2.5 Residuals of Fiber Equations

The solution algorithm for the fiber equations requires a means for checking convergence of the solution. In the fiber model a simple residual is used for this purpose.

The conservation equation for a general variable $\phi$ at a cell $P$ can be written as

where $a_P$ is the center coefficient, $a_{nb}$ are the influence coefficients for the neighboring cells, $S_c$ is the constant part of the source term, and $S_P$ is the linear part of the source term.

The residual $R^\phi$ computed by the fiber model is the imbalance in Equation  2.5-1 summed over all fiber cells.

This is called the absolute residual. Relative residuals are defined as the change of the absolute residuals between two subsequent iterations divided by the absolute residual.