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Machine learning (ML)‐based parameterizations have been developed for Earth System Models (ESMs) with the goal to better represent subgrid‐scale processes or to accelerate computations. ML‐based parameterizations within hybrid ESMs have successfully learned subgrid‐scale processes from short high‐resolution simulations. However, most studies used a particular ML method to parameterize the subgrid tendencies or fluxes originating from the compound effect of various small‐scale processes (e.g., radiation, convection, gravity waves) in mostly idealized settings or from superparameterizations. Here, we use a filtering technique to explicitly separate convection from these processes in simulations with the Icosahedral Non‐hydrostatic modeling framework (ICON) in a realistic setting and benchmark various ML algorithms against each other offline. We discover that an unablated U‐Net, while showing the best offline performance, learns reverse causal relations between convective precipitation and subgrid fluxes. While we were able to connect the learned relations of the U‐Net to physical processes this was not possible for the non‐deep learning‐based Gradient Boosted Trees. The ML algorithms are then coupled online to the host ICON model. Our best online performing model, an ablated U‐Net excluding precipitating tracer species, indicates higher agreement for simulated precipitation extremes and mean with the high‐resolution simulation compared to the traditional scheme. However, a smoothing bias is introduced both in water vapor path and mean precipitation. Online, the ablated U‐Net significantly improves stability compared to the non‐ablated U‐Net and runs stable for the full simulation period of 180 days. Our results hint to the potential to significantly reduce systematic errors with hybrid ESMs. Plain Language Summary: Due to their computational costs, it is currently not feasible to run more accurate high‐resolution climate models on a global domain on climate (century) time‐scales. However, high‐accuracy climate simulations are needed for more robust and detailed projections of our future climate. Here, we develop and evaluate various machine learning‐based convection parameterizations learned on reconstructed and coarse‐grained high‐resolution subgrid fluxes to solve this problem, and benchmark their performance. The data set is chosen from simulations of the Icosahedral Non‐hydrostatic modeling framework (ICON) in a realistic setting of the tropical Atlantic and at storm‐resolving resolutions. We focus only on convective subgrid fluxes that are isolated from other components. We improve the best ML algorithms further by excluding variables that cause unphysical correlations. Finally, we explain the learned relations of the best data‐driven schemes based on physical process understanding, test their performance when coupled to the ICON model, and achieve stable coupled simulations for 180 days as well as improved precipitation predictions. Key Points: We train/benchmark machine learning models on convective fluxes derived from realistic coarse‐grained data of storm‐resolving simulationsShapley values reveal that the best offline model, a U‐Net, learns non‐causal links to precipitation and shows poor online performanceA model, without non‐causal precipitation connections, runs more stable coupled to ICON and indicates better precipitation predictions [ABSTRACT FROM AUTHOR]

Understanding the regional climate response to land cover change requires a realistic sub‐grid representation of vegetation cover in the land surface scheme (LSS) of climate models. The Community Land Model (CLM) is considered one of the most advanced LSSs; however, when coupled with the Weather Research and Forecasting (WRF) model, the tiling vegetation cover approach was deactivated. Here, we reactivated the theoretical sub‐grid vegetation cover representation in WRF‐CLM and applied it to assess the impacts of deforestation on regional climate in the Southeast Asian Massif region. We found that CLM‐tiling performs more accurate simulations of surface air temperature and precipitation compared to other LSSs using the in situ observations. Importantly, CLM‐tiling successfully captures the theoretical sensitivity of evapotranspiration (ET) and temperature to sub‐grid deforestation, aligning with Noah‐mosaic, and it substantially improves the spatial pattern responses of simulated ET and temperature to regional deforestation. Plain Language Summary: The selection of appropriate land surface schemes (LSSs) is crucial for studying land‐atmosphere interactions in the Weather Research and Forecasting (WRF) model. While most LSSs adopt a dominant vegetation cover approach, where each grid cell is assigned a single land cover type, only Noah‐mosaic can represent sub‐grid vegetation cover changes. However, several studies have mistakenly assumed that the default coupled Community Land Model (CLM) in WRF is capable of simulating such changes, which may have affected their conclusions. In this study, we modified the CLM‐default by reactivating the tiling vegetation cover approach (CLM‐tiling), which accurately represents sub‐grid vegetation cover changes. Our application of the CLM‐tiling in the Southeast Asian Massif region led to improved simulations of air temperature and precipitation compared to other LSSs. Moreover, we found that CLM‐tiling successfully exhibited theoretical climate sensitivity to sub‐grid forest loss, improving the spatial pattern responses of simulated evapotranspiration and temperature to regional deforestation. Key Points: Default WRF‐CLM lacked theoretical sub‐grid vegetation cover representation, failing to capture climate response to sub‐grid deforestationCLM‐tiling could successfully capture the sensitivity of evapotranspiration and temperature to sub‐grid deforestationInvolving sub‐grid vegetation cover representation in WRF‐CLM improved the spatial pattern responses of simulated climate to deforestation [ABSTRACT FROM AUTHOR]

