Numerical convergence of discrete extensions in a space‐time finite element, fictitious domain method for the Navier–Stokes equations

Anselmann, Mathias; Bause, Markus

doi:10.1002/pamm.202100011

Cited by 1 publication

(2 citation statements)

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“…Remark The numerical results presented in Section 5 and Reference 56 show that the space‐time convergence behavior of the CutFEM approach is not deteriorated by the application of the iterated numerical integration on the cut cells. This also holds if irregular (tiny) cuts are present.…”

Section: Implementational Aspectsmentioning

confidence: 83%

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Cut finite element methods and ghost stabilization techniques for space‐time discretizations of the Navier–Stokes equations

Anselmann

Bause

2022

Numerical Methods in Fluids

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We propose and analyze numerically a new fictitious domain method, based on higher order space-time finite element discretizations, for the simulation of the nonstationary, incompressible Navier-Stokes equations on evolving domains. The physical domain is embedded into a fixed computational mesh such that arbitrary intersections of the moving domain's boundaries with the background mesh occur. The key ingredients of the approach are the weak formulation of Dirichlet boundary conditions by Nitsche's method, the flexible and efficient integration over all types of intersections of cells by moving boundaries and the spatial extension of the discrete physical quantities to the entire computational background mesh including fictitious (ghost) subdomains of fluid flow. To prevent spurious oscillations caused by irregular intersections of mesh cells, a penalization ensuring the stability of the approach and defining implicitly the extension to host domains is added. These techniques are embedded in an arbitrary order, discontinuous Galerkin discretization of the time variable and an inf-sup stable discretization of the spatial variables. The convergence and stability properties of the approach are studied, firstly, for a benchmark problem of flow around a stationary obstacle and, secondly, for flow around moving obstacles with arising cut cells and fictitious domains. The parallel implementation is also addressed.

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Section: Implementational Aspectsmentioning

confidence: 83%

“…Section 5 ) illustrate the robustness of the extension and stabilization. The restriction of the ghost penalty stabilization to a strip around the fluid domain is studied in a further work; compare Reference 56 . A superiority of the latter stabilization is not observed.…”

Section: Space‐time Finite Element Discretization With Cutfemmentioning

confidence: 99%