A Variational Context for FSI Simulations Introducing Arbitrary Boundary Constraints

Abstract

We present a method for understanding Fluid Structure Interaction simulations in continuous media, an important class of phenomena that cover several fields of applications and research lines. Specialized literature has experienced a compelling need for improving the predictive skills of the models for simulations of fluid flow under arbitrary boundary conditions. In the present work, complex boundary conditions are those imposed by devious domains through where the fluid flows. We show a modeling procedure based on the Virtual Power Balance that results in a variational equation. The main consequence of this modeling procedure is the characterization of kinematic admissible loadings (stress-like and force-like loadings). Within the variational framework, we employ a numerical solver based on Lattice Boltzmann Method. The solver obtains the complete description of the desired phenomena like equilibrium conditions, constitutive equations, among other relevant features. Numerical experiments are presented to show the potential of the modeling procedure studied in this work to deal with several complex boundary constraints.