This repository implements different energy stable schemes for the iNSE problem in ALE formalism.
You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
 
 
 
Cristobal Bertoglio 653985b980 py dir 3 months ago
py py dir 3 months ago
tex Updated gitignore 3 months ago
.gitignore Updated gitignore 3 months ago
README.rst Added tex folder 3 months ago

README.rst

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> <head> </head>

NavierStokes

This repository implements via finite element solvers for incompressible Navier-Stokes (iNSE) equations in Arbitrary Lagrangian-Eulerian (ALE) formalism the schemes proposed on [RA20].

It aims to replicate the energy results shown in the article [RA20] for both Monolithic and Chorin-Temam solvers. TeX submissions are added for reference.

Solvers

Both monolithic solver and a fractional step solver are implemented.

  • Monolithic solver for the iNSE-ALE problem with linearized convective term and Taylor-Hood (P2/P1) stable finite element space.
  • Fractional step solver for the iNSE-ALE problem with linealized convective term and P1/P1 finite element space. Chorin-Temam schemes proposed here are described in [RA20].

Flow model

A rectangle domain is taken with fully Dirichlet homogeneous boundary conditions and non-zero initial velocity profile. Further description of the problem also can be found in the reference.

Usage

Since the repository aims to directly reproduce the results of the reference, no configuration files where implemented to further customize the problem. Nevertheless, the solvers are easily modified since its implementation is done via FEniCS [LO12].

To run the simulations and generate the figures depicted in our article, execute:

python main.py

Dependencies

  • Python >= 3.5
  • FEniCS >= 2019.1.0

Reference

[RA20](1, 2, 3) Aróstica R., Bertoglio C. (2020) On monolithic and Chorin-Temam schemes for incompressible flows in moving domains. Applied Mathematics Letters, doi: https://doi.org/10.1016/j.aml.2020.106830 ISBN: 978-3-642-23099-8
[LO12]Logg A., Mardal K.-A., Wells G. N. (2012) Automated Solution of Differential Equations by the Finite Element Method. Springer, Berlin, Heidelberg, doi: https://doi.org/10.1007/978-3-642-23099-8
</html>