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258 records · Page 15

Mixing Cell Model: A One-Dimensional Numerical Model for Assessment of Water Flow and Contaminant Transport in the Unsaturated Zone

This report describes the Mixing Cell Model code, a one dimensional model for water flow and solute transport in the unsaturated zone under steady state or transient flow conditions. The model is based on the principles and assumptions underlying mixing-cell model formulations. The unsaturated zone is discretized into a series of independent mixing cells. Each cell may have unique hydrologic, lithologic, and sorptive properties. Ordinary differential equations describe the material (water and solute) balance within each cell. Water-flow equations are derived from the continuity equation, assuming that unit gradient conditions exist at all times in each cell. Pressure gradients are considered implicitly through model discretization. Unsaturated hydraulic conductivity and moisture contents are determined by the material specific moisture-characteristic curves. Solute-transport processes include explicit treatment of advective processes, first order chain decay, and linear sorption reactions. Dispersion is addressed through implicit and explicit dispersion. Implicit dispersion is an inherent feature of all mixing-cell models and originates from the formulation of the problem in terms of mass balance around fully mixed volume elements. Expressions are provided that relate implicit dispersion to the physical dispersion of the system. Two FORTRAN codes were developed to solve the water flow and solute-transport equations: (1) the Mixing Cell Model for Flow (MCMF) solves transient water-flow problems and (2) the Mixing Cell Model for Transport (MCMT) solves the solute-transport problem. The transient water-flow problem is typically solved first by estimating the water flux through each cell in the model domain as a function of time using the MCMF code. These data are stored in either ASCII or binary files that are later read by the solute transport code (MCMT). Code output includes solute pore water concentrations, water and solute inventories in each cell and at each specified output time, and water and solute fluxes through each cell and specified output time. Computer run times for coupled transient water flow and solute transport were typically several seconds on a 2 GHz Intel Pentium IV desktop computer. The model was benchmarked against analytical solutions and finite element approximations to the partial differential equations (PDE) describing unsaturated flow and transport. Differences between the maximum solute flux estimated by the mixing cell model and the PDE models were typically less than two percent. This revision includes an option for a fixed concentration lower boundary condition for diffusive fluxes for versions 020321 and later.

54 ENVIRONMENTAL SCIENCES↗

An Integrated Multiscale Experimental-Numerical Analysis on Reconsolidation of Salt-Clay Mixture for Disposal of Heat-Generating Waste (Final NEUP Technical Report)

The overall purpose of this research is to improve understanding of THMC coupling effect on the reconsolidation of granular (or crushed) salt-clay mixture used for seal systems of shafts and drifts in salt repositories. This proposed work is partially motivated by the recent work on the Waste Isolation Pilot Plant (WIPP) that shows the promising sealing capability of clay-salt mixture compared to crushed salt. In particular, primary emphasis is to develop a fully integrated multiscale experiment-numerical study to determine and explain what leads to the superior sealing ability of the clay-salt mixture. These research activities are designed to seek further understanding of (1) why clay additives may enhance the fluid trapping and (2) whether this flow barrier effect may prevail under different combinations of temperature, confining pressure, deviatoric stress and other foreseeable environmental factors. If successful, this enhanced flow trapping ability of the seal provides significant improvement to the seal and repository performance and therefore make the repository safer in the long-term. The experiment component includes microstructural investigation and macroscopic tests on a reconsolidated salt-clay mixture. In the microstructural study, the goal is to (1) characterize microscopic distributions of distinct phases (e.g., clay, salt crystal boundaries, trapped brine, and pore) to examine the connectivity of the pore network inside the salt-clay mixture with different amounts of clay additive and moisture content and (2) analyze multiscale imaging data to reconstruct the polycrystalline microstructures for numerical simulations. Meanwhile, macroscopic tests are performed to analyze how clay alters the failure/creep mechanisms in the salt-clay mixture. Microscopic and macroscopic experimental observations will both be used to calibrate and validate a multiscale model that explicitly simulates the capillary and multiphase flow in the connected pores and the deformation due to the presence of intra-crystalline brine at the pore scale via a new polyhedral discrete element–lattice Boltzmann method (DEM-LBM) coupling model. The pore-scale simulations are homogenized via an upscaling procedure that converts pore-scale information (e.g. force exerted on grain boundary, sliding, pressure-solution) to continuum measures (e.g. Cauchy stress, Darcy’s flow) at each integration point in the macroscopic multiphase TMHC model. This multiscale scheme will allow coupling be- tween high-fidelity simulations of brine-salt-clay interaction and the macroscopic TMHC model. The multiscale model helps the understanding of how the trapped brine inclusion affects the pressure-solution mechanism with the presence of clay and moisture. This work brings new insight into the sealing capacity of salt-clay mixture under elevated temperature over a long period of time - a key to evaluating the potential of salt-clay mixture usage for salt repositories.

