DeepAI
Log In Sign Up

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

06/07/2019
by   Andreas Hessenthaler, et al.
0

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.

READ FULL TEXT
07/18/2020

On Algorithmic Estimation of Analytic Complexity for Polynomial Solutions to Hypergeometric Systems

The paper deals with the analytic complexity of solutions to bivariate h...
02/11/2020

On numerical approximations to fluid-structure interactions involving compressible fluids

In this paper we introduce a numerical scheme for fluid-structure intera...
05/28/2022

Benchmarks for infinite medium, time dependent transport problems with isotropic scattering

The widely used AZURV1 transport benchmarks package provides a suite of ...
06/10/2022

A priori error analysis of linear and nonlinear periodic Schrödinger equations with analytic potentials

This paper is concerned with the numerical analysis of linear and nonlin...
04/22/2022

A consistent co-rotational formulation for aerodynamic nonlinear analysis of flexible frame structures

The design of structures submitted to aerodynamic loads usually requires...
11/26/2019

Error-estimate-based Adaptive Integration For Immersed Isogeometric Analysis

The Finite Cell Method (FCM) together with Isogeometric analysis (IGA) h...