A Self-organizing Adaptive-resolution Particle Method with Anisotropic Kernels

AbstractAdaptive-resolution particle methods reduce the computational cost for problems that develop a wide spectrum of length scales in their solution. Concepts from self-organization can be used to determine suitable particle distributions, sizes, and numbers at runtime. If the spatial derivatives of the function strongly depend on the direction, the computational cost and the required number of particles can be further reduced by using anisotropic particles. Anisotropic particles have ellipsoidal influence regions (shapes) that are locally aligned with the direction of smallest variation of the function. We present a framework that allows consistent evaluation of linear differential operators on arbitrary distributions of anisotropic particles. We further extend the concept of particle self-organization to anisotropic particles, where also the directions and magnitudes of anisotropy are self-adapted. We benchmark the accuracy and efficiency of the method in a number of 2D and 3D test cases

A Mesh-Free Solid-Mechanics Approach for Simulating the Friction Stir-Welding Process

In this chapter, we describe the development of a new approach to simulate the friction stir-welding (FSW) process using a solid-mechanics formulation of a mesh-free Lagrangian method called smoothed particle hydrodynamics (SPH). Although this type of a numerical model typically requires long calculation times, we have developed a very efficient parallelization strategy on the graphics processing unit (GPU). This simulation approach allows the determination of temperature evolution, elastic and plastic deformation, defect formation, residual stresses, and material flow all within the same model. More importantly, the large plastic deformation and material mixing common to FSW are well captured by the mesh-free method. The parallel strategy on the GPU provides a means to obtain meaningful simulation results within hours as opposed to many days or even weeks with conventional FSW simulation codes

Particle-based adaptive coupling of 3D and 2D fluid flow models

peer reviewedThis paper proposes the notion of model adaptivity for fluid flow modelling, where the under- lying model (the governing equations) is adaptively changed in space and time. Specifically, this work introduces a hybrid and adaptive coupling of a 3D bulk fluid flow model with a 2D thin film flow model. As a result, this work extends the applicability of existing thin film flow models to complex scenarios where, for example, bulk flow develops into thin films after striking a surface. At each location in space and time, the proposed framework automatically decides whether a 3D model or a 2D model must be applied. Using a meshless approach for both 3D and 2D models, at each particle, the decision to apply a 2D or 3D model is based on the user-prescribed resolution and a local principal component analysis. When a particle needs to be changed from a 3D model to 2D, or vice versa, the discretization is changed, and all relevant data mapping is done on-the-fly. Appropriate two-way coupling conditions and mass conservation considerations between the 3D and 2D models are also developed. Numerical results show that this model adaptive framework shows higher flexibility and compares well against finely resolved 3D simulations. In an actual application scenario, a 3 factor speed up is obtained, while maintaining the accuracy of the solution.U-AGR-6054 - IAS-AUDACITY ADONIS - BORDAS Stéphan

Fast neighbor lists for adaptive-resolution particle simulations

Particle methods provide a simple yet powerful framework for simulating both discrete and continuous systems either deterministically or stochastically. The inherent adaptivity of particle methods is particularly appealing when simulating multiscale models or systems that develop a wide spectrum of length scales. Evaluating particle–particle interactions using neighbor-finding algorithms such as cell lists or Verlet lists, however, quickly becomes inefficient in adaptive-resolution simulations where the interaction cutoff radius is a function of space. We present a novel adaptive-resolution cell list algorithm and the associated data structures that provide efficient access to the interaction partners of a particle, independent of the (potentially continuous) spectrum of cutoff radii present in a simulation. We characterize the computational cost of the proposed algorithm for a wide range of resolution spans and particle numbers, showing that the present algorithm outperforms conventional uniform-resolution cell lists in most adaptive-resolution settings

