SYSTEM Command

• Summary
• Synopsis
• Argument List
• Argument Descriptions

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Summary:

This command allows user to specify to Prophet a new system of partial differential equations (PDEs) and associated boundary conditions (BCs), interface constraints (ICs), and auxiliary functions. The PDE system description must be complete, including all necessary operators (PDE terms, BCs, ICs, and functions) needed to completely specify the system. If the geometric and physical operators known to Prophet are insufficient to fully describe the PDE system of interest, one or more new operator routines will have to be created and compiled into Prophet.

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Synopsis:

     system name=system_name
     +   sysvars=var1,var2,var3,...
     +   term0=R*geo_op.phy_op(in1,...|out1,...)@{region1,...}
     +   ...
     +   termNT-1=R*geo_op.phy_op(in1,...|out1,...)@{region1,...}
     +   tmpvars=tmp1,tmp2,tmp3,...
     +   func0=R*phy_op(in1,...|out1,...)@{region1,...}
     +   ...
     +   funcNF-1=R*phy_op(in1,...|out1,...)@{region1,...}
     +   init0=''field:expression''
     +   ...
     +   initN-1=''field:expression''

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Argument List:

• NAME
• SYSVARS
• TERM0, TERM1, ...
• TMPVARS
• FUNC0, FUNC1, ...
• INIT0, INIT1, ...

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Argument Descriptions:

The following list itemizes the valid arguments, their units, and their meaning.

NAME: [string]

name of the PDE system to be defined.

SYSVARS: [string]

-separated, ordered list of the solution variables for the PDE system. The PDE terms (see below) will be ordered in the matrix equation according to the order of the associated solution variavles in the SYSVARS list.

TERM0, TERM1, ...: [string]

of a single term of the PDE system. Prophet currently limits PDE systems to 78 PDE terms, named term0...term77.

For region-based PDE terms, the general form is:

termi=R*geo_op.phy_op(in1,in2,...|out1,out2,...)@{region1,region2,...}

For boundary conditions or interface constraints, the general form is:

termi=R*geo_op.phy_op(in1,in2,...|out1,out2...)@{reg1/reg2,reg3/reg4,...}

• R: any real number, with a minus sign if appropriate (minus sign by itself is invalid)
• geo_op: one of the geometric operators known to Prophet
• phy_op: one of the physical operators (a.k.a., flux routines) known to Prophet
• in1,in2,...: comma-separated list of sysvars, tmpvars, and other defined fields needed to compute this PDE term. If there are no input fields, "0" (the number zero) should precede the vertical bar.
• out1,out2,...: comma-separated list of sysvars (PDEs) in which this term appears
• region1,region2,...: comma-separated list of regions in which this term is relevant
• reg1/reg2,reg3/reg4...: comma-separated list of boundaries or interfaces (written as two region names, or a region name and a boundary name, separated by a slash "/") to which this term should be applied

TMPVARS: [string]

-separated, ordered list of the temporary (auxiliary) variables computed and possibly used in the PDE system. These variables can not involve differential operators, or they must be part of the PDE system. The temporary variables are computed in the order given by [the TMPVARS list | the FUNC statements], so a TMPVAR must be listed first if it is used in the computation of another TMPVAR.

FUNC0, FUNC1, ...: [string]

of a single function of the PDE system. Such auxiliary functions involve only local computations, so that the geo_op, which is always "nodal", is omitted from the function description. Prophet currently limits PDE systems to 57 auxiliary functions, named func0...func56.

The general form of a PDE function is:

funci=R*phy_op(in1,in2,...|out1,out2,...)@{region1,region2,...}

• R: any real number, with a minus sign if appropriate (minus sign by itself is invalid)
• phy_op: one of the physical operators (a.k.a., flux routines) known to Prophet
• in1,in2,...: comma-separated list of sysvars, tmpvars, and other defined fields needed to compute this function. If there are no input fields, "0" (the number zero) should precede the vertical bar
• out1,out2,...: comma-separated list of tmpvars that this function computes
• region1,region2,...: comma-separated list of regions in which this function is relevant

INIT0, INIT1, ...: [string]

command to initialize fields. If a field already exists at the time the system is executed, the initialization is not performed. The basic syntax is
initN=''FieldName:Expression''
for which N is an integer, ``FieldName'' is the name of the field to be initialized, and ``Expression'' evaluates to the initial value of that field. Currently, Prophet is limited to 57 initialization functions. Example of usage:
init3="mn:0.19"
The above will check to see if the field mn exists; if it doesn't, the field will be created and given the initial value of 0.19.

Less Used System Commands

SPAWN: [string]

list of field names which should be created on the domain when this system is solved, if they are not already present. Another feature of the spawn variable is conditional creation. A variable may be marked as being necessary if another variable exists. For example,
+ spawn=''psi,boronActive:boron''
In this example, ``psi'' is always created, but ``boronActive'' is created only if ``boron'' is present.

NFUNC: [integer]

keyword should no longer be used, as it is unnecessary. Prophet has learned how to count the number of functions. The previous meaning was the specification of the number of function terms in the PDE system.

NTERM: [integer]

keyword should no longer be used, as it is unnecessary. Prophet has learned to count the number of terms on its own. The previous meaning was the specification of the number of PDE terms in the PDE system.

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