FLOW7 - A Finite Element Code for Fluid Flow

FLOW7 uses the finite element method to solve for the steady state velocity and pressure in a two dimensional fluid flow region. The fluid is presumed to be incompressible. The governing equations are the Navier Stokes equations with the continuity equation.

FLOW7 is derived from the FLOW6 code, but is currently under development. Intended alterations will include:

• Sparse matrix storage for the jacobian;
• CGS or BICGSTAB iteration;

Files you may copy include:

• flow7.f90, the source code;

The list of routines includes:

• MAIN solves a 2D steady incompressible flow using finite elements.
• BOUNDARY_INTEGRAL sets data useful for boundary integrals.
• BOUNDARY_INTEGRAL_FREESLIP sets boundary integral data for the freeslip.
• BOUNDARY_INTEGRAL_STEP sets boundary integral data for the step.
• BOUNDARY_INTEGRAL_PRINT prints data useful for boundary integrals.
• BOUNDARY_SHAPE returns the tangent and normal vectors along the boundary.
• BOUNDARY_SHAPE_CAVITY returns the boundary of the cavity problem.
• BOUNDARY_SHAPE_CHANNEL returns the boundary of the channel problem.
• BOUNDARY_SHAPE_FREESLIP returns the boundary of the freeslip problem.
• BOUNDARY_SHAPE_STEP returns the boundary of the step problem.
• BOUNDARY_VALUE evaluates boundary condition functions.
• C_CAP capitalizes a single character.
• COEF_READ reads the coefficient data from a file.
• COEF_WRITE writes the coefficient data to a file for possible restart.
• ELEMENT_PRINT prints out the elements.
• ELEMENT_WRITE writes element information to a file.
• EQN_NABOR_PRINT prints the equation neighbor array.
• EQN_NABOR_SET sets up the equation neighbor array.
• EQUATION_PRINT prints the equation types.
• FP computes the jacobian matrix A of the Navier Stokes residual.
• FP_BAND_INFO_PRINT prints information about the banded jacobian.
• FP_BAND_WIDTH computes the lower band width of the Jacobian matrix.
• FP_DIF estimates the jacobian matrix by finite differences.
• FX computes the residual RES of the Navier Stokes equations.
• GEOMETRY sets up the geometry for any problem.
• GEOMETRY_CAVITY sets up the geometry for the cavity problem.
• GEOMETRY_CHANNEL sets up the geometry for the channel problem.
• GEOMETRY_FREESLIP sets up the geometry for the freeslip problem.
• GEOMETRY_STEP sets up the geometry for the step problem.
• GET_UNIT returns a free FORTRAN unit number.
• HELLO says hello, prints the program name, date and limits.
• INIT zeroes out data used by the program.
• IVEC_MERGE merges two sorted integer arrays.
• IVEC_ORDER_TYPE determines if an integer array is (non)strictly ascending/descending.
• IVEC_SORT_BUBBLE_A ascending sorts an integer array using bubble sort.
• MONTH_TO_MONTH_NAME returns the name of a given month.
• NODE_NABOR_PRINT prints the node neighbor array.
• NODE_NABOR_SET sets up the node neighbor array.
• NEWTON applies Newton iteration, seeking a solution of FX(G) = 0.
• NODE_WRITE writes solution information to a file.
• PRESS_INTERP interpolates pressure values at non-pressure nodes.
• REF_BF_L3 evaluates a reference element linear basis function.
• REF_BF_Q6 evaluates shape functions for a 6 node triangle.
• REF_MAP_Q6 returns the interpolation map for data on a 6 node triangle.
• REF_QUAD1 sets abscissas and wquad1s for 1D Gauss-Legendre quadrature.
• REF_QUAD2 sets up the 2D reference triangle quadrature rule.
• S_EQI is a case insensitive comparison of two strings for equality.
• SETBAS evaluates the basis functions at each quadrature point.
• SGB_CHECK checks the dimensions of a general band matrix.
• SGB_FA factors a matrix stored in LINPACK general band storage.
• SGB_PRINT prints nonzero entries of a banded matrix.
• SGB_SL solves a system factored by DGB_FA.
• STOKES solves the Stokes equations.
• SVEC_AMAX returns the maximum absolute value in a real vector.
• TRANS_Q6 calculates the biquadratic reference element transformation.
• UVP_NORM_H1 returns the H1 norm of the solution.
• UVP_NORM_L2 returns the L2 norms of velocity magnitude, and pressure.
• UVP_NORM_LMAX returns the infinity norms of velocity magnitude, and pressure.
• UVP_PRINT prints out the solution.
• UVP_QUAD_VALUE evaluates U, V and P at a quadrature point in a given element.
• UVP_VALUE evaluates U, V and P at any point in a given element.
• X_OF_XSI computes X and Y given XSI and ETA coordinates.
• XY_PRINT prints the X and Y coordinates of the nodes.

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