Simulating fluid‐structure interaction problems usually requires a considerable computational effort. In this article, a novel semi‐implicit finite volume scheme is developed for the coupled solution of free surface shallow water flow and the movement of one or more floating rigid structures. The model is well‐suited for geophysical flows, as it is based on the hydrostatic pressure assumption and the shallow water equations. The coupling is achieved via a nonlinear volume function in the mass conservation equation that depends on the coordinates of the floating structures. Furthermore, the nonlinear volume function allows for the simultaneous existence of wet, dry and pressurized cells in the computational domain. The resulting mildly nonlinear pressure system is solved using a nested Newton method. The accuracy of the volume computation is improved by using a subgrid, and time accuracy is increased via the application of the theta method. Additionally, mass is always conserved to machine precision. At each time step, the volume function is updated in each cell according to the position of the floating objects, whose dynamics is computed by solving a set of ordinary differential equations for their six degrees of freedom. The simulated moving objects may for example represent ships, and the forces considered here are simply gravity and the hydrostatic pressure on the hull. For a set of test cases, the model has been applied and compared with available exact solutions to verify the correctness and accuracy of the proposed algorithm. The model is able to treat fluid‐structure interaction in the context of hydrostatic geophysical free surface flows in an efficient and flexible way, and the employed nested Newton method rapidly converges to a solution. The proposed algorithm may be useful for hydraulic engineering, such as for the simulation of ships moving in inland waterways and coastal regions. [ABSTRACT FROM AUTHOR]

Subgrid variability of snow is important in studying surface‐atmosphere interactions as it affects grid‐scale processes. However, this dynamic variability is currently not well‐represented in most land‐surface models (LSMs). A stochastic snow model using the Fokker‐Planck Equation (FPE) has been developed specifically for representing subgrid variability of snow. In this study, the FPE snow model was coupled into the Rapid Update Cycle (RUC) LSM, which provides lower boundary conditions for the operational NOAA Rapid Refresh and High‐Resolution Rapid Refresh weather prediction systems. This coupled land‐surface model with subgrid snow processes is named the RUC‐Stochastic Snow (SS) LSM. The performance of RUC‐SS LSM and RUC LSM is analyzed in detail in initial offline single‐column testing over two 13‐km × 13‐km grid cells. The results show that RUC‐SS LSM has a much better capability in estimating snow cover fraction than RUC LSM, especially during the late part of the snow‐melting season. The simulated duration of the partially snow‐covered period at the snow‐melting stage is extended from a few days with RUC LSM to about one month with the RUC‐SS LSM, thus improving prediction of surface energy budget components. For example, the latent and sensible heat fluxes and skin temperature increase gradually in the RUC‐SS LSM during the transition from full coverage to snow‐free conditions. In contrast, this transition happens too quickly in RUC LSM, and the energy‐budget components change too abruptly. The results of RUC‐SS demonstrate its capability to account for subgrid variability of snow cover and show that considering subgrid variability of snow in LSMs is important for simulating surface‐atmosphere interactions. Key Points: A stochastic snow model is integrated into a land‐surface model to represent snow subgrid variability and its change over timeThis subgrid snow treatment is tested in an offline mode of the land‐surface model to demonstrate its effectivenessThe effects of snow subgrid variability on energy components and skin temperature in land‐surface models are quantified [ABSTRACT FROM AUTHOR]

