The use of a Newton iteration algorithm for solution of the governing equations requires the user to provide initial estimates of the solution variables. It may sometimes be difficult to obtain good initial estimates of species composition, especially when one is not familiar with the chemistry system being studied. In such cases, it may be necessary to approach the problem from points that are more intuitive. For example, in a thermal problem, a good initial estimate of gas species is often the thermodynamic equilibrium composition at the initial temperature. For this purpose, an optional equilibrium calculation (used by default if no initial guess is provided), minimizes the Gibb’s free energy of the system in order to determine the equilibrium gas mole fractions. This method of determining the initial estimate of the gas-phase composition is automatically initiated when the user does not supply any initial estimates for the gas-phase species’ mole fractions. If equilibrium composition does not provide immediate convergence for the reactor conditions of interest, the user may increase the residence time (thereby driving the conditions closer to equilibrium) from the target conditions until a solution is reached. This solution can then be used as the initial estimate for the desired residence time. Such gradual approach to a desired solution is facilitated by the Continuation capability, and generally requires very little computational time. For a plasma system, a similar approach could be used to obtain a solution where the initial guess is difficult to obtain. In this case, the user might assume an initial guess for the gas-phase composition close to that of the reagent gases entering the reactor, and set the power deposition level very low. Then gradually increasing the reactor power using the continuation capability can lead to the desired solution.

Initial estimates of surface site fractions are often more difficult, but also have less impact on the ability of the Newton algorithm to reach a solution. A general rule of thumb for all species types is to provide an estimate for every species in the system, even if these numbers are small. An initial guess of 1 X 10^-7, for example, is generally much better than allowing the application to set the initial fraction to zero. All initial estimates will be normalized, such that the sums of gas mole fractions, surface site fractions, and bulk species fractions are all equal to one.

The user has an option to either solve the gas energy equation or to keep the temperature fixed at the initial specified value. There are some cases when the user may choose not to solve the gas energy equation. For example, the reactor temperature may have been accurately measured, while heat losses are difficult to estimate. In cases where the energy equation is solved, the user has an option to solve the system of equations in one or two steps. The default is to use two steps: first solve for the species composition at the fixed temperature estimate provided by the user, and then solve simultaneously the energy equation and the species composition using the first solution as the initial guess. This two-stage method provides more robust convergence for thermal systems, where the reaction rates’ exponential dependence on the gas temperature is the primary source of equation stiffness and nonlinearities. For plasma systems, when one is solving for the electron energy equation, convergence is usually most expedient with the one-step option with no fixed-temperature iteration.