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The incompressible Navier-Stokes equations solver in 2D domains

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CFD2D is open source software for Linux for solving the non-dimensionalized incompressible Navier-Stokes equations (NSE) inside an arbitrary two-dimensional domain inscribed in a unit square with Dirichlet and "do-nothing" boundary conditions. The space discretization is based on Finite Element Method (FEM) using an approximately uniform triangular mesh. The two choices of FE spaces are offered, these are of the so called MINI-element and of the Taylor-Hood element. The first element consists of continuous piecewise linears with a cubic bubble function for the velocity field, and the second of continuous piecewise quadratics for the same. The pressure field is approximated via piecewise linears in both cases. Both stationary and time-dependent regimes supported. Elementary graphing tools are provided. GMRES and CG iterative algorithms are used for solving linear systems. Software "Triangle" is used for mesh generation.

CFD2D Web Site


Simulations, Mathematics


MIT License


  • Domain specified algebraically, with holes allowed in it
  • Two types of boundary conditions: Dirichlet and "do-nothing"
  • Both stationary and time-dependent cases
  • Simple input preparation
  • Simple execution from command line
  • Simple graphing tools for velocity and pressure
  • Efficient Delaunay triangulation of the domain
  • Simple graphing tool for mesh
  • Additional modules for Stokes flow and L2-projection of the initial data


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    Thanks for software and updates.

    Posted 06/08/2013
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Additional Project Details



Intended Audience

Science/Research, Education, End Users/Desktop, Engineering

User Interface

Console/Terminal, Command-line

Programming Language

C++, C



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