A multiscale molecular dynamics method for isothermal dynamic problems using the seamless heterogeneous multiscale method

An efficient space-angle subgrid scale discretisation of the neutron transport equation

The association between invasive and native species varies across spatial scales and is affected by phylogenetic relatedness, but these issues have rarely been addressed in aquatic ecosystems. In this study, we used a non-native, highly invasive species of Poaceae (tropical signalgrass) to test the hypotheses that (i) tropical signalgrass success correlates negatively with success of most native species of macrophytes at fine spatial scales, but its success correlates positively or at random with natives at coarse spatial scales, and that (ii) tropical signalgrass is less associated with native species belonging to the family Poaceae than with species belonging to other families (Darwin’s naturalization hypothesis). We used a dataset obtained at fine (0.25 m2) and coarse (ca. 1,000 m2) scales. The presence/absence of all species was recorded at both scales, and their biomass was also measured at the fine scale. We tested the association between tropical signalgrass biomass and individual native species with logistic regressions at the fine scale, and using the T-score index between tropical signalgrass and each native species at both scales. The likelihood of the occurrence of six species (submersed and free-floating) was negatively affected by tropical signalgrass biomass at the fine scale. T-scores showed that three species were less associated with tropical signalgrass than expected by chance, but 22 species co-occurred more than expected by chance at the coarse scale. Associations between species of Poaceae and tropical signalgrass were null at the fine scale, but were positive or null at the coarse scale. In addition to showing that spatial scale affects the patterns of association among the non-native and individual native species, our results indicate that phylogeny did not explain associations between the invasive and native macrophytes, at both scales.

In order to run reservoir simulation efficiently, a coarse scale (CS) dynamic model is created by upscaling of a fine scale (FS) static model. All history match (HM) changes usually done in the CS dynamic model need to be downscaled to FS for geological justifications and consistency maintenance between the FS static and CS dynamic models. This paper proposes a robust downscaling method for integration of FS static and CS dynamic models. The proposed method downscales a HMDM (dynamic model) to HMSM (static) in multiple steps. Scale-up the ISM (initial) to CS to create an IDM. Identify the cell changes between HMDM and IDM, and transfer the changes to FS to create a MSM (modified). Scale-up the MSM to CS to create to a MDM and calculate the ratios between HMDM and MDM for all cell properties. Transfer the ratios to FS to create a HMSM. Scale-up the HMSM to CS to confirm its identity to the HMDM. Selection of sampling and zone mapping methods is critical in all steps. The proposed method has been successfully applied in a giant carbonate oil field in the Caspian Sea that consists of a matrix dominated platform and a fracture/karst dominated rim. Due to the field's complex geology and high H2S content (15%), a dual porosity, dual permeability compositional model has been created to model compositional sour crude flow within/between matrix and fracture/karst. The FS static model contains a 236m × 236m horizontal grid with 593 layers while the CS dynamic model has the horizontal cell sizes in a range of 236m to 944m with 73 layers. Rock regions, permeability, and reservoir connectivity in the CS dynamic model were calibrated using the field historical production data (e.g., static pressure, PLT, interference test, and GOR/water-cut data) to create a HMDM. Since the HM process was performed only in the CS dynamic model, the FS static model and HMDM became inconsistent. Appling the proposed downscaling method has helped the HM team to resolve this issue and resulted in a seamless link between the FS static and CS dynamic models for current and future HM and model updates.

Where land surface air temperature data are not available, satellite land surface temperature are used. However, the coarse spatial resolution of satellite‐derived products may yield errors at the local scale. This work shows the differences between the MODIS Land Surface Temperature and Emissivity (MOD11A1) product and ground measurements at two different scales. We used data from 21 SNOTEL stations across the northern Front Range of Colorado to represent the coarse scale and 17 iButton temperature sensors across the Colorado State University Mountain Campus to represent the fine scale. We found significant differences in the temperature and its changes with elevation for the two spatial scales. At the fine scale, cold air drainage can induce an inversion of the temperature gradient with elevation. A higher correlation was found during the nighttime at the fine scale, while, at the coarse scale, higher correlations were observed during the daytime. On windy nights, temperatures do not cool as much as on calmer nights, and the coarse scale near‐surface temperature gradient with elevation persists, though the fine scale inversions do not develop. The near‐surface temperature gradients with elevation based on the MODIS pixels are similar to the ground‐based data at the coarse scale but not at the fine scale. Thus, one must be cautious in selecting the near‐surface temperature gradients with elevation for mountainous terrain when different scales are considered, and a proper validation of satellite products is necessary prior to their use to avoid the propagation of uncertainties.

