A three-dimensional numerical method for modelling weakly ionized plasmas

Astrophysical fluids under the influence of magnetic fields are often subjected to single-fluid or two-fluid approximations. In the case of weakly ionized plasmas however, this can be inappropriate due to distinct responses from the multiple constituent species to both collisional and non-collisional forces. As a result, in dense molecular clouds and proto-stellar accretion discs for instance, the conductivity of the plasma may be highly anisotropic leading to phenomena such as Hall and ambipolar diffusion strongly influencing the dynamics. Diffusive processes are known to restrict the stability of conventional numerical schemes which are not implicit in nature. Furthermore, recent work establishes that a large Hall term can impose an additional severe stability limit on standard explicit schemes. Following a previous paper which presented the one-dimensional case, we describe a fully three-dimensional method which relaxes the normal restrictions on explicit schemes for multifluid processes. This is achieved by applying the little known Super TimeStepping technique to the symmetric (ambipolar) component of the evolution operator for the magnetic field in the local plasma rest-frame, and the new Hall Diffusion Scheme to the skew-symmetric (Hall) component.Comment: 13 pages, 9 figures, accepted for publication in MNRA

CFD Modeling of Fluidized Beds

We review the mathematical modeling of fluidized suspensions with focus on the Eulerian (or multifluid) approach. After a brief survey of different modeling approaches adopted for multiphase flows, we discuss the Eulerian equations of motion for fluidized suspensions of a finite number of monodisperse particle classes, obtained by volume averaging. We present the problem of closure for the stress tensors and the interaction forces between the phases and report some of the constitutive relations used for them in the literature. Finally, we explain briefly the population balance modeling approach, which allows handling suspensions of particles continuously distributed over any of their properties of interest

The XDEM Multi-physics and Multi-scale Simulation Technology: Review on DEM-CFD Coupling, Methodology and Engineering Applications

The XDEM multi-physics and multi-scale simulation platform roots in the Ex- tended Discrete Element Method (XDEM) and is being developed at the In- stitute of Computational Engineering at the University of Luxembourg. The platform is an advanced multi- physics simulation technology that combines flexibility and versatility to establish the next generation of multi-physics and multi-scale simulation tools. For this purpose the simulation framework relies on coupling various predictive tools based on both an Eulerian and Lagrangian approach. Eulerian approaches represent the wide field of continuum models while the Lagrange approach is perfectly suited to characterise discrete phases. Thus, continuum models include classical simulation tools such as Computa- tional Fluid Dynamics (CFD) or Finite Element Analysis (FEA) while an ex- tended configuration of the classical Discrete Element Method (DEM) addresses the discrete e.g. particulate phase. Apart from predicting the trajectories of individual particles, XDEM extends the application to estimating the thermo- dynamic state of each particle by advanced and optimised algorithms. The thermodynamic state may include temperature and species distributions due to chemical reaction and external heat sources. Hence, coupling these extended features with either CFD or FEA opens up a wide range of applications as diverse as pharmaceutical industry e.g. drug production, agriculture food and processing industry, mining, construction and agricultural machinery, metals manufacturing, energy production and systems biology

Doctor of Philosophy

dissertationThe purpose of this research is the development of mathematical formalisms for the numerical modeling and simulation of multiphase systems with emphasis in polydisperse flows. The framework for these advancements starts with the William-Boltzmann equation which describes the evolution of joint distributions of particle properties: size, velocity, mass, enthalpy, and other scalars. The amount of statistical information that can be obtained from the direct evolution of particle distribution functions is extensive and detailed, but at a computational cost not yet suitable in usable computational fluid dynamics (CFD) codes. Alternatives to the direct evolution of particle distribution functions have been proposed and we are interested in the family of solutions involving the evolution of the statistical moments from the joint distributions. Rather than tracking every single particle characteristic from the joint distribution, transport equations for their joint moments are formulated; these equations share many of the properties of the regular transport equations formulated in the finite volume framework, making them very attractive for their implementation in current Eulerian CFD codes. The information they produce is general enough to provide the characteristic behavior of many multiphase systems to the point of improvement over the current Eulerian methodologies implemented on standard CFD modeling and simulation approaches. Based on the advantages and limitations of the solutions of the ongoing methodologies and the degree of the information provided by them, we propose formalisms to extend their modeling capabilities focusing on the influence of the size distribution in many of the related multiphase phenomena. The first methodology evolves joint moments based on the evolution of primitive variables (size among them) and conditional moments that are approximants of the joint moments at every time step. The second methodology reconstructs completely the marginal size distribution using the concept of parcel and approximate characteristic behavior of the rest of the conditional moments in each parcel. In both approaches, the representation of size distribution plays a fundamental role and accounts for the polydisperse nature of the system. Also, the numerics of the moment transport equations are to be consistent with the theory of general hyperbolic transport equations but the formulation of the discretization schemes are based on the properties of the underlying distribution. A final contribution is presented in the form of an appendix and it analyzes the role of maximum entropy-based methodologies on the formulation of Eulerian moment-based methods. Attempts to derive new transport equations on the framework of maximum entropy methodologies will be considered and reconstruction of distribution strategies will be presented as preliminary results that might impact future research on Eulerian moment-based methods