Network iterations

For network iterations two kinds of convergence criteria are applied: the residuals and the change in the solution must be both small enough.

For the mass and energy flow residuals $\tilde{q}^{\alpha}_i$ and $r^{\alpha}_{i,max}$ are calculated as specified in Equations (839) and (840) with $k_n=1$ and $q_i^{\alpha}$ equal to the mass flow (unit of mass/unit of time) and the energy flow (unit of energy/unit of time). For the element equation $\tilde{q}^{\alpha}_i$ is taken to be 1 (the element equation is dimensionless) and $r^{\alpha}_{i,max}$ is calculated based on the element equation residuals. The residual check amounts to

$$r^{\alpha}_{i,max} \le c_{1*} \tilde{q}^{\alpha}_i$$ (849)

where $c_{1*}$ takes the value $c_{1t}$, $c_{1f}$ and $c_{1p}$ for the energy balance, mass balance and element equation, respectively. In addition, an absolute check can be performed in the form

$$r^{\alpha}_{i,max} \le a_{1*}$$ (850)

where $a_{1*}$ takes the value $a_{1t}$, $a_{1f}$ and $a_{1p}$ for the energy balance, mass balance and element equation, respectively. Default is to deactivate the absolute check (the coefficients $a_{1*}$ are set to $10^{20}$).

In the same way the maximum change in solution in network iteration i ${c}^{\alpha}_{i,max}$ is compared with the maximum change in the solution since the start of the network iterations, i.e. the solution at the end of iteration i minus the solution at the beginning of the increment(before network iteration 1). This is done separately for the temperature, the mass flow, the pressure and the geometry. It amounts to the equation:

$${c}^{\alpha}_{i,max} \le c_{2*} {\Delta u}^{\alpha}_{i,max},$$ (851)

where $c_{2*}$ takes the value $c_{2t}$, $c_{2f}$, $c_{2p}$ and $c_{2a}$ for the temperature, the mass flow, the pressure and the geometry, respectively. In addition, an aboslute check can be performed in the form

$${c}^{\alpha}_{i,max} \le a_{2*},$$ (852)

where $a_{2*}$ takes the value $a_{2t}$, $a_{2f}$ and $a_{2p}$ for the temperature, the mass flow, the pressure and the geometry. Default is to deactivate the absolute check (the coefficients $a_{2*}$ are set to $10^{20}$).

The parameters $c_{1t}$, $c_{1f}$, $c_{1p}$, $c_{2}$, $c_{2f}$, $c_{2p}$, $c_{2a}$ and $a_{1t}$, $a_{1f}$, $a_{1p}$, $a_{2}$, $a_{2f}$, $a_{2p}$, $a_{2a}$ can be changed using the *CONTROLS,PARAMETERS=NETWORK card.

Both criteria are important. A convergent solution with divergent residuals points to a local minimum, convergent residuals with a divergent solution point to a singular equation system (i.e. infinitely many solutions).