ingeborggjerde / nitsche-method-for-navier-stokes-with-slip

Nitsche method for solving Navier-Stokes with slip boundary conditions

Solving the Navier Stokes equations with slip using a Nitsche method

This repository contains the code used to produce the results of the paper Nitsche's method for Navier-Stokes equations with slip boundary conditions, Ingeborg Gjerde and L. Ridgway Scott, Math. Comp. 91 (2022), 597-622.

Dependencies

• FEniCS 2019.1.0 (with python3)

Usage

The numerical results used in the article can be obtained by running the script run_convergence_test.py as follows

~/ns-with-slip$ python run_convergence_test.py --nrefs 4 --beta=-2.0

with 4 mesh refinements, friction parameter beta=-2.0 and the remaining variables initialized to a default value.

The user can specify the following variables:

• -- nrefs (int), number of mesh refinements, default = 4
• -- cyl_refinement (int), whether the mesh should be refined around the cylinder, 1=Yes and 0=No, default=0
• -- beta (float), friction parameter, default = -2.0 in which case one can use the potential flow solution
• -- nu (float), viscosity, default=1.0
• -- degree (int), polynomial degree, default=2
• -- ngammas (int), gives a range of n different Nitsche stabilization parameters to try, default=1
• -- normal_choice (str), gives the normal type, options are projected_normal and discrete_normal

Running e.g. with all default values,

~/ns-with-slip$ python run_convergence_test.py

produces the text file u_error_beta-2.0_uniform.txt located in /home/ns-with-slip/results which gives a latex table containing the errors and convergence rates for the H1-error of u-u_h.

Limitations

• The code assumes a cylinder radius R=1.0 and cylinder center in [0.0, 0.0]
• Due to some bug the code does not work in parallel

Citing

If you find this code useful, feel free to cite the paper.

nitsche-method-for-navier-stokes-with-slip's Issues

Add license to code

You should add a license to the code so that it is clear how it can be reused by others.
@IngeborgGjerde do you mind a MIT license?