Recent efforts in MPACT have focused on improving the performance of the 2D/1D subplane implementation to help target computational performance goals. This paper builds on previous efforts that targeted the use of subgrid treatments to improve the accuracy of control rod representation, presenting three additional applications of subgrid treatments with the goal of reducing the computational burden of simulations. These subgrid applications include treatment of spacer grids, thermal feedback, and axial reflector material representation. With these approaches, a single method of characteristics (MOC) plane can contain several different materials axially that are represented explicitly via subgrids on the coarse mesh finite difference (CMFD) mesh but are axially homogenized on the MOC mesh. This allows for a substantial reduction in the number of MOC planes needed in the calculation through the introduction of an approximate treatment, particularly with regard to the self-shielded cross sections and MOC-informed radial current coupling coefficients in CMFD. Several test problems ranging from single rod to quarter core are used to assess the solution accuracy and performance of these various subgrid representations. Overall, the accuracy of the approximations seems very reasonable, with extremely small differences in eigenvalue observed and maximum pin power errors in the 0.5% to 1.0% range. Several cases show substantial value in the compromise between accuracy and computational performance. Others highlight the new computational hurdles that future research will aim to resolve. [ABSTRACT FROM AUTHOR]

Abstract Interactions between water flow and patchy vegetation are governing the functioning of many ecosystems. Yet, numerical models that simulate those interactions explicitly at the submeter patch scale to predict geomorphological and ecological consequences at the landscape scale (order of km2) are still very computationally demanding. Here, we present a novel and efficient convolution technique to incorporate biogeomorphic feedbacks in numerical models across multiple spatial scales (from less than 1 m2 to several km2). This new methodology allows for spatially refining coarse‐resolution hydrodynamic simulations of flow velocities (order of m) around fine‐resolution patchy vegetation patterns (order of 10 cm). Although flow perturbations around each vegetation grid cell are not simulated with the same level of accuracy as with more expensive finer‐resolution models, we show that our approach enables spatial refinement of coarse‐resolution hydrodynamic models by resolving efficiently subgrid‐scale flow velocity patterns within and around vegetation patches (mean error, spatial variability, and spatial correlation improved by, respectively, 13%, 66%, and 49% on average in our test cases). We also provide evidence that our approach can substantially improve the representation of important biogeomorphic processes, such as subgrid‐scale effects on net sedimentation rate and habitable surface area for vegetation (respectively 66% and 39% better on average). Finally, we estimate that replacing a fine‐resolution model by a coarser‐resolution model associated with the convolution method could reduce the computational time of real‐life fluctuating flow simulations by several orders of magnitude. This marks an important step forward toward more computationally efficient multiscale biogeomorphic modeling.

Interactions between water flow and patchy vegetation are governing the functioning of many ecosystems. Yet, numerical models that simulate those interactions explicitly at the submeter patch scale to predict geomorphological and ecological consequences at the landscape scale (order of km2) are still very computationally demanding. Here, we present a novel and efficient convolution technique to incorporate biogeomorphic feedbacks in numerical models across multiple spatial scales (from less than 1 m2 to several km2). This new methodology allows for spatially refining coarse‐resolution hydrodynamic simulations of flow velocities (order of m) around fine‐resolution patchy vegetation patterns (order of 10 cm). Although flow perturbations around each vegetation grid cell are not simulated with the same level of accuracy as with more expensive finer‐resolution models, we show that our approach enables spatial refinement of coarse‐resolution hydrodynamic models by resolving efficiently subgrid‐scale flow velocity patterns within and around vegetation patches (mean error, spatial variability, and spatial correlation improved by, respectively, 13%, 66%, and 49% on average in our test cases). We also provide evidence that our approach can substantially improve the representation of important biogeomorphic processes, such as subgrid‐scale effects on net sedimentation rate and habitable surface area for vegetation (respectively 66% and 39% better on average). Finally, we estimate that replacing a fine‐resolution model by a coarser‐resolution model associated with the convolution method could reduce the computational time of real‐life fluctuating flow simulations by several orders of magnitude. This marks an important step forward toward more computationally efficient multiscale biogeomorphic modeling. Plain Language Summary: The functioning of many ecosystems, such as rivers, wetlands, and shallow seas, is governed by the interactions between water flow and small patches of vegetation. Powerful tools to investigate the formation and evolution of these ecosystems are computer programs that split the study area into different grid cells on which fundamental equations of water movement are solved. However, these programs (so‐called numerical models) necessitate a lot of computational power, as they require fine grid resolutions (a lot of small grid cells) to account for small patches of vegetation. In this paper, we present a new approach where the fundamental equations are solved at relatively coarse resolution (few large grid cells of tens of square meters). The water flow patterns are then recalculated at finer resolution (smaller grid cells of less than 1 m2) with a novel technique that requires only little computational power (so‐called convolution method). By comparing with laboratory measurements and the results from a numerical model at much finer resolution (grid cells of a few square centimeters), we provide evidence that this approach is a good compromise between accuracy and computational time, hence allowing to study the formation and evolution of large ecosystems with more extensive details. Key Points: Fine‐scale flow‐vegetation interactions can considerably impact large‐scale biogeomorphic feedbacksCurrent large‐scale biogeomorphic models are too coarse to include these fine‐scale interactionsOur computationally efficient method allows large‐scale models to account for fine‐scale interactions [ABSTRACT FROM AUTHOR]

