Solving the Algebraic Slip Mixture Model as a Hyperbolic System with Restrictions

Abstract

In this work the well established Algebraic Slip Mixture Model (ASMM) is revisited and studied. Since its presentation the related literature is centered in its derivation and the analysis of the closure laws needed for practical applications. In addition a rich mathematical and modelistic structure is present is this model. This structure is not much discussed, but is also valuable for the model implementation and use, particularly for high disperse-phase fractions.
So that, the incompressible ASMM is presented as a hyperbolic system with restrictions derived from the Two-Fluid model. The structure of the hyperbolic system is described, particularly the restriction given by the mixture mass conservation equation as is usual in incompressible problems, the importance
of the dispersed phase conservation equation with the corresponding eigenvalue analysis and the cases obtained for two different dispersed-phase flux functions. A numerical solver is implemented based on this analysis taking into account the eigenvalues information for the correct stabilization and the issues related with the incompressibility, which is treated by pressure correction methods.
The analysis allows to derive a semi-analytical solution for sedimentation cases and the consequent validation of the numerical solver designed for the problem.