42 ENGINEERING↗

Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. In this report we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate speed-up over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗

The Cirrus Parcel Model Comparison Project

The cirrus Parcel Model Comparison Project involves the systematic comparison of current models of ice crystal nucleation and growth for specified, typical, cirrus cloud environments. In Phase 1 of the project reported here, simulated cirrus cloud microphysical properties are compared for situations of "warm" (-40 C) and "cold" (-60 C) cirrus subject to updrafts of 4, 20 and 100 centimeters per second, respectively. Five models are participating in the project. These models employ explicit microphysical schemes wherein the size distribution of each class of particles (aerosols and ice crystals) is resolved into bins. Simulations are made including both homogeneous and heterogeneous ice nucleation mechanisms. A single initial aerosol population of sulfuric acid particles is prescribed for all simulations. To isolate the treatment of the homogeneous freezing (of haze drops) nucleation process, the heterogeneous nucleation mechanism is disabled for a second parallel set of simulations. Qualitative agreement is found amongst the models for the homogeneous-nucleation-only simulations, e.g., the number density of nucleated ice crystals increases with the strength of the prescribed updraft. However, non-negligible quantitative differences are found. Systematic bias exists between results of a model based on a modified classical theory approach and models using an effective freezing temperature approach to the treatment of nucleation. Each approach is constrained by critical freezing data from laboratory studies. This information is necessary, but not sufficient, to construct consistent formulae for the two approaches. Large haze particles may deviate considerably from equilibrium size in moderate to strong updrafts (20-100 centimeters per second) at -60 C when the commonly invoked equilibrium assumption is lifted. The resulting difference in particle-size-dependent solution concentration of haze particles may significantly affect the ice nucleation rate during the initial nucleation interval. The uptake rate for water vapor excess by ice crystals is another key component regulating the total number of nucleated ice crystals. This rate, the product of ice number concentration and ice crystal diffusional growth rate, partially controls the peak nucleation rate achieved in an air parcel and the duration of the active nucleation time period.

Lin, Ruei-Fong↗

The Role of Ontologies in Schema-based Program Synthesis

Program synthesis is the process of automatically deriving executable code from (non-executable) high-level specifications. It is more flexible and powerful than conventional code generation techniques that simply translate algorithmic specifications into lower-level code or only create code skeletons from structural specifications (such as UML class diagrams). Key to building a successful synthesis system is specializing to an appropriate application domain. The AUTOBAYES and AUTOFILTER systems, under development at NASA Ames, operate in the two domains of data analysis and state estimation, respectively. The central concept of both systems is the schema, a representation of reusable computational knowledge. This can take various forms, including high-level algorithm templates, code optimizations, datatype refinements, or architectural information. A schema also contains applicability conditions that are used to determine when it can be applied safely. These conditions can refer to the initial specification, to intermediate results, or to elements of the partially-instantiated code. Schema-based synthesis uses AI technology to recursively apply schemas to gradually refine a specification into executable code. This process proceeds in two main phases. A front-end gradually transforms the problem specification into a program represented in an abstract intermediate code. A backend then compiles this further down into a concrete target programming language of choice. A core engine applies schemas on the initial problem specification, then uses the output of those schemas as the input for other schemas, until the full implementation is generated. Since there might be different schemas that implement different solutions to the same problem this process can generate an entire solution tree. AUTOBAYES and AUTOFILTER have reached the level of maturity where they enable users to solve interesting application problems, e.g., the analysis of Hubble Space Telescope images. They are large (in total around 100kLoC Prolog), knowledge intensive systems that employ complex symbolic reasoning to generate a wide range of non-trivial programs for complex application do- mains. Their schemas can have complex interactions, which make it hard to change them in isolation or even understand what an existing schema actually does. Adding more capabilities by increasing the number of schemas will only worsen this situation, ultimately leading to the entropy death of the synthesis system. The root came of this problem is that the domain knowledge is scattered throughout the entire system and only represented implicitly in the schema implementations. In our current work, we are addressing this problem by making explicit the knowledge from Merent parts of the synthesis system. Here; we discuss how Gruber's definition of an ontology as an explicit specification of a conceptualization matches our efforts in identifying and explicating the domain-specific concepts. We outline the dual role ontologies play in schema-based synthesis and argue that they address different audiences and serve different purposes. Their first role is descriptive: they serve as explicit documentation, and help to understand the internal structure of the system. Their second role is prescriptive: they provide the formal basis against which the other parts of the system (e.g., schemas) can be checked. Their final role is referential: ontologies also provide semantically meaningful "hooks" which allow schemas and tools to access the internal state of the program derivation process (e.g., fragments of the generated code) in domain-specific rather than language-specific terms, and thus to modify it in a controlled fashion. For discussion purposes we use AUTOLINEAR, a small synthesis system we are currently experimenting with, which can generate code for solving a system of linear equations, Az = b.

