NAVIER_STOKES_2D_EXACT
Exact solutions to the
2D Incompressible Time-Dependent Navier Stokes Equations

NAVIER_STOKES_2D_EXACT, a MATLAB library which evaluates exact solutions to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 2D.

• Lukas: steady flow, pressure is zero everywhere;
• Poiseuille: steady flow, vertical velocity and right hand side are zero everywhere;
• Spiral: velocity is zero on the boundary of the unit square;
• Taylor: source term is zero everywhere.
• Vortex: a steady flow with the same velocity pattern as Taylor.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

NAVIER_STOKES_2D_EXACT is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

navier_stokes_2d_exact_test

NAVIER_STOKES_3D_EXACT, a MATLAB library which evaluates exact solutions to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 3D.

NAVIER_STOKES_MESH2D, MATLAB data files defining meshes for several 2D test problems involving the Navier Stokes equations for fluid flow, provided by Leo Rebholz.

SPIRAL_DATA, a MATLAB library which computes a velocity vector field that satisfies the continuity equation, writing the data to a file that can be plotted by gnuplot.

STOKES_2D_EXACT, a MATLAB library which evaluates exact solutions to the incompressible steady Stokes equations over the unit square in 2D.

Reference:

1. Maxim Olshanskii, Leo Rebholz,
   Application of barycenter refined meshes in linear elasticity and incompressible fluid dynamics,
   ETNA: Electronic Transactions in Numerical Analysis,
   Volume 38, pages 258-274, 2011.
2. Geoffrey Taylor,
   On the decay of vortices in a viscous fluid,
   Philosophical Magazine,
   Volume 46, 1923, pages 671-674.
3. Geoffrey Taylor, A E Green,
   Mechanism for the production of small eddies from large ones,
   Proceedings of the Royal Society of London,
   Series A, Volume 158, 1937, pages 499-521.

Source Code:

• grid_2d.m, returns a regular 2D grid.
• ns2de_gnuplot.m, writes the velocity vector field to files for GNUPLOT.
• r8vec_uniform_ab.m, returns a scaled pseudorandom R8VEC.
• resid_lukas.m, evaluates the Lukas Bystricky residuals.
• resid_poiseuille.m, evaluates the Poiseuille residuals.
• resid_spiral.m, evaluates the Spiral residuals.
• resid_taylor.m, evaluates the Taylor residuals.
• resid_vortex.m, evaluates the Vortex residuals.
• rhs_lukas.m, evaluates the Lukas Bystricky right hand sides.
• rhs_poiseuille.m, evaluates the Poiseuille right hand sides.
• rhs_spiral.m, evaluates the Spiral right hand sides.
• rhs_taylor.m, evaluates the Taylor right hand sides.
• rhs_vortex.m, evaluates the Vortex right hand sides.
• timestamp.m prints the YMDHMS date as a timestamp.
• uvp_lukas.m, evaluates the Lukas Bystricky flow field.
• uvp_poiseuille.m, evaluates the Poiseuille flow field.
• uvp_spiral.m, evaluates the Spiral flow field.
• uvp_taylor.m, evaluates the Taylor flow field.
• uvp_vortex.m, evaluates the Vortex flow field.