FLOW5
A Finite Element Code for Fluid Flow

FLOW5 is a FORTRAN90 program which uses the finite element method to solve for the steady state velocity and pressure in a fluid flow region.

The fluid is presumed to be incompressible.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

FLOW5 is available in a FORTRAN90 version.

Related Data and Programs:

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

FEM2D, a data directory which contains a description of the data files that can be used to describe a 2D finite element model.

FEM_IO, a MATLAB library which reads and writes the node, element and data files that define a finite element model.

FEM_TO_TEC, a MATLAB program which can convert an FEM model into a TEC graphics file.

FEM2D_PACK, a FORTRAN90 library which contains utilities for 2D finite element calculations.

FEM2D_POISSON, a FORTRAN90 program which solves Poisson's equation on a square, using the finite element method.

FLOW3, a FORTRAN90 program which uses the finite element method to solve for the steady state velocity and pressure in a fluid flow region.

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

MHD_FLOW, a FORTRAN90 program for the evolution of an MHD system.

NAST2D_F90, a FORTRAN90 program which uses the finite volume method to set up and solve the 2D incompressible Navier Stokes equations with heat.

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

TOMS866, a MATLAB library which is the Incompressible Flow Iterative Solution Software;
this library is commonly called IFISS;
this is ACM TOMS algorithm 866.

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:

• flow5.f90, the source code;
• flow5.sh, commands to compile and load the source code;

Examples and Tests:

• cavity.txt, the output file;
• cavity_elements.txt, the element file, suitable for input to the DISPLAY4 graphics program;
• cavity_uvp.txt, the node file, suitable for input to the DISPLAY4 graphics program;
• cavity.tec, a graphics file suitable for input to the TECPLOT graphics program;

List of Routines:

• MAIN is the main program for FLOW5.
• BSP evaluates the linear basis functions for pressure.
• DGB_FA factors a matrix stored in LINPACK general band storage.
• DGB_SL solves a system factored by DGB_FA.
• FP computes the jacobian matrix A of the Navier Stokes residual.
• FX computes the residual RES of the Navier Stokes equations.
• INTPRS interpolates the pressure at the midside nodes.
• NEWTON applies Newton iteration, seeking a solution of FX(G) = 0.
• QBF evaluates a nonisoparametric quadratic basis function.
• R8VEC_AMAX returns the maximum absolute value in a real vector.
• REFBSP evaluates a reference element linear basis function.
• REFQBF evaluates a reference element quadratic basis function.
• SETBAN computes the lower band width of the Jacobian matrix.
• SETBAS evaluates the basis functions at each quadrature point.
• SETQUAD sets the abscissas and weights for quadrature in a triangle.
• SETNOD assigns numbers to the nodes and elements.
• SETXY sets the X and Y coordinates of the nodes.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRANS calculates the biquadratic reference element transformation.
• UVPNORM returns the "norm" of the computed finite element solution.
• UVALQ evaluates velocities and pressure at a quadrature point in an element.
• WRITE_DISPLAY_FILE writes solution information to two files.
• WRITE_TECPLOT_FILE writes out solution information for use with TECPLOT.
• XOFXSI computes X and Y given XSI and ETA coordinates.

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