Development and implementation of the generalized continuum model for transport in porous media

Fluid flow phenomena in porous media have always attracted a lot of attention of scientists and engineers. Attempts to quantify the average transport in homogeneous media with a simple partial differential equation with constant coefficients disclosed significant inconsistencies comparing to experiments. Modern numerical simulations of porous networks confirmed that those inconsistencies are systematic and not caused by the observation error. The error appeared as a result of the, so called, anomalous or non-Fickian transport, which was in contrast to the normal regime, described by the Fick’s laws. The problem has been addressed through the introduction of more complex and substantial models to describe the phenomena. Although, these new approaches have resolved the problem of quantification, they have raised another question for researchers and engineers, how to choose the most suitable approach and, if it is possible, to parametrize the modeling choice at all. The models general lack of physical consistency makes it difficult to distinguish the model parameters. This leaves judging of suitability to the general accuracy of quantification only, which is often not the most important criterion. In other words, the model parameters are typically estimated by fitting the model to the experimental data, and are often not related to the real properties of the medium. Therefore, a model is often chosen a priory, based only on the experience of the researcher. In this work, we address the problem of model selection by introducing a new model: the Generalized Continuum Transport model. This model transforms into existing models at certain limits and, therefore, constrains the modeling choice through the introduction of the parameter space. It is shown that the Generalized Continuum Transport model limits to the advection-dispersion equation, the Continuous Time Random Walk, the Multi-Rate Mass Transfer and the Multiple-Porosity models, when corresponding configurations of the parameter space are applied. The model’s accuracy is studied by quantifying the breakthrough curves obtained from a fine scale porous network modeldemonstrating significant appearance of anomalous transport phenomena. The results show that the error of quantification is smaller than the error of the existing models. It is discussed that the parameters of the Generalized Continuum Transport model are related to the physical properties of porous media. Finally, it is presented that the parameter space of GCT can be constrained and related to the transport phenomena studied. Hence, the limits of GCT are controlled by the transport complexity and the desired accuracy and the modeling choice can be parametrized

Vorticity-divergence semi-Lagrangian global atmospheric model SL-AV20: dynamical core

SL-AV (semi-Lagrangian, based on the absolute vorticity equation) is a global hydrostatic atmospheric model. Its latest version, SL-AV20, provides global operational medium-range weather forecast with 20 km resolution over Russia. The lower-resolution configurations of SL-AV20 are being tested for seasonal prediction and climate modeling. The article presents the model dynamical core. Its main features are a vorticity-divergence formulation at the unstaggered grid, high-order finite-difference approximations, semi-Lagrangian semi-implicit discretization and the reduced latitude–longitude grid with variable resolution in latitude. The accuracy of SL-AV20 numerical solutions using a reduced lat–lon grid and the variable resolution in latitude is tested with two idealized test cases. Accuracy and stability of SL-AV20 in the presence of the orography forcing are tested using the mountain-induced Rossby wave test case. The results of all three tests are in good agreement with other published model solutions. It is shown that the use of the reduced grid does not significantly affect the accuracy up to the 25 % reduction in the number of grid points with respect to the regular grid. Variable resolution in latitude allows us to improve the accuracy of a solution in the region of interest

Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time

100 Years of Earth System Model Development

This is the final version. Available from American Meteorological Society via the DOI in this recordToday’s global Earth System Models began as simple regional models of tropospheric weather systems. Over the past century, the physical realism of the models has steadily increased, while the scope of the models has broadened to include the global troposphere and stratosphere, the ocean, the vegetated land surface, and terrestrial ice sheets. This chapter gives an approximately chronological account of the many and profound conceptual and technological advances that made today’s models possible. For brevity, we omit any discussion of the roles of chemistry and biogeochemistry, and terrestrial ice sheets

