jburkardt

NAVIER_STOKES_2D_EXACT\ Exact solutions to the\ 2D Incompressible Time-Dependent Navier Stokes Equations {#navier_stokes_2d_exact-exact-solutions-to-the-2d-incompressible-time-dependent-navier-stokes-equations align=”center”} ========================================================

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

• Lucas: 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: steady vortex flow.

Licensing: {#licensing align=”center”}

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

Languages: {#languages align=”center”}

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 a Python version.

Related Data and Programs: {#related-data-and-programs align=”center”}

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

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

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

Reference: {#reference align=”center”}

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: {#source-code align=”center”}

• ns2de.cpp, the source code.
• ns2de.hpp, the include file.

Examples and Tests: {#examples-and-tests align=”center”}

• ns2de_prb.cpp, a sample calling program.
• ns2de_prb_output.txt, the output file.

Lucas Bystricky flow:

• lucas_commands.txt, commands to draw the velocity field.
• lucas_data.txt, velocity field data.
• lucas.png, a PNG plot of the velocity field.

Poiseuille flow:

• poiseuille_commands.txt, commands to draw the velocity field.
• poiseuille_data.txt, velocity field data.
• poiseuille.png, a PNG plot of the velocity field.

Spiral flow:

• spiral_commands.txt, commands to draw the velocity field.
• spiral_data.txt, velocity field data.
• spiral.png, a PNG plot of the velocity field.

Taylor flow:

• taylor_commands.txt, commands to draw the velocity field.
• taylor_data.txt, velocity field data.
• taylor.png, a PNG plot of the velocity field.

Vortex flow:

• vortex_commands.txt, commands to draw the velocity field.
• vortex_data.txt, velocity field data.
• vortex.png, a PNG plot of the velocity field.

List of Routines: {#list-of-routines align=”center”}

• GRID_2D returns a regular 2D grid.
• NS2DE_GNUPLOT writes the Navier-Stokes solution to files for GNUPLOT.
• R8VEC_AMAX returns the maximum absolute value in an R8VEC.
• R8VEC_AMIN returns the minimum absolute value in an R8VEC.
• R8VEC_LINSPACE creates a vector of linearly spaced values.
• R8VEC_MAX returns the value of the maximum element in an R8VEC.
• R8VEC_MIN returns the value of the minimum element in an R8VEC.
• R8VEC_NORM_L2 returns the L2 norm of an R8VEC.
• R8VEC_UNIFORM_AB_NEW returns a scaled pseudorandom R8VEC.
• RESID_LUCAS returns Lucas Bystricky residuals.
• RESID_POISEUILLE returns Poiseuille residuals.
• RESID_SPIRAL evaluates Spiral residuals.
• RESID_TAYLOR returns Taylor residuals.
• RESID_VORTEX returns Vortex residuals.
• RHS_LUCAS evaluates Lucas Bystricky right hand sides.
• RHS_POISEUILLE evaluates Poiseuille right hand sides.
• RHS_SPIRAL evaluates Spiral right hand sides.
• RHS_TAYLOR returns Taylor right hand sides.
• RHS_VORTEX returns Vortex right hand sides.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• UVP_LUCAS evaluates Lucas Bystricky’s solution.
• UVP_POISEUILLE evaluate Poiseuille solutions.
• UVP_SPIRAL evaluates Spiral solutions.
• UVP_TAYLOR evaluates Taylor solutions.
• UVP_VORTEX evaluates Vortex solutions.

You can go up one level to the C++ source codes.

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Last revised on 26 July 2015.