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Advanced Mathematical and Computational Models for Complex Multiphase Flows

Final Activity Report Summary - ALTAY (Advanced mathematical and computational models for complex multiphase flows)

The 'Advanced mathematical and computational models for complex multiphase flows' (ALTAY) project aimed to advance the mathematical and computational modelling of multiphase flows by means of a new theory concerning thermodynamically compatible systems and extended irreversible thermodynamics.

A hierarchy of hyperbolic governing equations for multiphase compressible flow in conservation-law form has been developed based on the formalism for thermodynamically compatible systems of hyperbolic conservation laws. This approach enables the formulation of classes of hyperbolic conservation-form equations using generalised potentials and variables. Its core aspect is a phenomenological modelling of continuous media where by using thermodynamic laws the structure of the governing balance laws can be determined. In this context the mixture is supposed to be a continuum medium in which the multiphase flow character is taken into account. The resulting system of partial differential equations is hyperbolic and all balance equations can be cast in conservation form.

The conservation form of the governing equations provides a solid basis for the development of high-order accurate numerical methods. A finite volume method based on the solution of the Riemann problem has been developed to solve equations of the proposed models. Due to the complexity of the governing equations the solution of the Riemann problem cannot be easily obtained. Therefore, the recently proposed GFORCE method that evaluates the numerical fluxes by centred numerical schemes was applied. The advantage of the GFORCE is its simplicity and robustness.

The method has been implemented into a high-resolution compressible computational fluid dynamics code (CNS3D) developed by Prof. Drikakis and his collaborators in the Fluid Mechanics and Computational Sciences (FMaCS) group at Cranfield University. The code was further applied to several one- and two-dimensional test problems, including the interaction of a shock wave with a bubble, and the results were found in a good agreement with available experimental data and exact solutions. The project resulted in several journal and conference publications, some of which will appear in the open literature in the near future.