INOUT_FLOW
INOUT Flow Problem Solution Datasets

INOUT_FLOW is a dataset directory which contains velocity solutions to a time-dependent incompressible parameterized flow problem in in a cell with inflow and outflow.

The "INOUT" region is contained in the unit square, [0,1] x [0,1]. There is an inlet on the left side, from [0,0] to [0,0.2], and an outlet on the right side, from [1,0.8] to [1.0,1.0].

       +-----------------------+
       |+----------------------+
       ||                    --->
       ||                    ----->
       ||                    --->
       ||                     ++
       ||                     ||
       ||                     ||
       ||                     ||
       ||                     ||
       ++                     ||
      --->                    ||
      ----->                  ||
      --->                    ||
       +----------------------+|
       +-----------------------+
      

The time-dependent incompressible 2D Navier-Stokes equations are to be applied in the region. No-slip and no-penetration conditions are applied along the walls. The inlet on the lower left is open, and parabolic velocity inflow is specified, whose strength is controlled by a parameter alpha. At the outlet on the upper right, the flow is specified to have zero vertical component, and zero horizontal derivative. The dynamic viscosity is taken to be nu=1/300.

The steady state solution is computed for the particular value alpha=1/3. Using the steady state solution as initial condition, the time-dependent problem is solved over the interval 0<=t<=5, with alpha = 5/3 for timesteps 1 through 250, and then alpha = 1/3 for timesteps 251 through 500. The two instantaneous changes to alpha induce violent transient behaviors.

The goal is to extract typical modes of behavior of the solution. Such a set of modes may then be used as a finite element basis that is highly tuned to the physics of the problem, so that a very small set of basis functions can be used to closely approximate the behavior of the solution over a range of values of alpha.

Licensing:

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

Related Data and Programs:

CASE1_FLOW, a dataset directory which 401 solutions of a flow problem in a channel;

CAVITY_FLOW, a dataset directory which contains 500 time steps of Navier-Stokes flow in a driven cavity;

CVT_BASIS_FLOW, a FORTRAN90 program which can be used to analyze this data, and compute a small set of "basis vectors" using CVT techniques.

INOUT, a FORTRAN77 program which solves a time dependent Navier Stokes problem.

INOUT_FLOW_DISPLAY, a MATLAB library which displays a single velocity field solution for the INOUT flow;

INOUT_FLOW_MOVIE, a MATLAB library which creates an animation of the velocity solutions for the INOUT cell;

INOUT_FLOW2, a dataset directory which contains 800 time steps of Navier-Stokes flow in a region with specified inflow and outflow;

POD_BASIS_FLOW, a FORTRAN90 program which can be used to analyze this data, and compute a small set of "basis vectors" using POD techniques.

TCELL_FLOW, a dataset directory which contains 500 time steps of Navier-Stokes flow in a 2D T-shaped region.

TRIANGULATION_PLOT, a FORTRAN90 program which can be used to draw an image of the nodes and elements used in the triangulation of the region.

VECTOR_PLOT, a FORTRAN90 program which can be used to draw an image of the velocity vector field over the region.

Reference:

• John Burkardt, Max Gunzburger, Hyung-Chun Lee,
  Centroidal Voronoi Tessellation-Based Reduced-Order Modelling of Complex Systems,
  SIAM Journal on Scientific Computing,
  Volume 28, Number 2, 2006, pages 459-484.

Example Datasets:

Grid files you may copy include:

• xy.txt, the XY coordinates associated with the nodes.
• elements.txt, a grouping of the nodes into 6 node quadrative finite elements.
• inout_grid.png, a PNG image of the grid.

Steady state velocity files you may copy include:

• steady.txt, the steady state velocity field.
• steady_vec.png, a PNG image of the steady state velocity field, created by VECTOR_PLOT.
• steady_dir.png, a PNG image of the steady state direction field, created by VECTOR_PLOT.

The following files contain the velocity values at the 500 successive timesteps computed by the finite element simulation:

• up001.txt.
• up002.txt.
• up003.txt.
• up004.txt.
• up005.txt.
• up006.txt.
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You can go up one level to the DATASETS directory.