What About Boundary Conditions?

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Proper specification of boundary conditions is crucial to the solution of a PDE system.

In a FlexPDE script, boundary conditions are presented as the boundary is being described.

The primary types of boundary condition are VALUE and NATURAL.

The VALUE (or Dirichlet) boundary condition specifies the value that a variable must take on at the boundary of the domain.

The NATURAL boundary condition specifies a flux at the boundary of the domain. (The precise meaning of the NATURAL boundary condition depends on the PDE for which the boundary condition is being specified. Details are discussed in the Chapter "Natural Boundary Conditions")

In the diffusion problem presented above, for example, we may add fixed values on the bottom and top edges, and zero-flux conditions on the sides as follows:

…

BOUNDARIES

REGION 1

START(0,0)

VALUE(u) = 0    LINE TO (1,0)       { fixed value on bottom }

NATURAL(u)=0   LINE TO (1,1)       { insulated right side }

VALUE(u)=1   LINE TO (0,1)       { fixed value on top }

NATURAL(u)=0   LINE TO CLOSE   { insulated left side }

…

Notice that a VALUE or NATURAL statement declares a condition which will apply to the subsequent boundary segments until the declaration is changed.