Novel unified and extended mixture theories: theory and numerics

OMNIA proposes a unique combination of mathematical physics and numerical analysis to achieve new, provably structure-preserving discretizations of novel unified and extended mixture theories. This project is based on the firm belief that to obtain reliable numerical results, especially in a complex field such as mixture theories, where exact solutions are lacking, a deep understanding of the basic mathematical modelling framework is required.So far, there is no mixture theory capable of describing the processes occurring in a multiphase flow in a closed and comprehensive manner, respecting the laws of thermodynamics and the principle of causality. For this reason, OMNIA, after adequately addressing numerically what is most exhaustive in the literature, aims to establish a theoretical framework to extend the existing model to derive a non-equilibrium mixture theory which simultaneously includes fundamental processes such as convective and dissipative effects but also dispersive processes.Finally, to address the resulting complex monolithic model, finite volume methods with novel structure preserving properties will be developed, that not only accurately solve the obtained system respecting its thermodynamic properties at a discrete level, but also preserve additional mathematical characteristics. Namely, new semi-implicit, asymptotic-preserving numerical methods will be devised which are capable of preserving the curl free constraints endowed by the model.