/navier-stokes-nitsche-vms

Code used for developing the simulations in arXiv:2307.03589

Primary LanguagePython

Repository Description

This repository contains the code utilized to generate the results presented in the paper titled 'Nitsche method for Navier-Stokes equations with slip boundary conditions: convergence analysis and VMS-LES stabilization.'

Models Provided

Two models are included in this repository:

  • Stationary Navier-Stokes Equation with Slip Boundary Conditions: This model is suitable for low Reynolds numbers. It employs the Nitsche method for solution.

  • Non-stationary Navier-Stokes Equation with Slip Boundary Conditions: This model includes a non-stationary term and is applicable for high Reynolds numbers. The VMS-LES Nitsche scheme is employed for stabilization.

Tests Conducted

Three tests are conducted in this work:

  1. Test 1: Convergence Test

    • Scripts: conv_test_nits.py and convergence_test_unsteady.py

  2. Test 2: Lid Driven Cavity Test

    • Scripts: lid_driven_steady_noslip.py, lid_driven_steady_slip.py, lid_driven_unsteady_noslip.py, and lid_driven_unsteady_slip.py

  3. Test 3: Flow Past through a Circular Cylinder

    • Scripts: flow_past_cylinder_noslip.py and flow_past_cylinder_slip.py

Dependencies

The code is dependent on FEniCS 2019.1.0 with Python 3. Please ensure that this dependency is satisfied before running the scripts.