### 11.2.3. Residual Normalization Procedure

As described above, the raw residual, [r], is calculated as the imbalance in the linearized system of discrete equations. The raw residuals are then normalized for the purpose of solution monitoring and to obtain a convergence criteria. An overview of the normalization procedure is given below.

For each solution variable, , the normalized residual is given in general by:

| (11–53)

where is the raw residual control volume imbalance, a p is representative of the control volume coefficient, and is a representative range of the variable in the domain. The exact calculation of a p and is not simple and is not presented here. However, some important notes are:

1. The normalized residuals are independent of the initial guess.

2. a p is the central coefficient of the discretized control volume equation and therefore includes relevant advection, diffusion, source linearization, and other terms.

3. For steady-state simulations, the time step is used only to underrelax the equations and is therefore excluded from the normalization procedure. This ensures that the normalized residuals are independent of the time step. The transient term is included in a p for transient simulations.

4. For multiphase, if equations are coupled through an interphase transfer process (such as interphase drag or heat transfer), the residuals are normalized by the bulk a p.

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