This repository implements different energy stable schemes for the iNSE problem in ALE formalism.
Go to file
Cristobal Bertoglio cefb7a13dc corrections 2022-04-13 17:42:13 +02:00
cbme2022 corrections 2022-04-13 17:42:13 +02:00
py py dir 2021-09-01 06:40:16 +02:00
tex added conference abstract 2022-04-08 14:01:42 +02:00
.gitignore stores pdf conference 2022-04-08 16:31:44 +02:00
README.rst Added tex folder 2021-08-31 09:03:30 +02:00
article_published.pdf Fixed gitignore for pdf 2022-04-08 16:21:24 +02:00


<html xmlns="" xml:lang="en" lang="en"> <head> </head>


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.


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.


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 >= 3.5
  • FEniCS >= 2019.1.0


[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: 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: