The Shock Normal Program is invoked through the command SNP.
This produces the program control window.
The computation of the shock normal is performed in a number of steps which are activated by the 5 buttons beginning with Open File. Each step performs a self-contained set of operations at the end of which decisions must be made or options can be exercised before continuing onto the next set of operations. Buttons containing red text are disabled indicating that indufficient information is available to process this step OR that the step has already been processed and there have been no changes which would cause the recalulation to produce values different than those previously computed.
At anytime during the process clicking on the Info Page button will
bring a page containing the current status and results of the computation.
The format of this page is shown below.
The first step in any shock normal computation is to open the data file
containing the shock data profiles. This is done through the Open
File button. Clicking on this button brings up a file open widget.
This widget can be used to search through the system directories to locate files containing shock data profiles. Select the profile to be used and click open. This opens the data file and then activates the Plot Data button.
The shock normal package does contain two example shock data profiles. There are found in the TclSN directory and are called ShockData and ShockData2. The two data sets are identical with the exception that ShockData2 contains the total plasma temperature and makes use of the pressure and heat flux equations in the normal solution.
Clicking on the Plot Data button produces a series of plots of the
input data in the panel below. Plotted are the plasma density and temperature,
and the magnetudes of the bulk velocity and magnetic field.
Once the plots are displayed the Plot Data is disabled. At this point
the time intervals to be used in the determination of the shock normals should
be selected. These are selected by positioning the mouse in the data plot at
a desired time and left clicking. This produces a vertical line at the selected
time. Positioning the mouse over a selected time and right clicking will remove
the selected time.
The first selected time by definition is interpreted as the time of the shock.
It is displayed as a red line. This time is not used
by program per-se but is used to determine which sides of the shock the later
times are on. The next two times selected to the left (cyan
) and right (yellow) of the bracket the data
which will be used in the calculations.
Once both sets of times are selected the Surface Plot button is enabled
The Surface Plot portion in the shock normal determination has performs several functions, the most noticable of which is the output of a difference between the upstream and downstream Rankine-Hugoniot equations for a complete set of shock normals. At the same time the shock normals using the Velocity Coplanarity, Magnetic Coplanarity and Abraham-Shrauner methods are computed.
The surface plot is displayed in the area to the right of the data plot. The
locations of the shock normals derived from the Velocity Coplanarity,
Magnetic Coplanarity and Abraham-Shrauner methods are displayed
as VC, MC, and AS respectively.
The surface can be produced at a number of solution resolutions and grid
resolutions. The surface resolution defines the spacing used to compute
the differences in the Rankine-Hugoniot solutions and grid resolution defines
the grid size used in the output mesh. When the grid resolution is smaller
than the solution resolution, unfilled grids are filled using a 2D least
squares smoothing.
The purpose of the surface plot is to show the number of solution minimia and to allow a selection of an initial normal vector which will allow for a rapid convergence to a solution. An initial shock normal is selected by placing the cursor over the location in the surface plot at which to start the shock normal iteration and left clicking. The selection appears on the plot as a +. The selection can be removed by placing the cursor over it an right clicking. Once the initial normal solution has been selected the Surface Plot button is disabled and the Solve RH button is enabled.
The Solve RH button initiates the minimization of the Rankine-Hugoniot equations using the Levenberg-Marquardt technique resulting in an estimate of the shock normal. The solution is displayed on the surface plot as an *. Once the solution has been displayed the RH Solve button is disabled and the RH Asymtote button is enabled.
When there are multiple minima in the surface plot there are multiple normal solutions. This generally occurs when the pressure equation is not used in the minimization due to the lack of both the electron and ion temperatures in the shock data. To determine which solution is the correct solution it is necessary to look at the asymtotic upstream and downstream shock solution.