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

Summary 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 partiti...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2019-04, Vol.89 (12), p.519-532
Main Authors: Horváth, Tamás L., Rhebergen, Sander
Format: Article
Language:English
Subjects:
Computational fluid dynamics
discontinuous Galerkin
Divergence
Energy
Fluid flow
Galerkin method
hybridized
Navier‐Stokes
Nonlinear programming
Pressure dependence
Robustness (mathematics)
Slabs
space time
Time dependence
time‐dependent domains
Velocity distribution
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Summary:Summary 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(div)‐conforming and exactly divergence‐free, even on time‐dependent domains. Numerical examples demonstrate the convergence properties and performance of the method. 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, where 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(div)‐conforming and exactly divergence‐free, even on time‐dependent domains.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.4707