Bures, Tomas↗

GCSS Cirrus Parcel Model Comparison Project

The Cirrus Parcel Model Comparison Project, a project of GCSS Working Group on Cirrus Cloud Systems (WG2), involves the systematic comparison of current models of ice crystal nucleation and growth for specified, typical, cirrus cloud environments. The goal of this project is to document and understand the factors resulting in significant inter-model differences. The intent is to foment research leading to model improvement and validation. In Phase 1 of the project reported here, simulated cirrus cloud microphysical properties are compared for situations of "warm" (-40 C) and "cold" (-60 C) cirrus subject to updrafts of 4, 20 and 100 cm/s, respectively. Five models participated. These models employ explicit microphysical schemes wherein the size distribution of each class of particles (aerosols and ice crystals) is resolved into bins. Simulations are made including both homogeneous and heterogeneous ice nucleation mechanisms. A single initial aerosol population of sulfuric acid particles is prescribed for all simulations. To isolate the treatment of the homogeneous freezing (of haze drops) nucleation process, the heterogeneous nucleation mechanism is disabled for a second parallel set of simulations. Qualitative agreement is found for the homogeneous-nucleation-only simulations, e.g., the number density of nucleated ice crystals increases with the strength of the prescribed updraft. However, non-negligible quantitative differences are found. Detailed analysis reveals that the homogeneous nucleation formulation, aerosol size, ice crystal growth rate (particularly the deposition coefficient), and water vapor uptake rate are critical components that lead to differences in predicted microphysics. Systematic bias exists between results based on a modified classical theory approach and models using an effective freezing temperature approach to the treatment of nucleation. Each approach is constrained by critical freezing data from laboratory studies, but each includes assumptions that can only be justified by further laboratory data. Consequently, it is not yet clear if the two approaches can be made consistent. Large haze particles may deviate considerably from equilibrium size in moderate to strong updrafts (20-100 cm/s) at -60 C when the commonly invoked equilibrium assumption is lifted. The resulting difference in particle-size-dependent solution concentration of haze particles may significantly affect the ice nucleation rate during the initial nucleation interval. The uptake rate for water vapor excess by ice crystals is another key component regulating the total number of nucleated ice crystals. This rate, the product of ice number concentration and ice crystal diffusional growth rate, which is sensitive to the deposition coefficient when ice particles are small, partially controls the peak nucleation rate achieved in an air parcel and the duration of the active nucleation time period. The effects of heterogeneous nucleation are most pronounced in weak updraft situations. Vapor competition by the nucleated (heterogeneous) ice crystals limits the achieved ice supersaturation and thus suppresses the contribution of homogeneous nucleation. Correspondingly, ice crystal number density is markedly reduced. Definitive laboratory and atmospheric benchmark data are needed for the heterogeneous nucleation process. Inter-model differences are correspondingly greater than in the case of the homogeneous nucleation process acting alone.

Lin, Ruei-Fong↗