Theoretical and numerical analysis of hydrostatics and low-Mach number flows of two-phase granular mixtures
(2012)
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- Authors
- Supervisors
- Papalexandris, Miltiadis
- Abstract
- (en) In this Doctoral Thesis we are concerned with the theoretical and numerical analysis of hydrostatics and low-Mach number flows of fluid saturated granular materials. In the first part, we generalize the concept of low-Mach number approximation to multi-phase flows and apply it to derive the low-Mach number equations for the mixtures of interest. In the second part, we develop a projection-type, successive-over-relaxation method for the computation of hydrostatics of such mixtures. We also prove that this method is formally convergent. The second part concludes with the presentation and discussion of representative numerical results. In the third part, we develop an existence theory for hydrostatics of two-phase granular mixtures. By employing weak-convergence methods and by choosing suitable non-linear test functions, we prove the existence of at least one weak solution, in the sense of distributions. This gives a positive answer to the open question of the well-posedness of continuum models for granular materials at equilibrium. In the fourth part, we present an algorithm for the calculation of constant density flows of the mixtures of interest. This algorithm combines a predictor-corrector time-integration scheme with a projection method for the computation of the pressure of each phase. It also incorporates a detection and treatment methodology for the material interfaces that develop in such flows. The efficiency and robustness of the proposed algorithm are tested via a series of numerical tests. Finally, this algorithm is employed to perform the first ever simulations of unsteady shear flows of granular mixtures, the characteristics of which are discussed in detail.
- Affiliations
Citations
Varsakelis, C. (2012). Theoretical and numerical analysis of hydrostatics and low-Mach number flows of two-phase granular mixtures. https://hdl.handle.net/2078.5/159647