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arXiv · 1812.00218

A locally conservative and energy-stable finite element for the Navier--Stokes problem on time-dependent domains

Tamas L. Horvath·Sander Rhebergen
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Abstract

We present a finite element method for the incompressible Navier--Stokes problem that is locally conservative, energy-stable and pressure-robust on time-dependent domains. To achieve this, the space--time formulation of the Navier--Stokes problem is considered. The space--time domain is partitioned into space--time slabs which in turn are partitioned into space--time simplices. A combined discontinuous Galerkin method across space--time slabs, and space--time hybridized discontinuous Galerkin method within a space--time slab, results in an approximate velocity field that is $H({\rm div})$-conforming and exactly divergence-free, even on time-dependent domains. Numerical examples demonstrate the convergence properties and performance of the method.

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Tamas L. Horvath, Sander Rhebergen. 2018-12-01. A locally conservative and energy-stable finite element for the Navier--Stokes problem on time-dependent domains. https://doi.org/10.1002/fld.4707

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