Modelling binary alloy solidification with adaptive mesh refinement

The solidification of a binary alloy results in the formation of a porous mushy layer, within which spontaneous localisation of fluid flow can lead to the emergence of features over a range of spatial scales. We describe a finite volume method for simulating binary alloy solidification in two dimensions with local mesh refinement in space and time. The coupled heat, solute, and mass transport is described using an enthalpy method with flow described by a Darcy-Brinkman equation for flow across porous and liquid regions. The resulting equations are solved on a hierarchy of block-structured adaptive grids. A projection method is used to compute the fluid velocity, whilst the viscous and nonlinear diffusive terms are calculated using a semi-implicit scheme. A series of synchronization steps ensure that the scheme is flux-conservative and correct for errors that arise at the boundaries between different levels of refinement. We also develop a corresponding method using Darcy's law for flow in a porous medium/narrow Hele-Shaw cell. We demonstrate the accuracy and efficiency of our method using established benchmarks for solidification without flow and convection in a fixed porous medium, along with convergence tests for the fully coupled code. Finally, we demonstrate the ability of our method to simulate transient mushy layer growth with narrow liquid channels which evolve over time

Performance and scaling of locally-structured grid methods for partial differential equations

Abstract. In this paper, we discuss some of the issues in obtaining high performance for block-structured adaptive mesh refinement software for partial differential equations. We show examples in which AMR scales to thousands of processors. We also discuss a number of metrics for performance and scalability that can provide a basis for understanding the advantages and disadvantages of this approach. Introduction A broad range of applied PDE problems exhibit multiscale behavior, i.e. variation in the solution over scales that are much smaller than the global large scales in the problem. Examples include flame fronts arising in the burning of hydrocarbon fuels and nuclear burning in supernovae; in geophysical problems, ocean currents, effects of localized features in orography or bathymetry, and tropical cyclones; and in plasma physics, a variety of small scale effects due to nonlinear instabilities and localized kinetic effects. In all of these problems, the fundamental mathematical description is given in terms of various combinations of PDE of classical type (elliptic, parabolic, hyperbolic). To effectively compute solutions to such problems, we need simulation capabilities with the following features

