CAVITY_FLOW
Driven Cavity Flow Datasets

CAVITY_FLOW is a dataset directory which contains velocity solutions to a time-dependent incompressible parameterized flow problem in a 2D driven cavity.

The "CAVITY" region is the unit square, [0,1]x[0,1], open on the top, along which a tangential flow is specified, with walls along the sides and bottom.

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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 top of the region is open, and here a purely tangential velocity is specified, whose strength is controlled by a parameter alpha. 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_DISPLAY, a MATLAB program which displays a single velocity field solution for the driven cavity;

CAVITY_FLOW_MOVIE, a MATLAB program which animates the velocity solutions for the driven cavity;

CVT_BASIS_FLOW, a FORTRAN90 program which extracts dominant solution modes from a set of flow solutions using Centroidal Voronoi Tessellation (CVT) methods.

INOUT_FLOW, a dataset directory which contains 500 time steps of Navier-Stokes flow in a region with specified inflow and outflow;

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 extracts dominant solution modes from a set of flow solutions using Proper Orthogonal Decomposition (POD).

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.

Datasets:

• xy.txt, the XY coordinates associated with the nodes.
• elements.txt, a grouping of the nodes into 6 node quadratic finite elements.
• steady.txt, the steady state velocity field.
• cavity_grid.png, a PNG image of the grid.
• cavity_flow.png, a PNG image of the steady state velocity field.
• cavity_flow_direction.png, a PNG image of the steady state vector direction field.

There are 500 files containing velocity values at successive timesteps from a finite element simulation:

• up001.txt.
• up002.txt.
• up003.txt.
• up004.txt.
• up005.txt.
• up006.txt.
• up007.txt.
• up008.txt.
• up009.txt.
• up010.txt.
• up011.txt.
• up012.txt.
• up013.txt.
• up014.txt.
• up015.txt.
• up016.txt.
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• up495.txt.
• up496.txt.
• up497.txt.
• up498.txt.
• up499.txt.
• up500.txt.

You can go up one level to the DATASETS directory.