A partition of unity approach to fluid mechanics and fluid-structure interaction

Abstract

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains challenging largely due to the need to balance computational feasibility, efficiency, and solution accuracy. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of a 2D mock aortic valve simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.

34 pages, 15 figure

References in corpus (5)

• A Nitsche-based cut finite element method for a fluid--structure interaction problem
• A fictitious domain approach with distributed Lagrange multiplier for fluid-structure interactions
• Direct numerical simulation of particulate flows with an overset grid method
• A Nitsche cut finite element method for the Oseen problem with general Navier boundary conditions
• A coupled mitral valve -- left ventricle model with fluid-structure interaction

Cited by in corpus (4)

• Efficient split-step schemes for fluid-structure interaction involving incompressible generalised Newtonian flows
• A multimesh finite element method for the Navier-Stokes equations based on projection methods
• Time-periodic steady-state solution of fluid-structure interaction and cardiac flow problems through multigrid-reduction-in-time
• A Class of Analytic Solutions for Verification and Convergence Analysis of Linear and Nonlinear Fluid-Structure Interaction Algorithms