Using Stationary Studies in Plasma Models
Preparing a plasma model to be solved using a stationary study can be more difficult than with a time-dependent study. However, the initial effort can be very rewarding because models tend to solve faster, parameterization are easy to setup, and because of the possibility to use the Optimization module.
The easiest discharges to solve with a stationary approach are inductively coupled plasma and DC. It is also possible to solve wave heated discharge models when the input power is used instead of deposited power.
Below are a few points to have in mind when using a stationary study:
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Initial conditions of the various species densities play a key role in obtaining a solution. If the initial densities are too far from the solution the solver might not be able to converge. If the initial densities are too low the solver might tend to go to the zero density solution and fail while trying to do so.
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Complex chemistries with more than one species (that is, argon and oxygen) tend to be difficult to model. In part, this is related with the previous point. It can happen that the initial mass fraction is not preserved. In these cases, one of the following strategies is needed: add point constraint for the mass fraction of a species at some point of the reactor wall; use the Species Group feature to preserve the mass fraction of a given species group; or add an Inlet to a given species.
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Finer meshes are often needed when comparing with a time-dependent approach.
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The solver settings can be adjusted to make convergence possible in some difficult cases, and can also be adjusted to increase the solution time in easier models like ICP reactors. If a model fails to converge, it could be because the default solver settings are too aggressive. There is always a tradeoff between speed and robustness, and the default settings cannot satisfy all cases. The key solver setting which can be changed to help with convergence can be found in the Fully Coupled node under Stationary Solver. In the Method and Termination section, there are parameter called Restriction for step-size increase (default value 1) and Restriction for step-size update (default value 1.5). These controls how much the damping factor can change between subsequent iterations. If it is difficult to obtain convergence it is worth lowering these values. This means the solver will have to take more iterations to solve, but it should be more stable. Decreasing the Restriction for step-size update to 1.2 or 1.1 can greatly improve the model stability.
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Sometimes it is extremely difficulty to obtain a solution. In this cases a good strategy is to use the solutions of a time-dependent study to provide initial conditions for the stationary study. As an example, solving for corona discharges directly with a stationary study is not recommended. The strategy should be to use the time-dependent solver to get a solution for an easy case (that is, using a low applied voltage) and feed this solution into the stationary solver where parameterizations can be done.
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When using the Microwave Plasma interface make sure that the input power is used instead of deposited power.