Reactive Flow and Transport Through Complex Systems

The meeting focused on mathematical aspects of reactive flow, diffusion and transport through complex systems. The research interest of the participants varied from physical modeling using PDEs, mathematical modeling using upscaling and homogenization, numerical analysis of PDEs describing reactive transport, PDEs from fluid mechanics, computational methods for random media and computational multiscale methods

Grain growth for astrophysics with Discontinuous Galerkin schemes

Depending on their sizes, dust grains store more or less charges, catalyse more or less chemical reactions, intercept more or less photons and stick more or less efficiently to form embryos of planets. Hence the need for an accurate treatment of dust coagulation and fragmentation in numerical modelling. However, existing algorithms for solving the coagulation equation are over-diffusive in the conditions of 3D simulations. We address this challenge by developing a high-order solver based on the Discontinuous Galerkin method. This algorithm conserves mass to machine precision and allows to compute accurately the growth of dust grains over several orders of magnitude in size with a very limited number of dust bins.Comment: 17 pages, 22 figures, Accepted for publication in MNRA

A framework for polydisperse pulp phase modelling in flotation

Froth flotation is one of the most widely-used mineral processing operations. The pulp zone in flotation tanks is polydisperse in general and serves as a medium for the interaction between the solid particles and the gas bubbles in a liquid continuum, leading to particle–bubble attachment/detachment and bubble coalescence/breakage phenomena. To better predict the hydrodynamics and inform the design of e cient flotation equipment, it is therefore important to accurately model and simulate the evolution of the size distribution of the dispersed phases. This has created an urgent need for a framework that can model the pulp phase in an e cient manner, which is not currently available in the literature. The available software products are not e cient enough to allow for a tractable modelling of industrial-scale flotation cells and in some cases they cannot model the polydispersity of the dispersed phase at all. This work presents an e cient numerical framework for the macroscale simulation of the polydisperse pulp phase in froth flotation in an open-source finite element computational fluid dynamics (CFD) code that provides an e cient solution method using mesh adaptivity and code parallelisation. A (hybrid finite element–control volume) finite element framework for modelling the pulp phase has been presented for the first time in this work. An Eulerian–Eulerian turbulent flow model was implemented in this work including a transport equation for attached and free solid particles. Special care was taken to model the settling velocity of the free solids and the modification of the liquid viscosity due to the presence of these particles. Bubble polydispersity was modelled using the population balance equation (PBE), which was solved using the direct quadrature method of moments (DQMOM). Appropriate functions for bubble coalescence and breakage were chosen in the PBE. Mesh adaptivity was applied to the current problem to produce fully-unstructured anisotropic meshes, which improved the solution e ciency, while all simulations were executed on a multicore architecture. The model was validated for 2D simulations of a bubble column against experimental results available in the literature. After successful validation, the model was applied to the simulation of the pulp phase in a flotation column for monodisperse and polydisperse solids. Polydispersity of the solids was modelled for the first time in this work using three separate solid size classes. A clear dependence of the flotation rate on the particle size was noticed and the monodisperse solids simulations were shown to over-predict the flotation rate. Other than flotation, this open-source framework can be used for the simulation of a variety of polydisperse multiphase flow problems in the process industry

Hyperbolic Conservation Laws

[no abstract available

A variational framework for multi-scale defect modeling in strained electronics and processing of composite materials

