A monolithic and a partitioned Reduced Basis Method for Fluid-Structure Interaction problems

TL;DR

This paper compares monolithic and partitioned Reduced Basis Methods for Fluid-Structure Interaction problems, demonstrating their implementation and application on a benchmark test case with Re=100.

Contribution

It introduces and compares two reduced basis approaches—monolithic and partitioned—for FSI problems, providing implementation details and application to a standard benchmark.

Findings

Both methods successfully reduced computational complexity.

The monolithic approach solves fluid and solid simultaneously.

The partitioned approach uses a fixed point strategy for coupling.

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.