Direct Numerical Simulations of Reactive Transport Processes at Single Bubbles

Reactive mass transfer processes are found in many chemical engineering applications. Though these phenomena have been object of investigation for long time already, a complete understanding of the physico-chemical mechanisms involved has not been achieved yet. More detailed insights about these processes, in particular the local interplay between the two-phase hydrodynamics, mass transfer and chemical reactions, have been obtained in recent years by means of Direct Numerical Simulations. However, this type of simulation is nowadays still computationally demanding. Being the concentration boundary layers at bubble interfaces remarkably thinner than the velocity boundary layer, an accurate solution of the species concentration transport equations requires a numerical resolution significantly higher than that needed for the two-phase hydrodynamics. Two different numerical techniques have been developed in this work with the aim of alleviating the multiscale issue. In both the cases, the hydrodynamic problem is tackled by means of an Arbitrary Lagrangian-Eulerian Interface-Tracking method. Instead, they differ regarding the treatment of the mass transfer. The former technique relies on the so-called Radial Basis Functions by which a finite-difference method on unstructered sets of points is formulated. The latter employs a finite-volume discretisation on a mesh obtained from a specialised refinement of the grid used for the two-phase hydrodynamics. In the present research, a systematic analysis of the reactive mass transfer from single rising bubbles with significant interface deformations, i.e. technically relevant diameters, has been carried out by means of 3D Direct Numerical Simulations. Two distinct reaction prototypes representative of many applications have been considered. Simulations from slow to fast reaction intensities allowed to assess the influence of different chemical time scales on these processes. Additionally, the impact of low to moderate dissolving species diffusivities has been investigated. The last part of the study has been dedicated to the comparison of the simulation results with the predictions of the film theory

Individual-based modeling and predictive simulation of fungal infection dynamics

The human-pathogenic fungus Aspergillus fumigatus causes life-threatening infections in immunocompromised patients and poses increasing challenges for the modern medicine. A. fumigatus is ubiquitously present and disseminates via small conidia over the air of the athmosphere. Each human inhales several hundreds to thousands of conidia every day. The small size of conidia allows them to pass into the alveoli of the lung, where primary infections with A. fumigatus are typically observed. In alveoli, the interaction between fungi and the innate immune system of the host takes place. This interaction is the core topic of this thesis and covered by mathematical modeling and computer simulations. Since in vivo laboratory studies of A. fumigatus infections under physiological conditions is hard to realize a modular software framework was developed and implemented, which allows for spatio-temporal agent-based modeling and simulation. A to-scale A. fumigatus infection model in a typical human alveolus was developed in order to simulate and analyze the infection scenario under physiological conditions. The process of conidial discovery by alveolar macrophages was modeled and simulated with different migration modes and different parameter configurations. It could be shown that chemotactic migration was required to find the pathogen before the onset of germination. A second model took advantage of evolutionary game theory on graphs. Here, the course of infection was modeled as a consecutive sequence of evolutionary games related to the complement system, alveolar macrophages and polymorphonuclear neutrophilic granulocytes. The results revealed a central immunoregulatory role of alveolar macrophages. In the case of high infectious doses it was found that the host required fully active phagocytes, but in particular a qualitative response of quantitatively sufficient polymorphonuclear neutrophilic granulocytes.Der human-pathogene Schimmelpilz Aspergillus fumigatus verursacht tödliche Infektionen und Erkrankungen vorrangig bei immunsupprimierten Patienten und stellt die moderne Medizin vor zunehmende Herausforderungen. A. fumigatus ist ubiquitär präsent und verbreitet sich über sehr kleine Konidien durch Luftströmungen in der Athmosphäre. Mehrere Hundert bis Tausende dieser Konidien werden täglich durch jeden Menschen eingeatmet. Die geringe Größe der infektiösen Konidien erlauben es dem Pilz bis in die Alveolen der Lunge des Wirtes vorzudringen,in denen eine Primärinfektionen mit A. fumigatus am häufigsten stattfindet. Die Alveolen sind der zentrale Schauplatz der Interaktion zwischen dem Pilz und dem angeborenen Immunsystem, welche Gegenstand dieser Arbeit ist. Diese Interaktion wird mit Hilfe von mathematischen Modellen und Computersimulationen nachgestellt und untersucht, da eine A. fumigatus Infektion im Nasslabor in vivo unter physiologischen Bedingungen nur sehr schwer realisiert werden kann. Als Grundlage für dieses Vorhaben wurde ein modulares Software-Paket entwickelt, welches agentenbasierte Modellierung und entsprechende Simulationen in Raum und Zeit ermöglicht. Ein maßstabsgetreues mathematisches Infektionsmodell in einer typischen menschlichen Alveole wurde entwickelt und die Suchstrategien von Alveolarmakrophagen unter der Berücksichtigung verschiedener Parameter wie Migrationsgeschwindigkeit, dem Vorhandensein von Chemokinen, dessen Diffusion und Chemotaxis untersucht. Es zeigte sich, dass Chemotaxis, notwendig ist, um die Konidie rechtzeitig finden zu können. In einem weiteren Modell, welches auf das Konzept evolutionärer Spieltheorie auf Graphen zurückgegriff, wurde der Infektionsverlauf als aufeinanderfolgende Serie evolutionärer Spiele mit dem Komplementsystem, Alveolarmakrophagen und Neutrophilen nachgestellt. Aus den Simulationsergebnissen konnte eine zentrale immunregulatorische Rolle von Alveolarmakrophagen entnommen werden