With the recent advances in material processing technologies and the introduction of the material genome initiative, material processing has gained an increased level of attention in the research community. Primary challenges in most material processing technologies and specifically in composite materials are the uncertainties concerning the material’s performance under loading whether it be static, dynamic or cyclic. That is due to the variabilities in these technologies that may lead to the formation of defects within the material parts at critical location during processing. This dissertation presents a deterministic defect modeling framework based on a system of variationally consistent formulations that allow for the modeling of the material processing stage and incorporate multi-physics coupling for multi-constituent materials. A stabilized and novel discontinuity capturing formulation is developed to model multi-phase flow of the materials and their defect while sharply capturing the jumps in material properties, material compressibility and kinetic reaction across the multi-phase interfaces. The method is based on employing structured non-moving meshes to solve the Navier-Stokes equations employing a finite element method (FEM) stabilized via the Variational Multiscale Method (VMS). Within VMS framework a discontinuity capturing method is derived that allows for sharp discontinuity capturing of the physical discontinuities of across phases within a single numerical element allowing for highly accurate and discrete representation of the interfacial physical phenomena. In addition, surface tension is incorporated into the formulation to discretely model jumps in the pressure field. The multi-phase interface is evolved employing a stabilized level-set method allowing for intricate motion of the two phases and the discontinuities within the Eulerian mesh. The formulation is then expanded to incorporate discontinuities in the governing system of equations allowing for modeling adjacent compressible-incompressible fluids within a unified formulation. Coupled with the thermal evolution within the constituents of the material and accounting for phase change and mass leading to mass transfer across the interface the materials, kinetic evolution of the material viscosities is modeled at the material points accounting for variability in the flow behavior as a function of kinetic curing. Finally, a previously developed isogeometric FEM method is expanded to model quantum defect evolution of strained electronics and the effect of straining on the electronic properties of these materials. Representative numerical tests involving complex multi-phase flows of physical instabilities, hydrodynamic collapse of bubbles and convective mass transfer along with electronic band-gap structures with strain effects are presented as validations and applications for the framework’s robustness. Finally, the chemo-thermo-mechanical coupling and real-life application is presented via a fully coupled problem involving processing of a composite bracket during the early curing stages

Behavior of the dispersed phase in a biphasic liquid-liquid Comportement de la phase dispersé dans un contacteur diphasique liquide-liquide

In this work two major hydrodynamic parameters: the holdup of the dispersed phase and the Sauter diameter are considered. In the first part, this is done for describing the hydrodynamics of interacting liquid–liquid dispersions with using different drop breakup, coalescence and growth models in a droplet population balance model. Based on the variational iteration method, different process cases have been performed and, it is possible to find the exact solution or a closed approximate solution of a problem. For the simultaneous growth and the coalescence terms a comparison between the present method and projection method which include discontinuous Galerkin and collocation techniques are made respectively. The results are encouraging and the new method has proven to be suitable to predict holdup and Sauter diameter profiles. In the second part, we extended the dual quadrature method of generalized moments (DuQMoGeM) to solve the population balance model for the hydrodynamics of liquidliquid extraction columns using a multi-compartment model. The DuQMoGeM results were compared to analytical solutions for batch and continuous well-mixed vessels and extraction columns, showing that it is accurate for predicting the evolution of the low order moments and the drop number distribution along with the column height. We also modeled a K¨ uhni column for which the simulation accurately predicted the steadystate experimental holdup, encouraging the DuQMoGeM usage to solve the population balance equation for heterogeneous systems and different columns

On adomian based numerical schemes for euler and navier-stokes equations, and application to aeroacoustic propagation

140 p.En esta tesis se ha desarrollado un nuevo método de integración en tiempo de tipo derivadas sucesivas (multiderivative), llamado ABS y basado en el algoritmo de Adomian. Su motivación radica en la reducción del coste de simulación para problemas en aeroacústica, muy costosos por su naturaleza transitoria y requisitos de alta precisión. El método ha sido satisfactoriamente empleado en ambas partes de un sistema híbrido, donde se distinguen la parte aerodinámica y la acústica.En la parte aerodinámica las ecuaciones de Navier-Stokes incompresibles son resueltas con unmétodo de proyección clásico. Sin embargo, la fase de predicción de velocidad ha sido modificadapara incluir el método ABS en combinación con dos métodos: una discretización espacial MAC devolúmenes finitos, y también con un método de alto orden basado en ADER. El método se ha validado respecto a los problemas (en 2D) de vórtices de Taylor-Green, y el desarrollo de vórticesde Karman en un cilindro cuadrado. La parte acústica resuelve la propagación de ondas descritaspor las ecuaciones linearizadas de Euler, empleando una discretización de Galerkin discontinua. El método se ha validado respecto a la ecuación de Burgers.El método ABS es sencillo de programar con una formulación recursiva. Los resultados demuestran que su sencillez junto con sus altas capacidades de adaptación lo convierten en un método fácilmente extensible a órdenes altos, a la vez que reduce el coste comparado con otros métodos clásicos