Multiscale systems that are characterized by a great range of spatial–temporal scales arise widely in many scientific domains. These range from the study of protein conformational dynamics to multiphase processes in, for example, granular media or haemodynamics, and from nuclear reactor physics to astrophysics. Despite the diversity in subject areas and terminology, there are many common challenges in multiscale modelling, including validation and design of tools for programming and executing multiscale simulations. This Theme Issue seeks to establish common frameworks for theoretical modelling, computing and validation, and to help practical applications to benefit from the modelling results. This Theme Issue has been inspired by discussions held during two recent workshops in 2013: ‘Multiscale modelling and simulation’ at the Lorentz Center, Leiden (http://www.lorentzcenter.nl/lc/web/2013/569/info.php3?wsid=569&venue=Snellius), and ‘Multiscale systems: linking quantum chemistry, molecular dynamics and microfluidic hydrodynamics’ at the Royal Society Kavli Centre. The objective of both meetings was to identify common approaches for dealing with multiscale problems across different applications in fluid and soft matter systems. This was achieved by bringing together experts from several diverse communities.

<p><b>Recent ecological studies have started integrate to spatial variation of ecological patterns into the study design rather than treating it as a statistical nuisance. In particular, the influence of the spatial scale at which ecological patterns are measured has gained much attention over the last two decades. Since, for example, sensory abilities as well as the ability to disperse vary among species, different species-specific responses to heterogeneous environments may be expected.</b></p> <p>Plant-insect interactions in heterogeneous landscapes, in particular, have gained much attention as experiments can be conducted on a more accessible scale and may yield new applications for crop and horticulture. Two hypotheses that describe insect herbivore aggregations in the landscape are: a) the resource concentration hypothesis which predicts higher numbers of specialist insect herbivores per unit biomass in dense and pure stands of their host plant, and b) the resource dilution hypothesis which predicts that insect herbivore numbers will decline with increasing plant density. I investigated resource dilution and resource concentration patterns in egg distributions of Pieris rapae and Tyria jacobaeae in relation to host plant density, which I defined differently by applying varying spatial scales of measurement. I also tested for effects of host plant density and the scale of measurement on flight patterns of P. rapae females.</p> <p>In a natural population of Lepidium oleraceum I investigated effects of scale of measurement of plant density, as well as white rust and hymenopteran parasitoids on P. rapae egg and larvae distributions. In a separate experiment I tested for any potential effects of arthropod predators on P. rapae egg distributions at different spatial scales. The number of P. rapae eggs per plant conformed to predictions made by the resource dilution hypothesis. However, such a pattern was only found for fine scale plant density but not for medium or coarse scale plant density. In contrast, the number of T. jacobaeae egg clutches per plant showed a resource concentration pattern for medium scale plant density but not for fine or coarse scale plant density. However, this result occurred only in one of two experiments with T. jacobaeae. A resource dilution pattern was also found for the number of visits per plant by P. rapae females at both coarse and fine scale measurement. Female flight paths were less directional when plants were present in the study area during fine scale observations and butterflies were attracted to areas containing host plants. Flight observations at coarse scale did not show any change in turning behaviour and butterflies moved at random across the study area. No effect of parasitism, or predation through arthropods was found on the distribution of P. rapae eggs. However, infection by white rust lead to a decreased number of eggs per plant in the natural L. oleraceum population. The results of my thesis underline the importance of spatial scale in ecological studies. Careful thought should be given to the scale of measurement and method of abstraction when describing real world patterns.</p>

In the coarse scale simulation of heterogeneous reservoirs, effective or upscaled flow functions, e.g., oil and water relative permeability and capillary pressure, can be used to represent heterogeneities at subgrid scales. The effective relative permeability is typically upscaled along with absolute permeability from a geostatistical model. However, the potentially important effects of smaller scale heterogeneities (on the centimeter to meter scale) in both capillarity and absolute permeability will not be captured by this approach. In this paper, we present a new two-stage upscaling procedure for two-phase flow. In the first stage, we upscale from the core (fine) scale to the geostatistical (intermediate) scale, while in the second stage we upscale from the geostatistical scale to the simulation (coarse) scale. The computational procedure includes numerical solution of the finite difference equations describing steady state flow over the local region to be upscaled, using either constant pressure or periodic boundary conditions. The two-stage method is applied to synthetic two-dimensional reservoir models with strong variation in capillarity on the fine scale. Results are presented in terms of both oil production rates and saturation fields. Accurate reproduction of the fine grid solutions (simulated on 500 × 500 grids) is achieved on coarse grids of 10 × 10 for different flow scenarios. It is shown that, although capillary forces are important on the fine scale, the assumption of capillary dominance in the first stage of upscaling is not always appropriate, and that the computation of rate dependent effective properties in the upscaling can significantly improve the accuracy of the coarse scale model. The assumption of viscous dominance in the second upscaling stage is found to be appropriate in all of the cases considered.