Modelling Fluid-Structure Interaction Problems with Coupled DEM-LBM

When studying the properties and behaviour of particulate systems, a multi-scale approach is an efficient way to describe interactions at different levels or dimensions; this means that phenomena taking place at one scale will inherently impact the properties and behaviour of the same system in a different scale. Numerical representation and simulation of fluid-structure interaction (FSI) systems is of particular interest in the present work. Conventional computational fluid dynamics (CFD) methods involve a top-down approach based on the discretisation of the macroscopic continuum Navier-Stokes equations; cells are typically much larger than individual particles and the hydrodynamic force is calculated for all the solid particles contained in singular a cell. Unlike traditional CFD solvers, the lattice Boltzmann method (LBM) is an alternative approach to simulate fluid flows in complex geometries in a mesoscale level. In LBM the fluid is deemed as a collection of cells, each one containing a particle that represents a density distribution function with a velocity field. The distinct element method (DEM) is in charge of handling the motion of particles and calculating the interparticle contact forces. The two methodologies LBM and DEM were selected among the available approaches to be combined in a single computational code to represent FSI systems. The key task to undertake was the implementation of a coupling code to exchange information between the two solvers LBM and DEM in a correct and efficient manner. The calculation of hydrodynamic forces exerted by the fluid on the particles is the major challenge in coupled FSI simulations. This was addressed by including the momentum exchange method, based on the link bounce-back technique, together with the immersed boundary method to deal with moving particles immersed in a fluid. In addition, in order to better understand the dynamics of FSI systems in a mesoscale level, the present work paid special attention to the accurate representation of individual particles displaying irregular geometries instead of the preferred spherical particles. This goal was achieved by means of X-ray microtomography digitisation of particles, allowing the capture of complex micro-structural features such as particle shape, texture and porosity. In this way a more realistic particle representation was achieved, extending its use to the implementation into computational simulations. The DEM-LBM coupling implementation carried out was tested quantitatively and qualitatively based on theoretical models and experimental data. Different cases were selected to simulate the dynamic process of packing particles, particle fluidisation and segregation, particles sedimentation, fluid permeability calculations and fluid flow through porous media. Results and predictions from simulations for a number of configurations showed good agreement when compared with analytical and experimental data. For instance, the relative error in terminal velocity of a non-spherical particle settling down in a column of water was 4.2%, showing an asymptotic convergence to the reference value. In different tests like the drag on two interacting particles and the flow past a circular cylinder at Re = 100, the corresponding deviations from the references published were 20% and 8.23% respectively. The extended Re range for the latter case followed closely the reference curve for the case of a rough cylinder, indicating the effects of the inherent staircase-like boundary in digital particles. Three dimensional simulations of applications such as fluidisation and sedimentation showed the expected behaviour, not only for spherical particles but also considering complex geometries such as sand grains. A symmetric array of spheres and randomly mixed particles were simulated successfully. Segregation was observed in a case configured with particles with different size and density. Hindered settling was also observed causing the slow settling of the small particles. Incipient fluidisation of spherical and irregular geometries was observed in relatively large computational domains. However, the minimum fluidisation velocity configured at the inlet was commonly 10 times larger than the calculated from the Ergun equation

