FLOW3
A Finite Element Code for Fluid Flow

FLOW3 is a FORTRAN90 program, using double precision arithmetic, which uses the finite element method to solve for the steady state velocity and pressure of an incompressible fluid in a 2D flow region.

FLOW3 writes a graphics dump file that can be read in and plotted by DISPLAY3.

Usage:

       flow3 < input_file > output_file
     

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 an executable FORTRAN90 program which solves a fluid flow problem in a channel.

DIRECTION_ARROWS is a MATLAB program that can be used to plot the vector direction field.

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.

FEM is a data directory which contains a description of the data files that can be used to describe a finite element model.

FEM_50 is a MATLAB finite element program in just 50 lines of code.

FEM_50_HEAT is modified version of FEM_50 suitable for solving the heat equation.

FEM_50_HEAT is modified version of FEM_50 suitable for solving the heat equation.

FEM_BASIS_T3_DISPLAY is a MATLAB program which displays a basis function associated with a linear triangle ("T3") mesh.

FEM_BASIS_T6_DISPLAY is a MATLAB program which displays a basis function associated with a quadratic triangle ("T6") mesh.

FEM_IO is a set of MATLAB routines for reading or writing the node, element and data files that define a finite element model.

FEM_TO_TEC is a MATLAB program that can convert an FEM model into a TEC graphics file.

FEM2D_POISSON is an executable FORTRAN90 program for solving Poisson's equation on a square, using the finite element method.

FEMPACK is a FORTRAN90 library of routines for finite element calculations.

FLOW5 is a FORTRAN90 program which is a later version of the FLOW3 program.

FLOW7 is a FORTRAN90 program which is a later version of the FLOW3 program.

FREE_FEM_NAVIER_STOKES is a FORTRAN90 program for solving the steady incompressible Navier Stokes equations on an arbitrary triangulated region, using the finite element method.

FREE_FEM_STOKES is an executable FORTRAN90 program for the steady incompressible 2D Stokes equations on an arbitrary triangulated region.

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

HOT_PIPE is a sample problem that can be run with FEM_50_HEAT.

HOT_POINT is a sample problem that can be run with FEM_50_HEAT.

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 by Griebel, Dornseifer and Neunhoeffer, for the 2D Navier Stokes equations with heat.

NSASM is a C library of routines, intended to be used with a MATLAB calling program, and which set up the sparse matrix needed for a Newton iteration to solve a finite element formulation of the steady incompressible 2D Navier Stokes equations.

PLTMG_SINGLE is a FORTRAN77 library of routines for solving elliptic partial differential equations using the finite element method with piecewise linear triangles and the multigrid approach.

PLOT_POINTS is an executable FORTRAN90 program that can make a plot of the nodes that define the region.

TABLE is a format used to store the input and output files used by the program.

TABLE_IO is a FORTRAN90 library which supplied the routines needed to read the data files.

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

TRIANGULATION_ORDER3 is a data directory which describes the format for an order 3 triangulation.

TRIANGULATION_ORDER3_CONTOUR is a MATLAB script which can be used to make contour plots of the pressure field from these files.

TRIANGULATION_ORDER6 is a data directory which describes the format for an order 6 triangulation.

TRIANGULATION_PLOT is a FORTRAN90 executable program which can be used to plot the elements that triangulate the region.

VECTOR_PLOT is a FORTRAN90 program which can be used to create vector plots of the velocity and velocity direction fields.

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 a velocity 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:

• flow3.f90, the source code;
• flow3.csh, commands to compile and load the source code;
• flow3_dictionary.txt, a list of internal variables.

