GIEM model

Deterministic models that are non-linear in c will be limited to specific applications. For example, in the generalized IEM (GIEM) model (Tsai and Fox 1995a Tsai and Fox 1998), which is restricted to binary mixing, the mixture fraction appears non-linearly 61... 

In this manner, the non-relaxing property of the IEM model is avoided, and a(f, f) can be chosen such that the limiting mixture-fraction PDF is Gaussian. Indeed, from DNS it is known that the conditional diffusion for the mixture fraction has a non-linear form that varies with time (see Fig. 6.2). In the GIEM model, this behavior is modeled by... 

However, if the correlation matrix p is rank-deficient, but the scalar dissipation matrix is full rank, the IEM model cannot predict the increase in rank of p due to molecular diffusion. In other words, the last term on the right-hand side of (6.105), p. 278, due to the diffusion term in the FP model will not be present in the IEM model. The GIEM model violates the strong independence condition proposed by Pope (1983). However, since in binary mixing the scalar fields are correlated with the mixture fraction, it does satisfy the weak independence condition. The expected value on the left-hand side is with respect to the joint PDF (c, f x, t). 

The BMC/GIEM model for micromixing in non-premixed turbulent reacting flows. 

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