# 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].

```       +-----------------------+
|+----------------------+
||                    --->
||                    ----->
||                    --->
||                     ++
||                     ||
||                     ||
||                     ||
||                     ||
++                     ||
--->                    ||
----->                  ||
--->                    ||
+----------------------+|
+-----------------------+
```
There are 1,681 nodes in a 41 by 41 evenly spaced grid. The nodes are organized into 800 6-node triangular elements which are quadratic in velocity and linear in pressure.

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.

### 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:

Steady state velocity files you may copy include:

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

You can go up one level to the DATASETS directory.

Last revised on 02 November 2005.