# A Class of Analytic Solutions for Verification and Convergence Analysis of Linear and Nonlinear Fluid-Structure Interaction Algorithms

## TL;DR

This paper introduces a comprehensive set of 16 analytic solutions for fluid-structure interaction problems, enabling verification and convergence analysis of numerical methods across static, transient, linear, and hyperelastic scenarios.

## Contribution

It provides a novel class of analytic solutions that facilitate verification and detailed convergence analysis of FSI algorithms in multiple dimensions and material behaviors.

## Key findings

- Validated convergence behavior of a monolithic FSI technique.
- Demonstrated applicability across linear and hyperelastic materials.
- Enabled systematic verification of FSI numerical methods.

## Abstract

Fluid-structure interaction (FSI) problems are pervasive in the computational engineering community. The need to address challenging FSI problems has led to the development of a broad range of numerical methods addressing a variety of application-specific demands. While a range of numerical and experimental benchmarks are present in the literature, few solutions are available that enable both verification and spatiotemporal convergence analysis. In this paper, we introduce a class of analytic solutions to FSI problems involving shear in channels and pipes. Comprised of 16 separate analytic solutions, our approach is permuted to enable progressive verification and analysis of FSI methods and implementations, in two and three dimensions, for static and transient scenarios as well as for linear and hyperelastic solid materials. Results are shown for a range of analytic models exhibiting progressively complex behavior. The utility of these solutions for analysis of convergence behavior is further demonstrated using a previously published monolithic FSI technique. The resulting class of analytic solutions addresses a core challenge in the development of novel FSI algorithms and implementations, providing a progressive testbed for verification and detailed convergence analysis.

---
Source: https://tomesphere.com/paper/1906.04033