General Galerkin methods for Unified Continuum modeling of fluid-structure interaction

Johan Jansson
Numerical Analysis
School of Computer Science and Communication


We describe an incompressible Unified Continuum (UC) model in Euler (laboratory) coordinates with a moving mesh for tracking the fluid-structure interface as part of the discretization, allowing simple and general formulation and efficient computation. The model consists of conservation equations for mass and momentum, a phase convection equation and a Cauchy stress and phase variable $\theta$ as data for defining material properties and constitutive laws. We target realistic 3D turbulent fluid-structure interaction (FSI) applications, where we show simulation results of a flexible flag mounted in the turbulent wake behind a cube as a qualitative test of the method, leaving adaptive error control for future work. The Unicorn implementation is published as part of the FEniCS Free Software system for automation of computational mathematical modeling.