A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin

Numerical weather prediction (NWP) is in a period of transition. As resolutions increase, global models are moving towards fully nonhydrostatic dynamical cores, with the local and global models using the same governing equations; therefore we have reached a point where it will be necessary to use a single model for both applications. The new dynamical cores at the heart of these unified models are designed to scale efficiently on clusters with hundreds of thousands or even millions of CPU cores and GPUs. Operational and research NWP codes currently use a wide range of numerical methods: finite differences, spectral transform, finite volumes and, increasingly, finite/spectral elements and discontinuous Galerkin, which constitute element-based Galerkin (EBG) methods.Due to their important role in this transition, will EBGs be the dominant power behind NWP in the next 10 years, or will they just be one of many methods to choose from? One decade after the review of numerical methods for atmospheric modeling by Steppeler et al. (Meteorol Atmos Phys 82:287–301, 2003), this review discusses EBG methods as a viable numerical approach for the next-generation NWP models. One well-known weakness of EBG methods is the generation of unphysical oscillations in advection-dominated flows; special attention is hence devoted to dissipation-based stabilization methods. Since EBGs are geometrically flexible and allow both conforming and non-conforming meshes, as well as grid adaptivity, this review is concluded with a short overview of how mesh generation and dynamic mesh refinement are becoming as important for atmospheric modeling as they have been for engineering applications for many years.The authors would like to thank Prof. Eugenio Oñate (U. Politècnica de Catalunya) for his invitation to submit this review article. They are also thankful to Prof. Dale Durran (U. Washington), Dr. Tommaso Benacchio (Met Office), and Dr. Matias Avila (BSC-CNS) for their comments and corrections, as well as insightful discussion with Sam Watson, Consulting Software Engineer (Exa Corp.) Most of the contribution to this article by the first author stems from his Ph.D. thesis carried out at the Barcelona Supercomputing Center (BSCCNS) and Universitat Politècnica de Catalunya, Spain, supported by a BSC-CNS student grant, by Iberdrola Energías Renovables, and by grant N62909-09-1-4083 of the Office of Naval Research Global. At NPS, SM, AM, MK, and FXG were supported by the Office of Naval Research through program element PE-0602435N, the Air Force Office of Scientific Research through the Computational Mathematics program, and the National Science Foundation (Division of Mathematical Sciences) through program element 121670. The scalability studies of the atmospheric model NUMA that are presented in this paper used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357. SM, MK, and AM are grateful to the National Research Council of the National Academies.Peer ReviewedPostprint (author's final draft

Un modèle de transport et de chimie atmosphérique à grande échelle adapté aux calculateurs massivement parallèles

We present in this thesis the development of a large-scale bidimensional atmospheric transport scheme designed for parallel architectures with scalability in mind. The current version, named Pangolin, contains a bi-dimensional advection and a simple linear chemistry scheme for stratospheric ozone and will serve as a basis for a future CTM. For mass-preservation, a van Leer finite-volume scheme was chosen for advection and extended to 2D with operator splitting. To ensure mass preservation, winds are corrected in a preprocessing step. We aim at addressing the "pole issue" of the traditional regular latitude-longitude by presenting a new quasi-area-preserving grid mapping the sphere uniformly. The parallelization of the model is based on the advection operator and a custom domain-decomposition algorithm is presented here to attain load-balancing in a message-passing context. To run efficiently on current and future parallel architectures, algebraic features of the grid are exploited in the advection scheme and parallelization algorithm to favor the cheaper costs of flops versus data movement. The model is validated on algebraic test cases and compared to other state-of-the-art schemes using a recent benchmark. Pangolin is also compared to the CTM of Météo-France, MOCAGE, using a linear ozone scheme and isentropic coordinates.Cette thèse présente un modèle bi-dimensionnel pour le transport atmosphérique à grande échelle, nommé Pangolin, conçu pour passer à l'échelle sur les achitectures parallèles. La version actuelle comporte une advection 2D ainsi qu'un schéma linéaire de chimie et servira de base pour un modèle de chimie-transport (MCT). Pour obtenir la conservation de la masse, un schéma en volume-finis de type van Leer a été retenu pour l'advection et étendu au cas 2D en utilisant des opérateurs alternés. La conservation de la masse est assurée en corrigeant les vents en amont. Nous proposons une solution au problème "des pôles" de la grille régulière latitude-longitude grâce à une nouvelle grille préservant approximativement les aires des cellules et couvrant la sphère uniformément. La parallélisation du modèle se base sur l'advection et utilise un algorithme de décomposition de domaines spécialement adapté à la grille. Cela permet d'obtenir l'équilibrage de la charge de calcul avec MPI, une librairie d'échanges de messages. Pour que les performances soient à la hauteur sur les architectures parallèles actuelles et futures, les propriétés analytiques de la grille sont exploitées pour le schéma d'advection et la parallélisation en privilégiant le moindre coût des flops par rapport aux mouvement de données. Le modèle est validé sur des cas tests analytiques et comparé à des schémas de transport à l'aide d'un comparatif récemment publié. Pangolin est aussi comparé au MCT de Météo-France via un schéma linéaire d'ozone et l'utilisation de coordonnées isentropes

2. PHYSICAL PARAMETERIZATIONS IN MODELS 1

OF WGNE/GMPP ACTIVITIES