Ice flow modelling of ice shelves and ice caps

Ice shelves and ice caps constitute a great proportion of the glacial ice mass that covers 10% of the global land surface and is vulnerable to climate change. Large scale ice flow models are widely used to investigate the mechanisms behind the observed physical processes and predict their future stability and variability under climate change. This thesis aims at providing general remarks on the application of ice flow models in studying glaciological problems through investigating the evolution of an Antarctic ice shelf under climate change and the mechanisms of fast ice flowing events (surges) in an Arctic ice cap. In addition discussions of the equivalence of two significantly different expressions for the rate factor in Glen’s flow are also provided. Off-line coupling between the Lambert Glacier-Amery Ice Shelf (LG-AIS) drainage system, East Antarctica, and the climate system by employing a hierarchy of models from general circulation models, through high resolution regional atmospheric and oceanic models, to a vertically integrated ice flow model has been carried out. The adaptive mesh refinement technique is specifically implemented for resolving the problem concerning grounding line migration. Sensitivity tests investigating the importance of various parameters and boundary conditions are carried out in ice flow models with different approximations for Austfonna Ice-cap, Svalbard to investigate the surge event in one of its basins, Basin 3. Inverse modelling of basal friction coefficient is specifically implemented. A continuum to discrete multi-model approach is implemented for simulations of Basin 3. LG-AIS drainage system will be rather stable in the face of future warming over 21st and 22nd centuries. Although the ice shelf thins in most of the simulations there is little grounding line retreat. The change of ice thickness and velocity in the ice shelf is mainly influenced by the basal melt distribution. And the Lambert, Fisher and Mellor glaciers are most sensitive to thinning of the ice shelf south of Clemence Massif. The sea level rise contribution of LG-AIS is modest as the increased accumulation computed by the atmosphere models outweighs ice stream acceleration. Using a temporally fixed basal friction field obtained through inverse modelling is insufficient to simulate the future changes of the fast flowing surging glacier in Basin 3. And the evolution of basal friction patterns, and in turn basal processes are among the most important factors during the surge in Basin 3. A system of processes and feedback involving till deformation and basal hydrology is more likely to explain both the seasonal accelerations and the ongoing inter-annual speed-up more than a hard-bed mechanism. The continuum to discrete multi-model approach provides the possible locations of the crevasses that can potentially cut through the full length of the ice and deliver surface melt water down to the bed. The calculated basal water flow paths according to hydraulic potential indicate that the summer speed up events and the initiation of the acceleration in the southern part of the basin can be explained by either a direct enhancement to the ice flow through basal lubrication or a lagged-in-time mechanism through the outflow of accumulated water in the over-deepening area. Keywords: ice flow modelling, climate change, sea level rise, future projection, basal sliding, basal hydrology, surface melt, surging glacier, Lambert Glacier-Amery Ice Shelf, Austfonna Ice-cap, Antarctic, SvalbardKymmentä prosenttia maapallon maapinta-alasta peittää tiivistyneen jään kerroksia, jotka eivät sula pois kesän aikana ja jotka virtaavat oman painonsa alla. Jäähyllyt ja lakijäätiköt muodostavat suuren osan näistä jäätiköiksi kutsutuista jäämassiiveista. Näiden tutkimus hyödyntää tietokoneohjelmia, jotka matemaattisten yhtälöiden mukaan kuvaavat jään fysikaalisia prosesseja. Tällaisten numeeristen mallien avulla voimme ymmärtää, kuinka jäätiköt käyttäytyvät sekä nykyisessä ympäristössään että tulevaisuudessa ilmaston muuttuessa. Tässä väitöskirjassa käytän numeerisia malleja tutkiakseni, kuinka Etelämantereen jääpeite muuttuu seuraavien 100–200 vuoden aikana ilmastonmuutoksen vaikutuksesta sekä sitä, mikä laukaisee arktisen lakijäätikön muutoksen pitkästä rauhallisen virtauksen kaudesta verrattain lyhytaikaiseen, nopeaan virtaustapahtumaan. Lisäksi tarkastelen kysymystä miksi kahta laajalti käytössä olevaa eriävää muotoilua voidaan käyttää Glenin virtauslain kertoimesta (laki kuvaa jännityksen ja venymän suhdetta). Näiden tutkimusten avulla aikomuksenani on parantaa numeeristen mallien käyttöä jäätikkötutkimuksessa. Lambertin jäätikkö – Ameryn jäähylly (Lambert Glacier – Amery Ice Shelf, LG-AIS) valumajärjestelmä on yksi Itä-Antarktikan suurimmista. Ameryn jäähylly käy tällä hetkellä läpi vakaata ja luonnollista virtauskautta poikien jäävuoria mereen. Ilmastonmuutoksen myötä tämän valumajärjestelmän kohtalo seuraavan 100–200 vuoden aikana on kuitenkin avoin. Numeerista jään virtauksen mallia käytetään tässä työssä valumajärjestelmän muutosten tutkimiseen. Malli ottaa huomioon lumen kertymisen ja jäätikön pohjan sulamisen ilmastomalleista saatujen pakotteiden puitteissa. Tulokset osoittavat, että vaikka Ameryn jäähylly saattaa sulaa merkittävästi, LG-AIS virtausjärjestelmä pysyy vakaana myös 2100- ja 2200-luvuilla. Myös jäämassan nettotuotto valtamereen tulee olemaan melko vähäistä, joten sen vaikutus merenpinnan korkeuteen on pieni. Austfonnan Basin 3 lakijäätikön Huippuvuorilla uskotaan olevan ajoittaisen nopean virtauksen tyypin jäätikkö. Siinä vallitsee pitkäaikainen, hidas virtaus, jonka lyhyet, hyvin nopean virtauksen kaudet väliin katkaisevat. Kahta eri jäävirtausmallia käyttäen olen yrittänyt selittää niitä mekanismeja, jotka vaikuttivat vuonna 2011 alkaneeseen liikkeen nopeutumiseen. Tulokset osoittavat, että jäätikön pohjan liike vaikuttaa voimakkaasti kiihtyvään virtaukseen ja hyvin todennäköisesti myös jäätikön alla sijaitsevan sedimentin muovautuminen ja jäätikön alaiseen hydrologiaan. Sitten vuoden 2008 tämän jäätikön virtaus on kiihtynyt portaittaisesti jokaisen kesän sulamiskauden päätyttyä. Diskreetti partikkelimalli, joka jakaa jäätikön pieniin partikkeleihin ja kykenee tuottamaan syviä halkeamia jäätikköön, käytetään portaittaisen kiihtymisen selittämiseen. Tämä malli tuottaa sellaisten halkeamien sijainnit, jotka voisivat toimia virtauskanavina sulamisvedelle ja viedä tätä jäätikön pohjan hydrologiseen järjestelmään. Mahdollisiksi selityksiksi portaittaiselle kiihtymiselle voidaan antaa joko sulamisveden liukastava vaikutus jäätikön pohjassa tai sitten jäätikön pohjaan kertyneen veden kelluttava vaikutus

