High-Order Added-Mass Partitioned Algorithms for Fluid-Structure Interaction Problems

Rensselaer Polytechnic Institute, Troy NY

Investigators

Abstract

This research project will dramatically improve computer algorithms used for the simulation of important problems in applied science, engineering, and bio-medicine, such as the modeling of blood flow in human veins, which provides critical data to evaluate surgical procedures and to design medical devices and implants. The area of fluid-structure interaction (i.e. coupling fluids with deforming solids), which this project addresses, is of current and growing interest due to its importance in many areas of engineering and applied science, including not only bio-medicine but also the modeling of flow-induced vibrations of structures (aircraft, undersea cables, wind turbines, buildings), wave energy devices, parachutes and airbags, acoustic lenses, thermal expansion in nuclear reactor cores, and shock-structure interactions (blast effects). Computing accurate solutions of fluid-structure interaction problems efficiently is very challenging due to their complex physical and geometrical properties, but also due to challenging mathematical issues. The new techniques developed by this project will address both these challenges. A wide class of important fluid-structure interaction (FSI) problems are difficult to simulate due to the so-called added mass instability. The focus of the research is on FSI problems coupling incompressible flow with elastic or rigid structures. Of particular interest are problems in which the mass of the fluid and that of the structure are similar, such as in applications of hemodynamics, where added-mass effects are strong. The overarching goal of this project is to develop stable and high-order accurate partitioned algorithms for FSI problems that overcome the numerical difficulties associated with complex fluid-solid couplings and strong added-mass effects. These algorithms will be based on newly devised Added-Mass Partitioned (AMP) schemes that represent a conceptual breakthrough in the field by providing a path forward to develop accurate schemes for fluid-structure interaction problems. An important property of AMP schemes is that they remain stable even for light solids when added-mass effects are significant. The new algorithms will be incorporated into a flexible computational framework that will allow efficient simulations for wide class of complex fluid-structure interaction problems.