MHD_FLOW
Magnetic-Hydrodynamic Flow

MHD_FLOW is a FORTRAN90 program, using double precision arithmetic, which computes the time-dependent, two dimensional behavior of a viscous magnetic fluid. The fluid is governed by the incompressible Navier-Stokes equations, the magnetic field by Maxwell's equations. A coupling parameter controls the interaction between the particle motions and magnetic fields.

Related Data and Programs:

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

CONTOUR_SEQUENCE4 is a MATLAB script that can be used to create images of the contour plots of the pressure.

DIRECTION_ARROWS is a MATLAB script that can plot one velocity 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.

DIRECTION_ARROWS_SEQUENCE is a MATLAB script that can plot a sequence of velocity direction fields stored in consecutively numbered files.

FREE_FEM_NAVIER_STOKES is an executable FORTRAN90 program which solves the 2D incompressible Navier Stokes equations in an arbitrary triangulated region.

FREE_FEM_STOKES is a program that solves the steady Stokes flow equations on a triangulated 2D region.

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

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

VECTOR_PLOT is an executable FORTRAN90 program which can be used to create a velocity field vector plot from the output data files of the BUMP program.

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 script that can plot one velocity 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.

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 script that can plot a sequence of velocity fields stored in consecutively numbered files.

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.
2. Max Gunzburger, Catalin Trenchea,
   Analysis and Discretization of an Optimal Control Problem for the Time-Periodic MHD Equations,
   Journal of Mathematical Analysis and Applications,
   Volume 308, Number 2, 2005, pages 440-466.

Source Code:

• mhd_flow.f90, the source code.
• mhd_flow.csh, commands to compile the source code.
• mhd_flow.out, the output from a run of the program.

The program writes the nodal coordinates and element node lists to files:

• xy.txt, the node coordinates.
• xy.png, a PNG image of the nodes.
• elements.txt, the list of nodes making up each element.
• elements.png, a PNG image of the elements..

The program writes the UV coordinates of velocity at the nodes to a file every so many time steps:

• uv001.txt, velocity at plot step 1.
• uv002.txt, velocity at plot step 2.
• uv003.txt, velocity at plot step 3.
• uv004.txt, velocity at plot step 4.
• uv005.txt, velocity at plot step 5.
• uv006.txt, velocity at plot step 6.
• uv007.txt, velocity at plot step 7.
• uv008.txt, velocity at plot step 8.

The MATLAB program DIRECTION_ARROWS can plot one velocity direction field, and DIRECTION_ARROWS_SEQUENCE can plot a sequence of velocity direction fields stored in consecutively numbered files:

• uv001_dir.png, velocity direction field.
• uv002_dir.png, velocity direction field.
• uv003_dir.png, velocity direction field.
• uv004_dir.png, velocity direction field.
• uv005_dir.png, velocity direction field.
• uv006_dir.png, velocity direction field.
• uv007_dir.png, velocity direction field.
• uv008_dir.png, velocity direction field.

The MATLAB program VELOCITY_ARROWS can plot the velocity field, and VELOCITY_ARROWS_SEQUENCE can plot a sequence of velocity fields stored in consecutively numbered files:

• uv001_vec.png, velocity field.
• uv002_vec.png, velocity field.
• uv003_vec.png, velocity field.
• uv004_vec.png, velocity field.
• uv005_vec.png, velocity field.
• uv006_vec.png, velocity field.
• uv007_vec.png, velocity field.
• uv008_vec.png, velocity field.

The program writes the components of the magnetic field at the nodes to a file every so many time steps:

• mag001.txt, magnetic field at plot step 1.
• mag002.txt, magnetic field at plot step 2.
• mag003.txt, magnetic field at plot step 3.
• mag004.txt, magnetic field at plot step 4.
• mag005.txt, magnetic field at plot step 5.
• mag006.txt, magnetic field at plot step 6.
• mag007.txt, magnetic field at plot step 7.
• mag008.txt, magnetic field at plot step 8.

The MATLAB program DIRECTION_ARROWS can plot the magnetic direction field:

• mag001_dir.png, magnetic direction field.
• mag002_dir.png, magnetic direction field.
• mag003_dir.png, magnetic direction field.
• mag004_dir.png, magnetic direction field.
• mag005_dir.png, magnetic direction field.
• mag006_dir.png, magnetic direction field.
• mag007_dir.png, magnetic direction field.
• mag008_dir.png, magnetic direction field.

The MATLAB program VELOCITY_ARROWS can plot the magnetic field:

• mag001_vec.png, magnetic field.
• mag002_vec.png, magnetic field.
• mag003_vec.png, magnetic field.
• mag004_vec.png, magnetic field.
• mag005_vec.png, magnetic field.
• mag006_vec.png, magnetic field.
• mag007_vec.png, magnetic field.
• mag008_vec.png, magnetic field.

The program writes the pressure at the nodes to a file every so many time steps:

• p001.txt, the pressures at plot step 1.
• p002.txt, the pressures at plot step 2.
• p003.txt, the pressures at plot step 3.
• p004.txt, the pressures at plot step 4.
• p005.txt, the pressures at plot step 5.
• p006.txt, the pressures at plot step 6.
• p007.txt, the pressures at plot step 7.
• p008.txt, the pressures at plot step 8.

The MATLAB program CONTOUR_SEQUENCE4 can be used to create JPG images of contour plots of the pressure:

• p001.png, the pressures at plot step 1.
• p002.png, the pressures at plot step 2.
• p003.png, the pressures at plot step 3.
• p004.png, the pressures at plot step 4.
• p005.png, the pressures at plot step 5.
• p006.png, the pressures at plot step 6.
• p007.png, the pressures at plot step 7.
• p008.png, the pressures at plot step 8.

List of Routines:

• MAIN is the main program for MHD_FLOW.
• BANDED solves a banded linear system.
• BANDWIDTH computes the half band width of the system matrix.
• BASIS_T3 evaluates a linear basis function.
• BASIS_T6 evaluates a quadratic basis function.
• ELEMENT_AREA sets the area of each element.
• ELEMENT_SET sets up the elements.
• ELEMENT_WRITE writes the element data to a file.
• EVAL evaluates the velocity and magnetic fields at a point.
• FILE_NAME_INC increments a partially numeric filename.
• GET_UNIT returns a free FORTRAN unit number.
• I4_MODP returns the nonnegative remainder of integer division.
• I4_WRAP forces an integer to lie between given limits by wrapping.
• INDX_SET sets the index array.
• JACOBIAN computes the Jacobian and right hand side of the Newton system.
• MAG_WRITE writes magnetic data to files.
• NEWTON updates the magneto-hydrodynamic state using Newton's method.
• P_NORMALIZE normalizes the pressure.
• P_WRITE writes pressure data to files.
• QUAD_RULE sets the weights and abscissas for quadrature.
• RHS sets the right hand side of each equation.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• UBDRY sets the parabolic inflow for velocity.
• UV_WRITE writes velocity data to files.
• XY_SET sets the node coordinates.
• XY_WRITE writes the coordinate data to a file.

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