navier_stokes_2d_exact

navier_stokes_2d_exact, a Fortran77 code which evaluates exact solutions to the incompressible time-dependent Navier-Stokes Equations (NSE) over an arbitrary domain in 2D.

• cavity: steady, polynomial in space, zero velocity boundary conditions on sides and bottoms, variable velocity on "top". This is NOT the standard "driven cavity" example;
• exppoly: time dependent, exponential growth in time, zero velocity boundary conditions on unit square;
• exptrig: time dependent, trigonometric in space, exponential growth in time, zero velocity boundary conditions on unit square; at t=1, this flow forms a spiral. At later times, the exponential growth seems to make the solution physically absurd and computationally intractable.
• GMS: time dependent, vortices do not decay to zero;
• Lukas: steady, zero pressure;
• NoFlow: steady, zero velocity, nonzero pressure;
• Poiseuille: steady, zero vertical velocity, zero source term;
• Spiral: time dependent, zero velocity on the unit square;
• Taylor: time dependent, zero source term, solution decays exponentially.
• Vortex: steady, same velocity pattern as Taylor.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

navier_stokes_2d_exact is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

navier_stokes_2d_exact_test

f77_exact, a Fortran77 code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).

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:

• navier_stokes_2d_exact.f, the source code.
• navier_stokes_2d_exact.sh, BASH commands to compile the source code.