Integration of dynamic data typically requires the solution of an inverse problem that can be computationally intensive and practically infeasible for fine scale reservoir models. In this paper we present a new methodology to directly update fine scale geostatistically-based reservoir models by combining gradual deformation parameterization for the fine scale geostatistical model and an upscaling technique for the coarse scale flow simulation model. The proposed methodology includes: Perturbation of the fine scale geostatistical model using the gradual deformation parameterization. Gradual deformation ensures the preservation of the overall geostatistical properties of the fine model. Generation of the coarse scale flow simulation model by upscaling the fine scale geostatistical model. Sensitivity computation of the flow simulation results with respect to the fine scale parameterization. This sensitivity computation is analytical and takes into account the upscaling process. Direct updating of the fine scale geostatistical model using classical optimization process. Direct updating ensures consistency between the fine and coarse scale models. The accuracy of the proposed methodology was improved by calibrating the flow simulation model. The objective of this calibration is to reduce the error introduced by the upscaling step during the flow simulation. We applied successfully our methodology for fine scale reservoir description by integrating permanent down-hole gauge measurements directly into a three-dimensional geostatistical model containing about two million grid blocks. This test is designed to highlight several key issues of the proposed methodology: Efficiency of the upscaling step coupled with gradient-based optimization to speed up the history matching process. Usefulness of the calibration step for a correct integration of upscaling techniques in history matching. Capability of the methodology for maintaining consistency and coherency between fine scale and coarse scale models. Improvement of the reservoir characterization by integrating dynamic data at the fine geostatistical scale. We conclude that the proposed methodology can be used effectively and efficiently for reservoir characterization purposes.

SUMMARYThis paper presents residual‐based turbulence models for problems with moving boundaries and interfaces. The method is developed via a hierarchical application of variational multiscale ideas and the models are cast in an arbitrary Lagrangian–Eulerian (ALE) frame to accommodate the deformation of domain boundaries. An overlapping additive decomposition of velocity and pressure fields into coarse and fine scale components leads to coarse and fine scale mixed‐field problems. The problem governing fine scales is subjected to a further decomposition of the fine scale velocity into overlapping components termed as fine scales level I and level II. In turn, in the bottom‐up integration of scales, the model for level II fine scales serves to stabilize the problem governing level I fine scales, and model for level I fields yields the turbulence models. From the computational perspective, the coarse scales are represented in terms of the standard Lagrange shape functions, whereas level I and level II scales are represented via quadratic and fourth order polynomial bubbles, respectively. Because of the bubble functions approach employed in the consistently derived fine scale models, the resulting method is free of any embedded or tunable parameters. The proposed turbulence models share a common feature with the LES models in that the largest scales in the flow are numerically resolved, whereas the subgrid scales are modeled. The method is applied to flow around a plunging airfoil at Re = 40,000, and results are compared with experimental and numerical data published in the literature. Also presented are the results for the plunging airfoil at Re = 60,000 to show the robustness and range of applicability of the method. Copyright © 2013 John Wiley & Sons, Ltd.

A variational multiscale approach to strain localization – formulation for multidimensional problems

To obtain design sensitivity in molecular dynamics (MD), finite differencing is impractical from the viewpoint of efficiency and accuracy since MD problems could include highly nonlinear design parameters and generally require a lot of computation time. In this paper, using a bridging scale decomposition method, we develop a multiscale adjoint design sensitivity analysis (DSA) method for the coarse-scale performance of atomistic-continuum dynamic systems considering fine scale effects. Due to the decomposition of total solution into fine and coarse scales using a mass-weighted projection operator that possesses the orthogonal property of complimentary projector to mass matrix, each scale can be independently considered in both response and sensitivity analyses. To reduce computing costs, using a generalized Langevin equation and a lattice mechanics, the fine scale MD region is confined locally while the coarse-scale finite element analysis is utilized in the whole domain. The multiscale adjoint sensitivity includes only explicitly design-dependent terms together with the original and adjoint responses so that one additional time integration process is sufficient to evaluate the design sensitivity. Numerical examples demonstrate the accuracy of the developed DSA method for various design variables in coarse and fine scales.

