demonstrated first separately for the corresponding fluid and solid solvers, followed by a self-convergence study on a coupled FSI problem (self-convergence refers to a convergence to a reference solution obtained with the same solver at higher resolution). To this end, a new three-dimensional fluid-structure interaction benchmark is proposed for a verification of the FSI codes, which consists of a fluid flow in a channel with one rigid and one flexible wall. It is shown that, due to a consistent problem formulation, including initial and boundary conditions, a high-order spatial convergence on a fully coupled FSI problem can be demonstrated. Finally, a developed framework is applied successfully to a Direct Numerical Simulation of a turbulent flow in a channel interacting with a compliant wall, where the fluid-structure interface is fully resolved.
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A spatially varying robin interface condition for fluid‐structure coupled simulations
We present a spatially varying Robin interface condition for solving fluid‐structure interaction problems involving incompressible fluid flows and nonuniform flexible structures. Recent studies have shown that for uniform structures with constant material and geometric properties, a constant one‐parameter Robin interface condition can improve the stability and accuracy of partitioned numerical solution procedures. In this work, we generalize the parameter to a spatially varying function that depends on the structure's local material and geometric properties, without varying the exact solution of the coupled fluid‐structure system. We present an algorithm to implement the Robin interface condition in an embedded boundary method for coupling a projection‐based incompressible viscous flow solver with a nonlinear finite element structural solver. We demonstrate the numerical effects of the spatially varying Robin interface condition using two example problems: a simplified model problem featuring a nonuniform Euler‐Bernoulli beam interacting with an inviscid flow and a generalized Turek‐Hron problem featuring a nonuniform, highly flexible beam interacting with a viscous laminar flow. Both cases show that a spatially varying Robin interface condition can clearly improve numerical accuracy (by up to two orders of magnitude in one instance) for the same computational cost. Using the second example problem, we also demonstrate and compare two models for determining the local value of the combination function in the Robin interface condition.
more » « less- NSF-PAR ID:
- 10449294
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal for Numerical Methods in Engineering
- Volume:
- 122
- Issue:
- 19
- ISSN:
- 0029-5981
- Page Range / eLocation ID:
- p. 5176-5203
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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