VELOCITY_ARROWS_GRID
Velocity Vector Plot,
Uniform Grid from Scattered Data

VELOCITY_ARROWS_GRID is a MATLAB routine which reads velocity data defined at possibly scattered points, and creates a vector plot of the velocity field on a uniform grid of user-specified density.

The program is mainly a preprocessor for MATLAB's quiver routine. It reads the (X,Y) coordinates of a set of points from a "node" file, and the corresponding horizontal and vertical velocities from a "velocity" file. It uses MATLAB's griddata facility to create an interpolatory function to the given data, which is then sampled on a regular grid and displayed.

The program is especially useful if simply displaying the original data is unsuitable, perhaps because there are too many points, or too few, or because the density of points varies greatly.

Both the node and velocity files are simple "table" files whose format is described online.

This program was written as a quick and convenient way to view finite element data. It can also be used for any situation in which a collection of points and velocities are available.

However, a small "sin" is committed when we use this program on finite element data, since we take only the node locations and velocities, but not the elements. We simply use MATLAB's grid data feature which constructs a cubic spline interpolant to scattered data. This is OK, and probably doesn't distort the data too much, but in fact, we are not actually viewing values of the finite element function, and there is no guarantee that this surrogate function will actually satisfy the boundary conditions or other characteristics of the finite element function.

VELOCITY_ARROWS_GRID is based in part on a plotting routine written by Professor Hyung-Chun Lee of Ajou University, Korea.

Usage:

The calling sequence is:

velocity_arrows_grid ( node_file, velocity_file, scale, number )

node_file

the name of the node file, which must be a quoted string;

velocity_file

the name of the velocity file, which must be a quoted string;

scale

a scale factor for the velocity vectors; A value of 1.0 is reasonable. A value of 0.0 results in automatic scaling.

number

the number of vectors to draw in one direction. This is actually the number that will appear in the longest dimension of the region. A value of 10 is reasonable to start with, which would result in 100 vectors if your region happens to be a square.

Related Data and Programs:

BUMP is a FORTRAN90 program which computes the pressure and velocity for a Navier Stokes flow in a channel with a bump.

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.

DIRECTION_ARROWS is a MATLAB program which plots the velocity direction field.

DIRECTION_ARROWS_GRID is a MATLAB program which plots the velocity direction field on a uniform grid of density specified by the user.

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 a FORTRAN77 program which computes the pressure and velocity for a Navier Stokes flow in an "H"-shaped region.

INOUT is a FORTRAN77 program which computes the pressure and velocity for a Navier Stokes flow in a square region with an inlet and an outlet.

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.

TABLE is a format used for the input files to this program.

TCELL is a FORTRAN77 program which computes the pressure and velocity for a Navier Stokes flow in a "T"-shaped region.

VECTOR_MAGNITUDE_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 contour plot of the vector magnitude.

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.

VECTOR_PLOT is a FORTRAN90 program which can read an XY file and a UV file and plot the velocity and velocity direction fields.

VELOCITY_ARROWS is a MATLAB program which plots a velocity field.

VELOCITY_ARROWS_GRID2 is a MATLAB program which reads a single file of node and velocity data, and using interpolation is able to display a velocity vector field along any uniform grid of points specified by the user.

VELOCITY_ARROWS_SEQUENCE is a MATLAB program which can process a set of many data files with names that are numbered in sequence.

VELOCITY_ARROWS_SEQUENCE2, is a MATLAB program which reads a single XYUV file of nodes and velocities, plots the data and writes it to a PNG file, and then repeats the process for the next file.

VELOCITY_ARROWS2 is a MATLAB program which plots a velocity field, and assumes that the node and velocity data are stored in a single table file.

Tar File:

A GZIP'ed TAR file of the contents of this directory is available. This is only done as a convenience for users who want ALL the files, and don't want to download them individually. This is not a convenience for me, so don't be surprised if the tar file is somewhat out of date.

• velocity_arrows_grid_m_src.tar.csh the commands used to create the GZIP'ed TAR file.
• velocity_arrows_grid_m_src.tar.gz the GZIP'ed TAR file.

Source Code:

• velocity_arrows_grid.m, is the main program;
• dtable_data_read.m, reads the data from a TABLE file;
• dtable_header_read.m, reads the header from a TABLE file;
• file_column_count.m, counts the number of "words" in a noncomment line of a TABLE file;
• file_row_count.m, counts the number of noncomment lines in a TABLE file;
• r8mat_transpose_print.m, prints a real matrix, transposed;
• r8mat_transpose_print_some.m, prints some of a real matrix, transposed;
• s_len_trim.m, returns the length of a string to the last nonblank;
• s_word_count.m, returns the number of words in a string;
• timestamp.m, prints the YMDHMS date as a timestamp;

Examples and Tests:

BIG_CAVITY is a fluid flow problem involving an irregular mesh of 8,185 nodes in a square region. If you try to plot the velocity at every point, you will get an unusable blur. Using this software, you can ask for a plot on a 10x10 grid or a 20x20 grid, for instance.

• nodes.txt, the coordinatees of 8185 nodes.
• velocity.txt, the velocity at the nodes.
• velocity_10x10.png, a PNG image of the plot of the velocity field on a 10x10 grid and scale factor 1.
• velocity_20x20.png, a PNG image of the plot of the velocity field on a 20x20 grid and scale factor 3.

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