Examples and Tests:

• flow3_input.txt, a description of some of the problems;
• flow3_input001.txt, input file for problem 1;
• flow3_output001.txt, output file for problem 1;
• flow3_march001.txt, marching file for problem 1;
• flow3_input002.txt, input file for problem 2;
• flow3_input003.txt, input file for problem 3;
• flow3_input004.txt, input file for problem 4;
• flow3_input005.txt, input file for problem 5;
• flow3_input006.txt, input file for problem 6;
• flow3_input007.txt, input file for problem 7;
• flow3_input008.txt, input file for problem 8;
• flow3_input009.txt, input file for problem 9;
• flow3_input751.txt, input file for problem 751;
• flow3_input796.txt, input file for problem 796;

List of Routines:

• MAIN is the main program for FLOW3.
• AFTER shuts down files and stops.
• BSP evaluates the basis functions associated with pressure.
• BUMP_BC computes the boundary conditions for velocity sensitivities.
• BUMP_BC1 computes the value of the boundary conditions for the
• BUMP_BC2 evaluates the velocity sensitivity boundary conditions.
• BUMP_COST evaluates the cost of the bump control.
• BUMP_DER differentiates the bump control cost with respect to the parameters.
• BUMP_FX measures the residual in the bump sensitivity equations.
• BUMP_SEN sets up the right hand side F associated with the
• BUMP_SPL sets up or updates the spline data that describes the bump.
• CH_CAP capitalizes a single character.
• CHKDAT performs some simple checks on the input data.
• CHKOPT is called at the end of an optimization to check the results.
• CHRCTD accepts a string of characters, and tries to extract a
• CHRCTI accepts a STRING of characters and reads an integer
• COST_GRADIENT returns the gradient of the cost functional.
• CUBSPL is given data and boundary conditions for a cubic
• DISC_COST computes the discrepancy cost integrals.
• DISC_DER computes the derivative of the discrepancy cost integrals
• DMEMRY allows the user to define the name of a real
• FLO_SPL_SET sets up or updates the spline data that describes the inflow.
• FLO_SPL_VAL computes boundary velocities specified by a parameterized spline.
• FLODUV differentiates the parabolic inflow with respect to parameter.
• FLOSEN sets up the right hand side F associated with the
• FLOSOL is given a set of flow parameters in PARA, and an
• FPRIME computes the jacobian of the Navier Stokes or Stokes functions.
• FPRNAB computes the jacobian of the Navier Stokes or Stokes residual
• FX computes the residual of the Navier Stokes or Stokes equations.
• GET_COST determines the cost of a solution G given a target solution GTAR.
• GET_UNIT returns a free FORTRAN unit number.
• GETDU estimates spatial derivatives of state variables at nodes.
• GETDU4 uses the Zienkiewicz-Zhou technique to attempt to improve the
• GETFIX computes GRADF, a correction for the finite difference
• GETGRD estimates the derivatives of the variables with respect to parameters.
• GETSEN computes the sensitivities of the state variables U, V and
• GQUAD1 returns the weights and abscissas for a 1 dimensional,
• HELLO prints out an introductory message.
• ILAENV is called from the LAPACK routines to choose problem-dependent
• IMEMRY allows the user to define the name of an integer variable,
• INIT initializes the program parameters.
• INPUT reads user input of the form "name = value".
• INTERV computes LEFT, the maximum value of I so that
• ISAMAX finds the index of the vector element of maximum absolute value.
• LBASE evalualates the IVAL-th Lagrange polynomial.
• LMEMRY allows the user to define the name of a logical variable,
• LSAME returns .TRUE. if CA is the same letter as CB regardless of
• LSPOLY evaluates a polynomial in (1, x, y, x*x, xy, y*y) at (x,y)..
• MARCH carries out a one, two or three dimensional "march".
• MARCH_FILE_OPEN opens the marching file.
• NAMELS reads a line of user input which is similar in form
• NEWTON solves the nonlinear system of equations.
• NODE_SET assigns numbers to the nodes.
• NODNAB returns the neighbor index number of node J relative to node I.
• NUSEN sets the right hand side of the NU_INV sensitivity equation.
• OSOLVE carries out the optimization algorithm for a fixed grid,
• PLDX evaluates the derivative of a piecewise linear function.
