Computing Accurate Fluxes

The COMSOL Multiphysics software provides three ways to compute accurate fluxes and reaction forces:

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The first approach involves the reaction force operator (reacf) that makes it possible to compute integrals of reaction forces or fluxes during results analysis. See reacf for details.

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The second, more general approach for calculating reaction forces and fluxes is to use weak constraints. Use this approach when you need reaction forces or fluxes in other contexts than calculating integrals of reaction forces or fluxes.


	Weak Constraints

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Some physics interfaces provide a third way of computing accurate fluxes. Under the section (if is selected in the dialog box), select the check box. The solver then computes variables storing an accurate boundary flux from each boundary into the adjacent domain (in addition to the standard extrapolated value). On interior boundaries, there are two flux variables corresponding to the flux into the domains on either side of the boundary. Unlike the other methods, these variables are available also on unconstrained boundaries. This method is active by default in Coefficient Form PDE, General Form PDE, heat transfer, and mass transport interfaces. There is also an check box that is selected by default. The smoothing can provide a more well-behaved flux value close to singularities. See also Boundary Flux Operators: uflux and dflux.

When using weak constraints in interfaces, the Lagrange multipliers are additional dependent variables in those physics interfaces. When using the reaction force operator, the reaction force operator of a certain dependent variable corresponds to the Lagrange multiplier of that dependent variable. The Lagrange multipliers correspond to the following quantities in the physics interfaces:

Table 3-6: Interpretation of Lagrange Multipliers
Physics Interface	Quantity
Electrostatics	Surface charge density
Magnetic Fields	Surface current
Electric Currents	Current density
Heat Transfer	Heat flux
Transport of Diluted Species	Flux
Solid Mechanics	Force per area
Pressure Acoustics	Normal displacement (acceleration for eigenfrequency studies)
Laminar Flow	Total force per area

The sign of the Lagrange multiplier is the same as the one used when applying the corresponding quantity explicitly in a flux condition. As a general rule, the sign corresponds to an action by the surroundings on the model, rather than the opposite.

The program computes only the part of the boundary flux captured by the Lagrange multiplier. You might have additional flux coming from boundary sources or nonidentity constraint matrices. This should not happen in the physics interfaces, though.


	Lagrange multipliers in axial symmetry are not equal to the reaction flux per area but rather per length and full revolution.


	Flux Calculation Example — Heat Transfer Model

The reaction forces are computed from the value of the residual vector at every node point where a constraint is applied. Therefore, the reaction forces should be thought of as discrete values at each node point rather than continuous fields.

The boundary flux variables are computed in a similar way to the reaction forces but with two important differences:

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First, on each boundary, the contributions to the residual vector from the boundary and from the adjacent domains are computed separately. This makes it possible to compute the flux into each adjacent domain even when there is no constraint on the boundary so that the full residual vector is zero.

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Second, the nodal fluxes computed from the residual vector are further processed and represented as a continuous field on the boundary. The integral of this flux field over a boundary is equal to the sum of the nodal fluxes.