## A monolithic approach for the numerical simulation of fluid structure interactrion problems

43rd AIAA Fluid Dynamics Conference, San Diego, CA, United States Of America, 24 - 27 June 2013

• Publication Type: Conference Paper / Full Text
• City: San Diego, CA
• Country: United States Of America
• Keywords: Finite element method, Fluid-structure interaction, Large displacement, Large-scale computation, Monolitic method, Unstructured finite volume method
• Istanbul Technical University Affiliated: Yes

#### Abstract

The current article presents a new numerical algorithm based on the Arbitrary Lagrangian-Eulerian (ALE) formulation for a fully coupled solution of the large-scale fluid-structure interaction (FSI) problems where the fluid is modeled by the incompressible Navier-Stokes equations and the structure is modeled by the St. Venant-Kirchhoff model. The governing equations of the fluid domain are discretized using an Arbitrary Lagrangian-Eulerian (ALE) formulation based on the side-centered unstructured finite volume method where the velocity vector components are defined at the mid-point of each cell face while the pressure is defined at the element centroid. The present arrangement of the primitive variables leads to a stable numerical scheme and it does not require any ad-hoc modifications in order to enhance the pressure-velocity coupling. The deformation of the solid domain is governed by the constitutive laws for the nonlinear Saint Venant-Kirchhoff material and the classical Galerkin finite element is used to discretise the governing equations in a Lagrangian frame. The time integration method for the structure domain is based on the Newmark type generalized-α method while the first-order backward difference is used in the fluid domain. The resulting large-scale algebraic linear equations from the discretization of fluid and solid domains are solved in a fully coupled form using new monolithic approaches. In order to account for nonlinearity due to unknown position of the solid boundary and the nonlinear constitutive equations for fluid and solid domains, several sub-iterations are performed. The parallel implementation of the fully coupled unstructured fluid-structure solver is based on the PETSc and HYPRE libraries for improving the efficiency of the code. The present numerical algorithm is initially validated for a steady Newtonian fluid interacting with an elastic bar behind a cylinder, a three-dimensional elastic solid in a steady channel flow and vortex induced vibration of a flag attached behind a rectangular rigid body.