• PLDX1 evaluates the X derivative of a piecewise linear basis function.
• PLOT_FILE_OPEN opens the plotting file.
• PLOT_FILE_WRITE writes geometry and solution information to a plot file.
• PLVAL evaluates a piecewise linear function at a given point.
• PLVAL1 evaluates the piecewise linear basis function.
• PPVALU evaluates a piecewise polynomial function or its derivative.
• PQDX evaluates the derivative of a piecewise quadratic function.
• PQDX1 evaluates the X derivative of the piecewise quadratic basis function.
• PQVAL evaluates a piecewise quadratic function at a given point.
• PQVAL1 evaluates the piecewise quadratic basis function.
• PR_BUMP prints out the boundary conditions for the bump sensitivities,
• PR_COST1 prints out the current cost function.
• PR_COST2 prints out the current cost function.
• PR_COST_SEN prints out the cost sensitivities.
• PR_DAT prints the user input file data.
• PR_DISC prints the discrepancy along the profile line.
• PR_DU2 prints out a comparison of the original dUdY vector and
• PR_FX3 prints out the maximum of the P, U, and V residuals.
• PR_GS2 prints the maximum finite coefficient differences and sensitivities.
• PR_PARAMETER prints out the current parameters.
• PR_PROFILE prints out the solution along the profile line.
• PR_PUV prints the nodal values of the finite differences and sensitivities.
• PR_SOLUTION prints out information about a single solution.
• PR_SPL_DATA prints the raw spline data for the simple cases ISHAPE = 1 or 2.
• PR_SPLN prints a spline interpolant or its derivatives.
• PR_WORK reports the amount of work carried out.
• PROBAS orthonormalizes N vectors of length M.
• PROJEC projects an M vector into an N dimensional subspace.
• QBF evaluates a quadratic basis function in a nonisoparametric element.
• QSOLVE seeks an optimal set of parameter values.
• REFBSP evaluates a linear basis function in the reference triangle.
• REFQBF evaluates one of the six quadratic basis functions,
• RINT_TO_RINT maps a real interval to another real interval.
• RSOLVE computes the flow solution for a given set of parameters.
• R4VEC_EVEN returns N real values, evenly spaced between ALO and AHI.
• S_BEFORE_SS_COPY copies a string up to a given substring.
• S_BLANK_DELETE removes blanks from a string, left justifying the remainder.
• S_CAP replaces any lowercase letters by uppercase ones in a string.
• S_EQI is a case insensitive comparison of two strings for equality.
• SCOPY copies a vector, x, to a vector, y.
• SDOT forms the dot product of two vectors.
• SETBAN computes the half band width of the Jacobian matrix.
• SETBAS evaluates the basis functions at each quadrature point.
• SETNAB sets up the node neighbor array.
• SETQXY sets the abscissas and weights for a quadrature rule on a triangle.
• SGBSCN scans a matrix stored in LINPACK/LAPACK "general band" mode,
• SGBTF2 computes an LU factorization of a real m-by-n band matrix A
• SGBTRF computes an LU factorization of a real m-by-n band matrix A
• SGBTRS solves a system of linear equations
• SGEMM performs one of the matrix-matrix operations
• SGEMV performs one of the matrix-vector operations
• SGER performs the rank 1 operation
• SGETF2 computes an LU factorization of a general m-by-n matrix A
• SGETRF computes an LU factorization of a general M-by-N matrix A
• SGETRS solves a system of linear equations
• SLASWP performs a series of row interchanges on the matrix A.
• SOLCON computes the flow solution for a given set of parameters.
• SSCAL scales a vector by a constant.
• SSWAP interchanges two vectors.
• STBSV solves one of the systems of equations
• STRSM solves one of the matrix equations
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRANS calculates the mapping from reference to physical elements.
• UPVALQ evaluates sensitivities at a quadrature point in a given element.
• UVAL evaluates the velocities and pressure at any point in a given element.
• UVALQ evaluates the velocities and pressure, and their X and Y
• XERBLA is an error handler for the LAPACK routines.
• XOFXSI is given the XSI, ETA coordinates of a point in an
• XY_PRINT prints the X and Y coordinates of the nodes.
• XY_SET sets the X and Y coordinates of the nodes.

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