OOF2: The Manual

Details

Description

Dirichlet boundary conditions assign fixed values to Fields. A separate boundary condition must be established for each component of a Field that is to be fixed. Dirichlet boundary conditions may be applied to both Edge and Point boundaries.

The field parameter specifies which Field is to be fixed. The field_component parameter specifies which component is to be fixed. It is a string representing the component index. The acceptable strings depend on the type of Field selected. The GUI presents a pull down menu listing the legal strings, but users using the text interface or editing scripts will need to know the possible values. For vector fields, the field_component must be 'x' or 'y'. For tensor fields (when implemented) the component must be one of 'xx', 'yy', 'xy', etc. For scalar fields the field_component is ignored. Note that because the input is a Python string, the quotation marks are required.

The equation and eqn_component parameters require a bit of explanation. The finite element machinery constructs a system of linear equations with N equations and N unknowns, where N is the number of nodes times the number of active field components. Each time a Dirichlet boundary condition is applied at a node, one unknown is removed from the problem, and all of a sudden there are too many equations, and one of them must be removed from the system before it is solved. That is, one of the equations becomes dependent on the others. The equation and eqn_component parameters specify which equation that is. In general, any equation containing the fixed Field may be chosen, but no equation component may be chosen more than once on a single boundary.

In simple problems with uncoupled fields, there is a natural choice for the dependent equation -- it is the equation for the component of the Flux that is conjugate to the fixed Field component. For example, when constraining the value of the x component of displacement, the x component of the force balance equation is dependent. But in complicated problems with coupled fields, the choice isn't always so obvious, and OOF2 relies on the user to identify the dependent equation. For example, if a Field contributes to two Fluxes, both of which have divergence equations, then either of the two equations may be selected.

The profile parameter determines the Field component values along the boundary. Profiles may be arbitrary functions of position, and are specified by providing a ProfileXTd object.

Example. 

    DirichletBC(field=Displacement, field_component='y',
                equation=Force_Balance, eqn_component='y',
                profile=ContinuumProfileXTd(function='y * sin(x/10)'),
                boundary='top')
	

This constrains the y component of the Displacement along the top boundary of the Mesh, making the y component of the Force_Balance equation dependent. The y displacement at point on the boundary is set to .