A Monolithic and a Partitioned, Reduced Basis Method for Fluid–Structure Interaction Problems

Monica Nonino,Francesco Ballarin,Gianluigi Rozza

doi:10.3390/fluids6060229

Abstract

The aim of this work is to present an overview about the combination of the Reduced Basis Method (RBM) with two different approaches for Fluid–Structure Interaction (FSI) problems, namely a monolithic and a partitioned approach. We provide the details of implementation of two reduction procedures, and we then apply them to the same test case of interest. We first implement a reduction technique that is based on a monolithic procedure where we solve the fluid and the solid problems all at once. We then present another reduction technique that is based on a partitioned (or segregated) procedure: the fluid and the solid problems are solved separately and then coupled using a fixed point strategy. The toy problem that we consider is based on the Turek–Hron benchmark test case, with a fluid Reynolds number Re=100.

Highlights

The bridging between approximation techniques and high-performance computing finds numerous fields of applications in the industry as well as in academia: it is sufficient to think about heat transfer problems, electromagnetic problems, structural mechanics problems, fluid problems, and acoustic problems
The rest of the work is structured as follows: in Section 2, we define the mathematical formalism behind coupled systems, and in particular, we introduce the Arbitrary Lagrangian Eulerian (ALE) formulation, which is used throughout the rest of the manuscript
We present some numerical results that were obtained by adopting a monolithic approach for the toy problem inspired by the Turek–Hron benchmark test case [31,32]; in particular, we refer to the test case FSI2 therein, which corresponds to a fluid with Reynolds number Re = 100

Summary

Introduction

The bridging between approximation techniques and high-performance computing finds numerous fields of applications in the industry as well as in academia: it is sufficient to think about heat transfer problems, electromagnetic problems, structural mechanics problems (linear/nonlinear elasticity), fluid problems, and acoustic problems In all of these examples, the models are described using a system of partial differential equations (PDE) that usually depends on a given number of parameters that describe the geometrical configuration of the physical domain over which the problem is formulated or that describe some physical quantities (e.g., the Reynolds number for a fluid or the Lamè constants for a solid) or some boundary conditions. This is usually performed using some wellestablished discretization technique, such as the Finite Element Method (FEM); another discretization method used, for example, in the compressible framework in computational fluid dynamics is the Finite Volume Method (FVM), and another possibility is the Cut Finite

Objectives

Methods

Results

Discussion

Conclusion