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”}
========================================================
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.
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”}
- 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.
- Geoffrey Taylor,\
On the decay of vortices in a viscous fluid,\
Philosophical Magazine,\
Volume 46, 1923, pages 671-674.
- 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”}
Examples and Tests: {#examples-and-tests align=”center”}
Lucas Bystricky flow:
Poiseuille flow:
Spiral flow:
Taylor flow:
Vortex flow:
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.
Last revised on 26 July 2015.