2020-12-11 16:03:48 +01:00
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NavierStokes
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============
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This repository implements via finite element solvers for incompressible
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Navier-Stokes (iNSE) equations in Arbitrary Lagrangian-Eulerian (ALE) formalism the schemes
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proposed on [RA20]_.
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In particular, it aims to replicate the energy results shown in the article [RA20]_
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for both Monolithic and Chorin-Temam solvers.
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Solvers
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-------
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Both monolithic solver and a fractional step solver are implemented.
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* Monolithic solver for the iNSE-ALE problem with linearized convective term
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and Taylor-Hood (P2/P1) stable finite element space.
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* Fractional step solver for the iNSE-ALE problem with linealized convective term
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and P1/P1 finite element space. The Chorin-Temam schemes proposed is described in [RA20]_.
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Flow model
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----------
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A rectangle domain is taken with fully Dirichlet homogeneous boundary conditions
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and non-zero initial velocity profile. Further description of the problem also can be found
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in the reference.
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Usage
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----------
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Since the repository aims to directly reproduce the results of the reference,
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no configuration files where implemented to further customize the problem.
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Nevertheless, the solvers are easily modified since its implementation is done via
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FEniCS [LO12]_.
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An ipynb file is included to reproduce the results and recommended to use.
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If desired to run the simulations only, execute::
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python main.py
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Dependencies
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------------
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- Python >= 3.5
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2020-12-11 16:06:10 +01:00
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- FEniCS >= 2019.1.0
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2020-12-11 16:03:48 +01:00
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Reference
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^^^^^^^^^^
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.. [RA20] Aróstica R., Bertoglio C. (2020) On monolithic and Chorin-Temam
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schemes for incompressible flows in moving domains.
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Applied Mathematics Letters, doi: https://doi.org/10.1016/j.aml.2020.106830
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ISBN: 978-3-642-23099-8
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.. [LO12] Logg A., Mardal K.-A., Wells G. N. (2012) Automated Solution of Differential
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Equations by the Finite Element Method.
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Springer, Berlin, Heidelberg, doi: https://doi.org/10.1007/978-3-642-23099-8
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