On Adomian Based Numerical Schemes for Euler and Navier-Stokes Equations, and Application to Aeroacoustic Propagation

In this thesis, an Adomian Based Scheme (ABS) for the compressible Navier-Stokes equations is constructed, resulting in a new multiderivative type scheme not found in the context of fluid dynamics. Moreover, this scheme is developed as a means to reduce the computational cost associated with aeroacoustic simulations, which are unsteady in nature with high-order requirements for the acoustic wave propagation. We start by constructing a set of governing equations for the hybrid computational aeroacoustics method, splitting the problem into two steps: acoustic source computation and wave propagation. The first step solves the incompressible Navier-Stokes equation using Chorin's projection method, which can be understood as a prediction-correction method. First, the velocity prediction is obtained solving the viscous Burgers' equation. Then, its divergence-free correction is performed using a pressure Poisson type projection. In the velocity prediction substep, Burgers' equation is solved using two ABS variants: a MAC type implementation, and a ``modern'' ADER method. The second step in the hybrid method, related to wave propagation, is solved combining ABS with the discontinuous Galerkin high-order approach. Described solvers are validated against several test cases: vortex shedding and Taylor-Green vortex problems for the first step, and a Gaussian wave propagation in the second case. Although ABS is a multiderivative type scheme, it is easily programmed with an elegant recursive formulation, even for the general Navier-Stokes equations. Results show that its simplicity combined with excellent adaptivity capabilities allows for a successful extension to very high-order accuracy at relatively low cost, obtaining considerable time savings in all test cases considered.Predoc Gobierno Vasc

Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7]

Solution of statistical inverse problems via the frequentist or Bayesian approaches described in earlier chapters can be a computationally intensive endeavor, particularly when faced with large-scale forward models characteristic of many engineering and science applications. High computational cost arises in several ways. First, thousands or millions of forward simulations may be required to evaluate estimators of interest or to characterize a posterior distribution. In the large-scale setting, performing so many forward simulations is often computationally intractable. Second, sampling may be complicated by the large dimensionality of the input space--as when the inputs are fields represented with spatial discretizations of high dimension--and by nonlinear forward dynamics that lead to multimodal, skewed, and/or strongly correlated posteriors. In this chapter, we present an overview of surrogate and reduced order modeling methods that address these computational challenges. For illustration, we consider a Bayesian formulation of the inverse problem. Though some of the methods we review exploit prior information, they largely focus on simplifying or accelerating evaluations of a stochastic model for the data, and thus are also applicable in a frequentist context.Sandia National Laboratories (Laboratory Directed Research and Development (LDRD) program)United States. Dept. of Energy (Contract DE-AC04-94AL85000)Singapore-MIT Alliance Computational Engineering ProgrammeUnited States. Dept. of Energy (Award Number DE-FG02-08ER25858 )United States. Dept. of Energy (Award Number DESC00025217

A standard test case suite for two-dimensional linear transport on the sphere

It is the purpose of this paper to propose a standard test case suite for two-dimensional transport schemes on the sphere intended to be used for model development and facilitating scheme intercomparison. The test cases are designed to assess important aspects of accuracy in geophysical fluid dynamics such as numerical order of convergence, "minimal" resolution, the ability of the transport scheme to preserve filaments, transport "rough" distributions, and to preserve pre-existing functional relations between species/tracers under challenging flow conditions. <br><br> The experiments are designed to be easy to set up. They are specified in terms of two analytical wind fields (one non-divergent and one divergent) and four analytical initial conditions (varying from smooth to discontinuous). Both conventional error norms as well as novel mixing and filament preservation diagnostics are used that are easy to implement. The experiments pose different challenges for the range of transport approaches from Lagrangian to Eulerian. The mixing and filament preservation diagnostics do not require an analytical/reference solution, which is in contrast to standard error norms where a "true" solution is needed. Results using the CSLAM (Conservative Semi-Lagrangian Multi-tracer) scheme on the cubed-sphere are presented for reference and illustrative purposes