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A Scipy-Fenics interface for incompressible Navier-Stokes

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# dolfin_navier_scipy

[![DOI](https://zenodo.org/badge/15728657.svg)](https://zenodo.org/badge/latestdoi/15728657)

This python module dns provides an interface between the FEM toolbox [FEniCS](www.fenicsproject.org) and [SciPy](www.scipy.org) in view of simulation and control of incompressible flows. Basically, FEniCS is used to discretize the incompressible Navier-Stokes equations in space. Then dns makes the discretized operators available in SciPy for use in model reduction, simulation, or control and optimization.

dns also contains a solver for the steady state and time dependent problems.

## Quick Start

To get started, create the needed subdirectories and run one of the tests/time_dep_nse_.py files, e.g.

` cd tests mkdir data mkdir results # export PYTHONPATH="$PYTHONPATH:path/to/repo/"  # add the repo to the path python3 time_dep_nse_expnonl.py `

Then, to examine the results, launch ` paraview results/vel_TH__timestep.pvd `

## Test Cases and Examples

A selection:

  • tests/mini_setup.py: a minimal setup for a steady-state simulation
  • tests/steadystate_schaefer-turek_2D-1.py: the 2D steady-state cylinder wake benchmark by Schäfer/Turek
  • tests/steadystate_rotcyl.py: the 2D cylinder wake with a freely rotating cylinder as benchmarked in Richter et al.
  • tests/time_dep_nse_.py: time integration with Picard and Newton linearization
  • tests/time_dep_nse_expnonl.py: time integration with explicit treatment of the nonlinearity
  • tests/time_dep_nse_bcrob.py: time integration of the cylinder wake with boundary controls
  • tests/time_dep_nse_krylov.py: time integration with iterative solves of the state equations via [krypy](https://github.com/andrenarchy/krypy)

## Dependencies

The latter is my home-brew module that includes the submodule lin_alg_utils with routines for solving the saddle point problem as it arises in the (v,p) formulation of the NSE.

Note: the branch lau-included already contains the module sadptprj_riclyap_adi

## Documentation

Documentation of the code goes [here](http://dolfin-navier-scipy.readthedocs.org/en/latest/index.html).

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