Parameterization of subgrid‐scale variability of land cover characterization (LCC) is an active area of research and can improve model performance compared to the dominant (i.e., most abundant tile) approach. The "Noah" land surface model implementation in the global Model for Prediction Across Scales‐Atmosphere (MPAS‐A), however, only uses the dominant LCC approach that leads to oversimplification in regions of highly heterogeneous LCC (e.g., urban/suburban settings). Thus, in this work we implement a subgrid tiled approach as an option in MPAS‐A, version 6.0, and assess the impacts of tiled LCC on meteorological predictions for two gradually refining meshes (92–25 and 46–12 km) focused on the conterminous United States for January and July 2016. Compared to the dominant approach, results show that using the tiled LCC leads to pronounced global changes in 2‐m temperature (July global average change approximately −0.4 K), 2‐m moisture, and 10‐m wind speed for the 92–25 km mesh. The tiled LCC reduces mean biases in 2‐m temperature (July U.S. average bias reduction approximately factor of 4) and specific humidity in the central and western United States for the 92–25 km mesh and improves the agreement of vertical profiles (e.g., temperature, humidity, and wind speed) with observed radiosondes; however, there is increased bias and error for incoming solar radiation at the surface. The inclusion of subgrid LCC has implications for reducing systematic temperature biases found in numerical weather prediction models, particularly those that employ a dominant LCC approach. Key Points: The use of tiled land cover characterization (LCC) has significant impacts on global meteorological predictions in MPAS‐ATiled LCC reduces bias and error for near‐surface temperature, moisture, and wind speed over the United StatesThe tiled LCC approach is important and can help mitigate systematic temperature biases in weather and climate models [ABSTRACT FROM AUTHOR]

Summary: Free‐surface flows in rivers, estuaries, and coastal areas are strongly dominated by the geometrical details of the study area. Nowadays, accurate bathymetric data are easily available on raster‐based digital elevation models with an impressive spatial resolution. These data are often accessible as large two‐dimensional arrays containing several millions of pixel values. Recent numerical methods are very efficient and rather accurate but far from being able to solve the governing differential equations on a computational grid with such a fine spatial resolution. In the present investigation, the unaltered pixel values from a digital elevation model are clustered to form subgrids of a coarser computational grid. Artificial cross‐flow between disconnected areas is inhibited by introducing cell clones and edge clones. Each clone consists of directly connected pixels. It is shown how the resulting computational grid is able to resolve geometrical details of complex study areas to pixel resolution and for any grid size. As an example, the performance of the proposed algorithm is tested to simulate a typical tidal flow in the San Francisco Bay and the Sacramento‐San Joaquin Delta area by using an extreme subgrid resolution given by a digital elevation model containing 196 000 000 pixels with 10 m pixel size. Unaltered pixel values from a digital elevation model are assembled to form subgrids of a coarser computational grid. Artificial cross‐flow between disconnected areas is inhibited by grid cloning. The resulting computational grid is able to resolve geometrical details of complex study areas to pixel resolution. A semi‐implicit finite difference–finite volume approximation of the governing equations yields a well‐posed piecewise linear system, which is solved by a converging Newton‐type method. The computed fluid volumes are assured to be everywhere nonnegative and wetting and drying are naturally resolved at pixel level. [ABSTRACT FROM AUTHOR]

