navier_stokes_3d_exact
navier_stokes_3d_exact,
a MATLAB code which
evaluates exact solutions to the incompressible time-dependent
Navier-Stokes equations (NSE) over an arbitrary domain in 3D.
The given velocity and pressure fields
are exact solutions for the 3D incompressible time-dependent
Navier Stokes equations.
To define a typical problem, one chooses a bounded spatial region
and a starting time, and then imposes boundary and initial conditions
by referencing the exact solution appropriately.
In the Ethier reference, a calculation is made for the cube centered
at (0,0,0) with a "radius" of 1 unit, and over the time interval
from t = 0 to t = 0.1, with parameters a = PI/4 and d = PI/2,
and with Dirichlet boundary conditions on all faces of the cube.
For the Poiseuille flow, a typical region is the infinite cylinder
along the x axis, with radius 1, for which the velocity is zero
on the boundary.
Licensing:
The information on this web page is distributed under the MIT license.
Languages:
navier_stokes_3d_exact is available in
a C version and
a C++ version and
a Fortran90 version and
a MATLAB version and
an Octave version and
a Python version.
Related Data and Programs:
navier_stokes_3d_exact_test
matlab_exact,
a MATLAB code which
evaluates exact solutions to a few selected examples of
ordinary differential equations (ODE) and partial differential
equations (PDE).
Reference:
-
Martin Bazant, Henry Moffatt,
Exact solutions of the Navier-Stokes equations having steady
vortex structures,
Journal of Fluid Mechanics,
Volume 541, pages 55-64, 2005.
-
Johannes Burgers,
A mathematical model illustrating the theory of turbulence,
Advances in Applied Mechanics,
Volume 1, pages 171-199, 1948.
-
C Ross Ethier, David Steinman,
Exact fully 3D Navier-Stokes solutions for benchmarking,
International Journal for Numerical Methods in Fluids,
Volume 19, Number 5, March 1994, pages 369-375.
Source Code:
-
resid_burgers.m,
evaluates the Burgers residual in the velocity and pressure equations
at any point (x,y,z) and time t.
-
resid_ethier.m,
evaluates the Ethier residual in the velocity and pressure equations
at any point (x,y,z) and time t.
-
resid_poiseuille.m,
evaluates the Poiseuille residual in the velocity and pressure equations
at any point (x,y,z) and time t.
-
uvwp_burgers.m,
evaluates the Burgers velocity and pressure field at any point (x,y,z)
and time t.
-
uvwp_ethier.m,
evaluates the Ethier velocity and pressure field at any point (x,y,z) and
time t.
-
uvwp_poiseuille.m,
evaluates the Poiseuille velocity and pressure field at any point
(x,y,z) and time t.
Last revised on 12 January 2020.