Aim: The objective of this study was to describe the spa tial patterns of selected soil properties and biomass yield at fine and coarse scale in a switchgrass field to determine the appropriate sampling approach to enable the calculation of means with minimum variance. Methodology: Spatial variability of biomas s yield and soil properties at fine (2.5 m sampling interval) and coarse (10 m sampling interval) scales were assessed through semivariogram analysis. The site located in Chickasha, Oklahoma, consisted of two soil types a Dale silt loam (fine - silty, mixed, superactive, thermic Pachic Haplustolls) and McLain silty clay loam (fine, mixed, superactive, thermic Pachic Argiustolls). Eighty soil samples were collected along two 100 m transects at 2.5 and 10 m intervals established across each soil type in both 20 12 and 2013. Results: The semivariograms revealed coarse scale organic carbon (OC) to be strongly correlated with range values from 56 – 78 m for both soils. Normalized difference vegetative index (NDVI) was

We study the convergence of multigrid schemes for the Helmholtz equation, focusing in particular on the choice of the coarse scale operators. Let $G_{\rm c}$ denote the number of points per wavelength at the coarse level. If the coarse scale solutions are to approximate the true solutions, then the oscillatory nature of the solutions implies the requirement $G_{\rm c} > 2$. However, in examples the requirement is more like $G_{\rm c} \gtrsim 10$, in a trade-off involving also the amount of damping present and the number of multigrid iterations. We conjecture that this is caused by the difference in phase speeds between the coarse and fine scale operators. Standard 5-point finite differences in two dimensions are our first example. A new coarse scale 9-point operator is constructed to match the fine scale phase speeds. We then compare phase speeds and multigrid performance of standard schemes with a scheme using the new operator. The required $G_{\rm c}$ is reduced from about 10 to about 3.5, with less damping present so that waves propagate over $>$ 100 wavelengths in the new scheme. Next, we consider extensions of the method to more general cases. In three dimensions, comparable results are obtained with standard 7-point differences and optimized 27-point coarse grid operators, leading to an order of magnitude reduction in the number of unknowns for the coarsest scale linear system. Finally, we show how to include perfectly matched layers at the boundary, using a regular grid finite element method. Matching coarse scale operators can easily be constructed for other discretizations. The method is therefore potentially useful for a large class of discretized high-frequency Helmholtz equations.

A computational multiscale method is proposed to simulate coupled, nonequilibrium thermomechanical processes. This multiscale framework couples together thermomechanical equations at the coarse scale with nonequilibrium molecular dynamics at the fine scale. The novel concept of distributed coarse scale thermostats enables subsets of fine scale atoms to be attached to different coarse scale nodes which act as thermostats. The fine scale dynamics is driven by the coarse scale mean field. A coarse-grained Helmholtz free energy is used to derive macroscopic quantities. This new framework can reproduce the correct thermodynamics at the fine scale while providing an accurate coarse-grained result at the coarse scale.

Subsurface flows are affected by geological variability over a range of length scales. The modeling of well singularity in heterogeneous formations is important for simulating flow in aquifers and petroleum reservoirs. In this paper, two approaches in calculating the upscaled well index to capture the effects of fine scale heterogeneity in near-well regions are presented and applied. We first develop a flow-based near-well upscaling procedure for geometrically flexible grids. This approach entails solving local well-driven flows and requires the treatment of geometric effects due to the nonalignment between fine and coarse scale grids. An approximate coarse scale well model based on a well singularity analysis is also proposed. This model, referred to as near-well arithmetic averaging, uses only the fine scale permeabilities at well locations to compute the coarse scale well index; it does not require solving any flow problems. These two methods are systematically tested on three-dimensional models with a variety of permeability distributions. It is shown that both approaches provide considerable improvement over a simple (arithmetic) averaging approach to compute the coarse scale well index. The flow-based approach shows close agreement to the fine scale reference model, and the near-well arithmetic averaging also offers accuracy for an appropriate range of parameters. The interaction between global flow and near-well upscaling is also investigated through the use of global fine scale solutions in near-well scale-up calculations.