### 15.10.4. Convergence Rate

A convergence rate can be defined by:

| (15–3)

where is the Normalized Residual at iteration , and is the Normalized Residual at an earlier iteration. With two exceptions, the convergence rate is evaluated using the current and previous iterations. The first exception corresponds to evaluating the residuals during the first coefficient iteration for a timestep in transient simulations. In this case, the rate is evaluated using the current residuals and the residuals from the first iteration from the previous timestep. The second exception corresponds to evaluating the residuals of the mesh displacement equations for both steady and transient simulations. In this case, the rate is evaluated using current residuals and the residuals from the first iteration from the previous solution of the displacement equations. In each of these cases, residual reduction values that are less than unity indicate convergence towards a steady state.

A residual reduction rate of 0.95 or smaller is considered typical for most situations, while a rate of 0.85 or smaller is considered to be very good. If your convergence behavior is slower than this (that is, rates are larger than 0.95), but is smooth, you should try increasing the timestep. Once the residuals are dropping monotonically, the timestep can often be safely increased to the characteristic time scale or greater in order to maximize the convergence rate. If there is no improvement, then the source of the convergence problem is probably not the timestep specification. For details, see Initial Condition Modeling.

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