A local mesh refinement approach for large-eddy simulations of turbulent flows

In this paper, a local mesh refinement (LMR) scheme on Cartesian grids for large-eddy simulations is presented. The approach improves the calculation of ghost cell pressures and velocities and combines LMR with high-order interpolation schemes at the LMR interface and throughout the rest of the computational domain to ensure smooth and accurate transition of variables between grids of different resolution. The approach is validated for turbulent channel flow and flow over a matrix of wall-mounted cubes for which reliable numerical and experimental data are available. Comparisons of predicted first-order and second-order turbulence statistics with the validation data demonstrated a convincing agreement. Importantly, it is shown that mean streamwise velocities and fluctuating turbulence quantities transition smoothly across coarse-to-fine and fine-to-coarse interfaces

A Cell-Centered Adaptive Projection Method for the IncompressibleNavier-Stokes Equations in Three Dimensions

We present a method for computing incompressible viscousflows in three dimensions using block-structured local refinement in bothspace and time. This method uses a projection formulation based on acell-centered approximate projection, combined with the systematic use ofmultilevel elliptic solvers to compute increments in the solutiongenerated at boundaries between refinement levels due to refinement intime. We use an L_0-stable second-order semi-implicit scheme to evaluatethe viscous terms. Results are presentedto demonstrate the accuracy andeffectiveness of this approach

Application of Lattice Boltzmann and Navier-Stokes Methods to NASA's Wall Mounted Hump

Lattice Boltzmann (LB) based Large Eddy Simulation (LES), Reynolds-averaged Navier-Stokes (RANS) as well as hybrid RANS/LES methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are applied to NASA's wall-mounted hump. Computational results are compared with experiments performed by Greenblatt et al. A detailed comparison between the accuracy and resolution requirements of the two approaches for turbulence resolving simulations, as well as the suitability of different grid paradigms (body-fitted curvilinear and block structured Cartesian) are presented. This test case is part of NASA's Revolutionary Computational Aerosciences (RCA) sub-project which addresses the technical challenge of predicting flow separation and reattachment accurately. Improvements in predictive accuracy by as much as 90% are demonstrated using LB as well as hybrid RANS/LES approaches compared to state-of-the-art steady state RANS simulations

A cell-centred finite volume method for the Poisson problem on non-graded quadtrees with second order accurate gradients

The final publication is available at Elsevier via https://doi.org/10.1016/j.jcp.2016.11.035 © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper introduces a two-dimensional cell-centred finite volume discretization of the Poisson problem on adaptive Cartesian quadtree grids which exhibits second order accuracy in both "the solution and its gradients, and requires no grading condition between adjacent cells. At T-junction configurations, which occur wherever resolution differs between neighboring cells, use of the standard centred difference gradient stencil requires that ghost values be constructed by interpolation. To properly recover second order accuracy in the resulting numerical gradients, prior work addressing block-structured grids and graded trees has shown that quadratic, rather than linear, interpolation is required; the gradients otherwise exhibit only first order convergence, which limits potential applications such as fluid flow. However, previous schemes fail or lose accuracy in the presence of the more complex T-junction geometries arising in the case of general non-graded quadtrees, which place no restrictions on the resolution of neighboring cells. We therefore propose novel quadratic interpolant constructions for this case that enable second order convergence by relying on stencils oriented diagonally and applied recursively as needed. The method handles complex tree topologies and large resolution jumps between neighboring cells, even along the domain boundary, and both Dirichlet and Neumann boundary conditions are supported. Numerical experiments confirm the overall second order accuracy of the method in the L-infinity norm. (C) 2016 Elsevier Inc. All rights reserved.This work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada (Grant RGPIN-04360-2014)

The Stratified Ocean Model with Adaptive Refinement (SOMAR)

