Solving parametric complex fluids models in rheometric flows

Inverse identification of complex fluid behaviors is a tricky task because sometimes there are several rheological parameters and the identification procedure itself is quite expensive from the computational time viewpoint. Standard inverse identification procedures solve the model for a choice of the model parameters, and then parameters are updated trying to minimize the gap between the model predictions and some available experimental measures. Thus, the model has to be evaluated for each trial set of the model parameters. When models involve a great number of degrees of freedom the identification procedure becomes a computationally expensive task. In this paper we propose a new procedure able to solve once the model for any value of the model parameters. For this purpose, all the model parameters are considered as extra-coordinates of the model. Thus, the model results finally defined in a multidimensional space including the physical space x, the time t and a number of extra-coordinates related to the model parameters. The solution of such model needs for circumventing the curse of dimensionality illness that suffer multidimensional models.