A multimesh finite element method for the Navier-Stokes equations based on projection methods
arXiv:1912.06392 · doi:10.1016/j.cma.2020.113129
Abstract
The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche's method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable variational formulation. In this contribution we extend the multimesh finite element method to the Navier-Stokes equations based on the incremental pressure correction scheme. For each step in the pressure correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The overall scheme yields expected spatial and temporal convergence rates on the Taylor-Green problem, and demonstrates good agreement for the drag and lift coefficients on the Turek-Schafer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a channel.
References in corpus (10)
- DOLFIN: Automated Finite Element Computing
- A Hybrid High-Order method for the incompressible Navier--Stokes equations based on Temam's device
- A Nitsche-based cut finite element method for a fluid--structure interaction problem
- Preconditioning immersed isogeometric finite element methods with application to flow problems
- A stabilized cut discontinuous Galerkin framework: I. Elliptic boundary value and interface problems
- Skeleton-stabilized ImmersoGeometric Analysis for incompressible viscous flow problems
- Variational Implementation of Immersed Finite Element Methods
- Scalable multigrid methods for immersed finite element methods and immersed isogeometric analysis
- A partition of unity approach to fluid mechanics and fluid-structure interaction
- Efficient implementation of finite element methods on non-matching and overlapping meshes in 3D