BUMP
Flow Over a Bump

BUMP is a FORTRAN90 program, using double precision arithmetic, which solves a 2D steady incompressible flow problem set in a channel with a small bump.

BUMP is a preliminary version of the code that eventually became the FLOW programs. The code was designed to solve for the flow field in a channel with a parameterized bump. Data for the flow profile downstream from the bump was given, and the idea was to determine a bump parameter value that produced the best match with the given profile. In later programs, this task became much more elaborate.

Related Data and Programs:

BUMP_ORIGINAL is a FORTRAN90 program which is the "original version" of the BUMP program.

CHANNEL is a FORTRAN90 program which solves a simple channel flow problem with no bump.

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PLOT_POINTS is a FORTRAN90 program which plots the nodes that define the region.

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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 is a MATLAB program which plots velocity fields.

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Reference:

1. John Burkardt, Max Gunzburger, Janet Peterson,
   Discretization of Cost and Sensitivities in Shape Optimization,
   in Computation and Control IV,
   edited by Bowers and Lund,
   Proceedings of the Fourth Bozeman Conference on Computation and Control,
   Birkhaeuser, 1995,
   bozeman_1994.pdf.
2. 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.
3. Hans Rudolf Schwarz,
   Methode der Finiten Elemente,
   Teubner Studienbuecher, 1980,
   ISBN: 3-519-02349-0.
4. Gilbert Strang, George Fix,
   An Analysis of the Finite Element Method,
   Cambridge, 1973,
   ISBN: 096140888X,
   LC: TA335.S77.
5. Olgierd Zienkiewicz,
   The Finite Element Method,
   Sixth Edition,
   Butterworth-Heinemann, 2005,
   ISBN: 0750663200.

Source Code:

• bump.f90, the source code.
• bump.csh, commands to compile the source code.

Examples and Tests:

The program writes out "XY" (node coordinate) and "UV" (velocity component) data files at each step. Test files you may copy include:

• bump_output.txt, printed output from a run of the program.
• xy_001.txt, grid information, step 1.
• uv_001.txt, velocity information, step 1.
• uv_001_vec.png, a PNG image of the velocity information.
• xy_002.txt, grid information, step 2.
• uv_002.txt, velocity information, step 2.
• uv_002_vec.png, a PNG image of the velocity information.
• xy_003.txt, grid information, step 3.
• uv_003.txt, velocity information, step 3.
• uv_003_vec.png, a PNG image of the velocity information.
• xy_004.txt, grid information, step 4.
• uv_004.txt, velocity information, step 4.
• uv_004_vec.png, a PNG image of the velocity information.
• xy_005.txt, grid information, step 5.
• uv_005.txt, velocity information, step 5.
• uv_005_vec.png, a PNG image of the velocity information.
• xy_006.txt, grid information, step 6.
• uv_006.txt, velocity information, step 6.
• uv_006_vec.png, a PNG image of the velocity information.
• xy_007.txt, grid information, step 7.
• uv_007.txt, velocity information, step 7.
• uv_007_vec.png, a PNG image of the velocity information.
• xy_008.txt, grid information, step 8.
• uv_008.txt, velocity information, step 8.
• uv_008_vec.png, a PNG image of the velocity information.

List of Routines:

• MAIN is the main program for BUMP.
• BSP evaluates the linear basis function associated with pressure.
• DAXPY computes constant times a vector plus a vector.
• DDOT forms the dot product of two vectors.
• DGBFA factors a real band matrix by elimination.
• DGBSL solves a real banded system factored by DGBCO or DGBFA.
• DSCAL scales a vector by a constant.
• FILE_NAME_INC increments a partially numeric filename.
• GET_UNIT returns a free FORTRAN unit number.
• GETG extracts the values of a quantity along the profile line.
• GRAM computes and stores the Gram matrix.
• I4_MODP returns the nonnegative remainder of integer division.
• I4_WRAP forces an integer to lie between given limits by wrapping.
• IDAMAX finds the index of the vector element of maximum absolute value.
• IGETL gets the local unknown number along the profile line.
• LINSYS solves the linearized Navier Stokes equation.
• NSTOKE solves the Navier Stokes equation using Taylor-Hood elements.
• PVAL computes a table of pressures at all the nodes.
• QBF evaluates the quadratic basis functions.
• REFBSP evaluates the linear basis functions in a reference triangle.
• REFQBF evaluates the quadratic basis functions on reference triangle
• RESID computes the residual.
• SETBAN computes the half band width.
• SETBAS evaluates the basis functions at each integration point.
• SETGRD sets up the geometric grid.
• SETLIN determines unknown numbers along the profile line.
• SETQUD sets midpoint quadrature rule information.
• SETXY sets the grid coordinates based on the value of the parameter.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRANS calculates the element transformation mapping.
• UBDRY sets the parabolic inflow in terms of the value of the parameter
• UBUMP calculates the sensitivity dU/dA on the bump.
• UVAL evaluates the velocities at a given quadrature point.
• UV_WRITE writes a velocity file.
• XY_WRITE creates node coordinate data.

You can go up one level to the FORTRAN90 source codes.