Monolithic Variational Multiscale Method for Fluid-Structure Interaction with Anisotropic Adaptive Meshing

Abstract : This paper presents a new immersed volume method for solving rigid body motions. The pro­posed method is developed in the context of the monolithic formulation. It consists in consid­ering a single grid and solving one set of equations with different material properties. A fast anisotropic mesh adaptation algorithm based on the variations of the distance function is then applied to ensure an accurate capture of the discontinuities at the fluid-solid interface. Such strategy gives rise to an extra stress tensor in the Navier-Stokes equations coming from the presence of the structure (rigid/elastic) in the fluid. The system is solved using a finite element variational multiscale (VMS) method, which consists in here of decomposition for the veloc­ity, the pressure and the extra constraint fields into coarse/resolved scales and fine/unresolved scales. We assess the behaviour and accuracy of the proposed formulation in the simulation of 2D and 3D time-dependent numerical examples such as: vortex shedding behind an obstacle and unsteady flow around 3D helicopter