A computational framework for the evolution of non-hydrostatic, baroclinic flows encountered in regional and coastal ocean simulations is presented, which combines the flexibility of Adaptive Mesh Refinement (AMR) with a suite of numerical tools specifically developed to deal with the high degree of anisotropy of oceanic flows and their attendant numerical challenges. This framework introduces a semi-implicit update of the terms that give rise to buoyancy oscillations, which permits a stable integration of the Navier-Stokes equations when a background density stratification is present. The lepticity of each grid in the AMR hierarchy, which serves as a useful metric for anisotropy, is used to select one of several different efficient Poisson-solving techniques. In this way, we compute the pressure over the entire set of AMR grids without resorting to the hydrostatic approximation, which can degrade the structure of internal waves whose dynamics may have large-scale significance. We apply the modeling framework to three test cases, for which numerical or analytical solutions are known that can be used to benchmark the results. In all the cases considered, the model achieves an excellent degree of congruence with the benchmark, while at the same time achieving a substantial reduction of the computational resources needed.Doctor of Philosoph

Simulation numérique 3D de la coextrusion des fluides polymériques et de l'effet d'enrobage

L'ensemble des travaux présentés dans cette thèse porte sur la simulation numérique des procédés de coextrusion par un modèle d'écoulement stratifié basé sur la méthode du champ de phase. L'avantage technologique offert par la coextrusion réside dans la possibilité de combiner des matériaux ayant des propriétés physiques très spécifiques dans un produit unique. Toutefois, les différences rhéologiques entre les divers matériaux sont elles-mêmes responsables d'un phénomène de distorsion de l'interface séparant deux couches adjacents. Les données expérimentales en coextrusion bicouches montrent que, en raison des différences de viscosité et d'élasticité entre le deux composants, le fluide le moins visqueux encapsule le fluide plus visqueux et le passage d'une configuration stratifiée à une encapsulée comporte une perte de qualité du produit final. Ce phénomène, dit d'enrobage représente donc un sujet de très grande actualité dans la recherche industrielle et la compréhension des mécanismes le générant sera utile pour l'amélioration des procédés de mise en forme des polymères. La nature intrinsèquement tridimensionnelle de l'enrobage a requis le développement d'un code pour la simulation tridimensionnelle basée sur la méthode des volumes finis pour la discrétisation des équations de Navier-Stokes pour les écoulement incompressibles et isothermes couplées avec une loi constitutive différentielle non linéaire (modèles de Giesekus ou PTT). La présence de deux fluides est prise en compte par une équation scalaire supplémentaire décrivant l'évolution de l'interface sur un maillage fixe. Cette équation offre une interprétation physique précise car elle est dérivée de la thermodynamique de séparation de phase d'un fluide binaire. Le modèle proposé est validé par confrontation avec les résultats expérimentaux et numériques disponibles dans la littérature. Une étude numérique de la coextrusion en filière rectangulaire est effectuée afin de mettre en évidence les facteurs influençant l'enrobage et la nature de son origineThe objective of the present work is the analysis of coextrusion processes by numerical simulation based on phase-field modeling of stratified confined flows. The study of such flows is motivated by the presence of complex phenomena appearing in a vast range of industrial operational coextrusion conditions due to the differences in the components properties and their viscoelastic behavior. The basic idea in coextrusion is to combine several layers of different polymers in a common die, to form a unique product with enhanced properties. However, the existence of fluid stratification in the die is responsible of a severe distortion of the interface between the fluid components, causing a loss of efficiency for the whole process. Experimental data show that, even if a stratified initial configuration is imposed at the die entry, one fluid eventually encapsulates the other in most of the flow condition analyzed. The intrinsically three-dimensional nature of this phenomenon has required the development of a three-dimensional flow solver based on the finite volume discretization of the Navier-Stokes equations for incompressible and isothermal flow, together with differential nonlinear constitutive equations (Giesekus, PTT models). The presence of two fluid phases is taken into account by a phase field model that implies the solution of an additional scalar equation to describe the evolution of the interface on a fixed Eulerian grid. This model, unlike others of the same family, has a thermodynamic derivation and can be physically interpreted. The proposed method is tested against experimental data and solutions already available in literature and a study of coextrusion in rectangular dies is performed to identify the dependence of encapsulation on the flow parametersST ETIENNE-Bib. électronique (422189901) / SudocSudocFranceF