MHD_CONTROL
Control of the MHD Equations

MHD_CONTROL is a FORTRAN90 program, using double precision arithmetic, which solves a control problem for a 2D time-dependent magneto-hydrodynamic system.

Related Data and Programs:

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

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.

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 FORTRAN90 program that solves the steady Stokes flow equations on a triangulated 2D region.

MHD_CONTROL is a dataset directory which contains the velocity and magnetic field values over 50 timesteps for a particular control problem.

MHD_CONTROL is a set of MATHEMATICA animations of the magnetic and velocity fields.

MHD_FLOW is an executable FORTRAN90 program for the (uncontrolled) evolution of an MHD system.

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.

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

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_GRID is a MATLAB program which reads files of node and velocity data, and, using interpolation, creates a vector plot with arrows placed 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.

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_control.f90, the source code.
• mhd_control.csh, commands to compile the source code.
• mag_ic_09x09.txt, a file containing an initial condition for the magnetic field on a 9 x 9 element grid.
• mag_ic_13x13.txt, a file containing an initial condition for the magnetic field on a 13 x 13 element grid.

List of Routines:

• MAIN is the main program for MHD_CONTROL.
• ADJOINT solves the linear adjoint equations for the control problem.
• BANDED is the banded equation solver.
• BASIS_LINEAR evaluates the linear basis functions associated with pressure.
• BASIS_QUAD evaluates a quadratic basis function.
• CH_CAP capitalizes a single character.
• CH_IS_DIGIT returns .TRUE. if a character is a decimal digit.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• COST_FNL evaluates the cost functional at a given time for a specific target
• DECOMPOSE breaks a 1-d vector into a 2-d vector by unknown and node
• DIGIT_INC increments a decimal digit.
• DIGIT_TO_CH returns the character representation of a decimal digit.
• ERROR computes the L^2 error in the state and target solutions.
• EVAL_2D evaluates vector dimensioned (nodes, 4) at the given point (x,y)
• EVAL evaluates the velocities and the magnetic field
• EVAL_RHS evaluates the rhs at the given point (x,y)
• FILE_COPY makes a copy of a file.
• FILE_DELETE deletes a named file if it exists.
• FILE_EXIST reports whether a file exists.
• FILE_IS_OPEN reports whether a file (specified by filename) is open.
• FILE_NAME_INC generates the next file name in a series.
• GEOMETRY sets up x,y coordinate arrays, node array associating local node number to
• GET_UNIT returns a free FORTRAN unit number.
• L2NORM calculates the L^2 norm of f.
• MAG_NSTOKE solves the Navier Stokes equations coupled with magnetic field
• OUTPUT outputs x, y, and velocities at each point
• POST_PROCESS resets the pressure, by computing the mean and subtracting
• R8UD_IO reads or writes fixed size vectors, using R8UD protocol.
• S_EQI is a case insensitive comparison of two strings for equality.
• SET_INITIAL sets the initial condition for the state solution.
• TARGET sets value of target solution when it is given explicitly by a function
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• UBDRY evaluates the velocity inlet profile.
• XY_WRITE writes the coordinate data to a file.

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