Modelling Fluid-Structure Interaction Problems with Coupled DEM-LBM

When studying the properties and behaviour of particulate systems, a multi-scale approach is an efficient way to describe interactions at different levels or dimensions; this means that phenomena taking place at one scale will inherently impact the properties and behaviour of the same system in a different scale. Numerical representation and simulation of fluid-structure interaction (FSI) systems is of particular interest in the present work. Conventional computational fluid dynamics (CFD) methods involve a top-down approach based on the discretisation of the macroscopic continuum Navier-Stokes equations; cells are typically much larger than individual particles and the hydrodynamic force is calculated for all the solid particles contained in singular a cell. Unlike traditional CFD solvers, the lattice Boltzmann method (LBM) is an alternative approach to simulate fluid flows in complex geometries in a mesoscale level. In LBM the fluid is deemed as a collection of cells, each one containing a particle that represents a density distribution function with a velocity field. The distinct element method (DEM) is in charge of handling the motion of particles and calculating the interparticle contact forces. The two methodologies LBM and DEM were selected among the available approaches to be combined in a single computational code to represent FSI systems. The key task to undertake was the implementation of a coupling code to exchange information between the two solvers LBM and DEM in a correct and efficient manner. The calculation of hydrodynamic forces exerted by the fluid on the particles is the major challenge in coupled FSI simulations. This was addressed by including the momentum exchange method, based on the link bounce-back technique, together with the immersed boundary method to deal with moving particles immersed in a fluid. In addition, in order to better understand the dynamics of FSI systems in a mesoscale level, the present work paid special attention to the accurate representation of individual particles displaying irregular geometries instead of the preferred spherical particles. This goal was achieved by means of X-ray microtomography digitisation of particles, allowing the capture of complex micro-structural features such as particle shape, texture and porosity. In this way a more realistic particle representation was achieved, extending its use to the implementation into computational simulations. The DEM-LBM coupling implementation carried out was tested quantitatively and qualitatively based on theoretical models and experimental data. Different cases were selected to simulate the dynamic process of packing particles, particle fluidisation and segregation, particles sedimentation, fluid permeability calculations and fluid flow through porous media. Results and predictions from simulations for a number of configurations showed good agreement when compared with analytical and experimental data. For instance, the relative error in terminal velocity of a non-spherical particle settling down in a column of water was 4.2%, showing an asymptotic convergence to the reference value. In different tests like the drag on two interacting particles and the flow past a circular cylinder at Re = 100, the corresponding deviations from the references published were 20% and 8.23% respectively. The extended Re range for the latter case followed closely the reference curve for the case of a rough cylinder, indicating the effects of the inherent staircase-like boundary in digital particles. Three dimensional simulations of applications such as fluidisation and sedimentation showed the expected behaviour, not only for spherical particles but also considering complex geometries such as sand grains. A symmetric array of spheres and randomly mixed particles were simulated successfully. Segregation was observed in a case configured with particles with different size and density. Hindered settling was also observed causing the slow settling of the small particles. Incipient fluidisation of spherical and irregular geometries was observed in relatively large computational domains. However, the minimum fluidisation velocity configured at the inlet was commonly 10 times larger than the calculated from the Ergun equation