spiral_data, a C++ code which samples a velocity vector field that satisfies the continuity equation, and writes the nodes and velocities to a file, suitable for display using gnuplot().
The continuous velocity field (U,V)(X,Y) that is discretely sampled here satisfies the homogeneous continuity equation, that is, it has zero divergence. In other words:
dU/dX + dV/dY = 0.This is by construction, since we have
U(X,Y) = 10 * d/dY ( PHI(X) * PHI(Y) ) V(X,Y) = -10 * d/dX ( PHI(X) * PHI(Y) )which guarantees zero divergence.
The underlying function PHI is defined by
PHI(Z) = ( 1 - cos ( C * pi * Z ) ) * ( 1 - Z )^2where C is a parameter.
The velocity data satisifes the (continuous) continuity equation; this in no way implies that it satisfies the momentum equations associated with Stokes or Navier-Stokes flow! Moreover, a flow solution for those equations would normally also require specifying a value for the scalar pressure field P(X,Y).
The computer code and data files made available on this web page are distributed under the GNU LGPL license.
spiral_data is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version..
gnuplot_test, C++ codes which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.
NAVIER_STOKES_2D_EXACT, a C++ code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations over an arbitrary domain in 2D.
STOKES_2D_EXACT, a C++ code which evaluates exact solutions to the incompressible steady Stokes equations over the unit square in 2D.