Validation of Partitioned FSI framework completed

June 30, 2023

2023   ·   multi-physics   programming  

Probelm Statement

In order to study the “coupling instability of low mass-ratio partitioned FSI simulations” I first needed to develop a robust partitioned numerical framework that was able to capably handle the challenges of problematic FSI simulation configurations. To this end, after much struggling and wondering in the dark, I was FINALLY able to develop a suite of 2D and 3D high-fidelity partitioned FSI codes. Achieving this feat is a source of real personal pride; as without proper guidance or an intimate knowledge of the fundamental instability intrinsic to the problem, great effort was required (often involving numerous protracted periods of brutal trial and error) to amass a complete and homogenous set of numerical tools to tackle this difficult problem.

In the end (having experimented on the gamut of available open-source resources) the majority of my eventually developed code-based was derived from a source (redbKIT-based) monolithic FSI solver. These solvers were decomposed from the original toolkit into their baseline elements and were then strategically reassembled and further built upon until a sufficiently robust partitioned FSI scheme was attained. In particular, was the required integration of appropriate conservative Dirchlet and Neummann interfacial boundary conditions into the (independently treated) fluid and structural solvers, respectively. These additions, as well as all of the other requisite algorithmic logic, interfacial data mapping, and iterative stabalization techniques were also added thus make the partitoned codes developed here a “semi”-unique product in their own right.

Coupling Features

Features unique to a partitioned strategy that I have integrated into my developed framework include:

  • Coupling Methods:
    • Anderson Acceleration
    • Generalized Broyden
    • Broyden’s Second Method
    • Multi-Vector Least Square
    • Dynamic Aitken Relaxation
    • Constant Relaxation
    • Pure Gauss-Seidel Iterations
  • Filtering Strategies:
    • QR1 Filtering
    • QR2 (Classic Gram-Schmidt) Filtering
    • QR2 (Modified Gram-Schmidt) Filtering
    • QR2 (Householder Reflections) Filtering
    • POD Filtering
  • Interface Mapping Techniques:
    • Nearest Neighbour Interpolation
    • Projection and Linear Interpolation
    • Radial Basis Function Interpolation
  • Extrapolation Methods:
    • Constant
    • Linear
    • Quadratic
    • Cubic
  • Work in Progress Tools:
    • Interface Tracking
    • Adaptive Regularization Least Squares
    • Selective Secant Inclusion
    • Truncated SVD Filtering

Framework Validation

To validate the accuracy of the developed partitioned framework, I successfully compared my results collected from three challenging FSI benchmarks againts both those results provided in the literature and that produced by established commercial software. These results served mainly to demonstrate the accuracy of the domain solvers themselves and, generally speaking, the robustness of the partitioned scheme to handle complex FSI problems with strong added-mass effects, high structural nonlinearity, and considerable mesh deformation. The benchmarks successfully reproduced included;

Benchmark Cases

  • 2D Incompressible Flow over a Vertically Cantilevered (Linear) Elastic Beam
  • 2D Incompressible Flow over a Horizonatlly Cantilevered (Nonlinear) Elastic Beam
  • 3D Pressure Pulse Propogation through an Elastic Tube

details of the validation procedure as well as the confirming results generated via the study are given on this website’s companion projects page.