HCELL_STEADY
Steady Fluid Flow in an H-shaped Region

HCELL_STEADY is a FORTRAN77 program, using double precision arithmetic, which solves the time-independent or "steady" Navier Stokes equations in a two-dimensional region called the "H Cell".

The "H-Cell" region is an H-shaped region.

          +----------------------------+
          |              :     :       |
    row 3 |   (3,1)      :(3,2): (3,3) |
          |              :     :       |
          +--------------+.....+-------+
                         |     |        
    row 2     empty      |(2,2)|  empty
                         |     |  
          +--------------+.....+-------+
          |              :     :       |
    row 1 |   (1,1)      :(1,2): (1,3) |
          |              :     :       |
          +----------------------------+

              col 1       col 2  col 3
      

Usage:

hcell_steady

runs the program, reading the file "up000.txt" for the initial values of the horizontal and vertical velocities, and the pressure, at each node. Output files include the series "up001.txt", "up002.txt" and so on, containing flow quantities at successive time steps.

Author:

Hyun-Chun Lee,
Ajou University, Korea,
in collaboration with Max Gunzburger, Janet Peterson, and John Burkardt.

Related Data and Programs:

BUMP is an executable FORTRAN90 program which solves a fluid flow problem in a channel including a bump which obstructs and redirects the flow.

CHANNEL is a program which computes the pressure and velocity for a Navier Stokes flow in a channel. It is available in a FORTRAN77 version and a FORTRAN90 version.

CVT_BASIS_FLOW extracts dominant solution modes from a set of flow solutions using CVT methods.

DIRECTION_ARROWS_GRID is a MATLAB program which reads files of node and velocity data, and, using interpolation, creates a velocity direction plot with arrows place on a uniform grid of the user's specification.

FFNS_SPARSE is a MATLAB program for solving the steady incompressible Navier Stokes equations on an arbitrary triangulated region, using the finite element method and MATLAB's sparse facility.

FFS_SPARSE is a MATLAB program for solving the steady incompressible Stokes equations on an arbitrary triangulated region, using the finite element method and MATLAB's sparse facility.

FREE_FEM_NAVIER_STOKES is a MATLAB program for solving the steady incompressible Navier Stokes equations on an arbitrary triangulated region, using the finite element method.

FREE_FEM_STOKES is a MATLAB program which computes the pressure and velocity for a Stokes flow.

HCELL is an executable FORTRAN77 program which solves the time-dependent Navier Stokes equations in an H-cell region.

HCELL_FLOW_DISPLAY is a MATLAB program which can plot the data produced by HCELL.

INOUT is an executable FORTRAN77 program which solves the Navier Stokes equations in the "In-Out" region.

MHD_CONTROL is an executable FORTRAN90 program which tries to control the evolution of an MHD system so that a particular state is achieved.

MHD_FLOW is an executable FORTRAN90 program for the evolution of an MHD system.

NAST2D is a C++ program which computes the pressure and velocity for a Navier Stokes flow.

NAST2D_F90 is a FORTRAN90 program which computes the pressure and velocity for a Navier Stokes flow.

TCELL solves the Navier Stokes equations in the T-Cell region.

POD_BASIS_FLOW is an executable FORTRAN90 program which extracts dominant solution modes from a set of flow solutions using POD methods.

VECTOR_STREAM_GRID is a MATLAB program which reads node and vector data from a file, computes an interpolatory function, evaluates on a uniform grid of points specified by the user, and displays a streamline plot of the vector field.

VELOCITY_ARROWS_GRID is a MATLAB program which reads files of node and velocity data, and, using interpolation, creates a vector plot with arrows place on a uniform grid of the user's specification.

Reference:

1. Max Gunzburger,
   Finite Element Methods for Viscous Incompressible Flows,
   A Guide to Theory, Practice, and Algorithms,
   Academic Press, 1989,
   ISBN: 0-12-307350-2,
   LC: TA357.G86.

Source Code:

• hcell_steady.f, the source code.
• hcell_steady.csh, commands to compile, link and load the source code.

Examples and Tests:

• nodes3.txt, the coordinates of the nodes associated with linear elements;
• nodes6.txt, the coordinates of the nodes associated with quadratic elements;
• datar6.txt, a text file containing node numbers, coordinates, and velocities.
• uvr6001.tec, a data file suitable for viewing with TECPLOT;

List of Routines:

• MAIN is the main program for HCELL_STEADY.
• CH_IS_DIGIT returns .TRUE. if a character is a decimal digit.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• DAXPY adds a multiple of one vector to another.
• DDOT forms the dot product of two vectors.
• DGBFA factors a double precision band matrix by elimination.
• DGBSL solves a double precision band linear system.
• DIGIT_INC increments a decimal digit.
• DIGIT_TO_CH returns the character representation of a decimal digit.
• DSCAL scales a vector by a constant.
• ELEMENT_NODE_BANDWIDTH determines the bandwidth associated with the grid.
• ELEMENT_NODE_WRITE writes the element node list to a file.
• FILE_NAME_INC generates the next file name in a series.
• HCELL_DOF_COUNT determines the number of degrees of freedom in the region.
• HCELL_DOF_SET assigns degrees of freedom to each node.
• HCELL_ELEMENT_COUNT determines the number of elements in the region.
• HCELL_ELEMENT_NODE determines the nodes that make up each element.
• HCELL_NODE_NUM determines the number of nodes in the region.
• HCELL_NODE_XY assigns coordinates to each node.
• IDAMAX finds the vector element of largest magnitude.
• NODE_EPS creates an EPS file containing an image of the nodes.
• NSTOKE solves the Navier-Stokes equations using Taylor-Hood elements.
• QUAD_A_SET sets quadrature information for the assembly routine.
• R8_HUGE returns a huge R8.
• REFBSP evaluates a linear basis functions on the reference triangle.
• REFQBF evaluates quadratic basis functions on the reference triangle.
• SETGRD sets up the grid for the problem.
• TRANS transforms data between the reference and physical elements.
• UBDRY evaluates boundary conditions at a node.
• UV_WRITE writes the velocity values for a given timestep to a file.
• UV_WRITE_TEC writes velocity information to a TECPLOT file.
• XY3_WRITE writes the coordinates of nodes of 3-node triangles to a file.
• XY6_WRITE writes the coordinates of nodes of 6-node triangles to a file.

You can go up one level to the FORTRAN77 source codes.