Specifying Boundary Conditions

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Specifying Boundary Conditions

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The following forms of boundary condition specification may be applied to boundary segments:


VALUE ( variable ) = expression

NATURAL ( variable ) = expression

LOAD ( variable ) = expression

CONTACT ( variable ) = expression

VELOCITY ( variable ) = expression

NOBC ( variable )


The variable designated in the boundary condition specification identifies (by explicit association) the equation  to which this boundary condition is to be applied.


Dirichlet  (Value) Boundary Conditions

A VALUE segment boundary condition forces the solution of the equation for the associated variable to the value of expression on a continuous series of one or more boundary segments.  The expression may be an explicit specification of value, involving only constants and coordinates, or it may be an implicit relation involving values and derivatives of system variables.


Generalized Flux (Natural) Boundary Conditions

NATURAL and LOAD segment boundary conditions are synonymous.  They represent a generalized flux boundary condition derived from the divergence theorem.  The expression may be an explicit specification, involving only constants and coordinates, or it may be an implicit relation involving values and derivatives of system variables.  The Natural boundary condition reduces to the Neumann boundary condition in the special case of  the Poisson equation.  See the User Guide chapter Natural Boundary Conditions for information on the implementation of Natural boundary conditions.


Contact Resistance (Discontinuous Variable) Boundary Conditions

Interior boundaries can be defined to have a contact resistance using the CONTACT(variable) boundary condition.  See "Jump Boundaries" in the next section.


Velocity (Time Derivative) Boundary Conditions

This boundary condition imposes a specified time derivative on a boundary value (time-dependent problems only).  This condition is especially useful in specifying moving boundaries, by applying it to the surrogate coordinate variable.  If you have declared a velocity variable which is applied to a coordinate, then you should lock the surrogate coordinate to the mesh velocity variable at the boundary using a VELOCITY() boundary condition.


Terminating the current BC

Boundary conditions, once stated, remain in effect until explicitly changed or until the end of the path. NOBC(VARIABLE) can be used to turn off a previously specified boundary condition on the current path.  It is equivalent in effect to NATURAL(VARIABLE)=0  (the default boundary condition), except that it will not lead to "Multiple Boundary Condition Specification" diagnostics.


Default Boundary Conditions

The default boundary condition for FlexPDE is NATURAL(VARIABLE)=0.



Note: The NEUMANN, DNORMAL and DTANGENTIAL boundary conditions supported in earlier versions have been deleted due to unreliable behavior.  They may be restored in later versions.  In most cases, derivative boundary conditions are more appropriately applied through the NATURAL boundary condition facility.