Wave-induced currents are an ubiquitous feature in coastal waters that can spread material over the surf zone and the inner shelf. These currents are typically under resolved in non-hydrostatic wave-flow models due to computational constraints. Specifically, the low vertical resolutions adequate to describe the wave dynamics – and required to feasibly compute at the scales of a field site – are too coarse to account for the relevant details of the three-dimensional (3D) flow field. To describe the relevant dynamics of both wave and currents, while retaining a model framework that can be applied at field scales, we propose a two grid approach to solve the governing equations. With this approach, the vertical accelerations and non-hydrostatic pressures are resolved on a relatively coarse vertical grid (which is sufficient to accurately resolve the wave dynamics), whereas the horizontal velocities and turbulent stresses are resolved on a much finer subgrid (of which the resolution is dictated by the vertical scale of the mean flows). This approach ensures that the discrete pressure Poisson equation – the solution of which dominates the computational effort – is evaluated on the coarse grid scale, thereby greatly improving efficiency, while providing a fine vertical resolution to resolve the vertical variation of the mean flow. This work presents the general methodology, and discusses the numerical implementation in the SWASH wave-flow model. Model predictions are compared with observations of three flume experiments to demonstrate that the subgrid approach captures both the nearshore evolution of the waves, and the wave-induced flows like the undertow profile and longshore current. The accuracy of the subgrid predictions is comparable to fully resolved 3D simulations – but at much reduced computational costs. The findings of this work thereby demonstrate that the subgrid approach has the potential to make 3D non-hydrostatic simulations feasible at the scale of a realistic coastal region. [ABSTRACT FROM AUTHOR]

A widely recognized issue found in most Earth System Models is that of convective precipitation being triggered too early during the day over land, often resulting in persistent light rainfall. In an effort to address this issue, a model-consistent subgrid convective trigger is demonstrated in the Community Earth System Model (CESM). Subgrid convective initiation is achieved by first calculating a convective threshold within the Community Atmosphere Model (version 5.3). The convective threshold is then passed to each subgrid land cover type within the Community Land Model (version 4.0) and convection is considered to be active if the convective threshold is exceeded and the convective available potential energy (CAPE) exceeds 70 J kg−1 (the default trigger). In total, three simulations are performed: (1) a Control (CTL) with the default CAPE trigger, (2) a simulation with the default CAPE trigger as well as the subgrid trigger (HCF trigger) applied over land and ocean, and (3) a simulation the same as the HCF trigger but only applied over land (HCF land). By including this subgrid trigger, convective onset time is delayed by 1-4 h; however, the time of peak precipitation is unchanged. This diurnal shift improves the number of hours the deep convective scheme is invoked from more than 75% to less than 50%, alleviating the overactivity problem. The delayed onset time of deep convection allows for greater CAPE accumulation and a greater proportion of precipitation generated outside the convective scheme. More CAPE consequently produces an overall increase in intense precipitation events. [ABSTRACT FROM AUTHOR]

The subgrid connection for the space-time finite integration technique is optimized based on the propagation condition of plane waves. This condition results in an algebraic equation determining the optimization parameters for the grid connection. Two-dimensional wave propagation simulations show that this method generates optimal subgrid connections that reduce unphysical wave reflections. [ABSTRACT FROM AUTHOR]

Many wildfire behavior modeling studies have focused on fires during extreme conditions, where the dominant processes are resolved and smaller-scale variations have less influence on fire behavior. As such, wildfire behavior models typically perform well for these cases. However, they can struggle in marginal conditions (e.g. low-intensity fire) as small-scale variations significantly influence fire physics at scales below grid resolution. In an effort to generalize wildfire behavior models and improve their overall performance, we have developed a new set of equations for wet and dry fuel to capture the finer-scale sub-grid variations in temperature and moisture. We explore the behavior of these equations in simple scenarios ranging from high- to low-intensity fire. Furthermore, we evaluate the performance against observations of surface fire. In all cases the proposed model performs well after peak temperature is reached; however, the rise of fuel temperature at the onset of combustion is faster than expected. • A new set of fuel equations for the conservation of mass and energy in wildfire behavior models is developed. • Sub-grid variations in temperature and moisture are modeled using closure methods. • In low-intensity fire scenarios, the model is sensitive to moisture content of the fuel and gas temperature changes. • Simulations are compared to experimental surface fires. [ABSTRACT FROM AUTHOR]

This study proposes an efficient method of local space-time grid refinement and examines the numerical stability and the accuracy of electromagnetic field analysis using the space-time finite-integration technique (FIT). The proposed subgrid method locally refines the space-time grid with three-division or four-division and is stable without inducing numerical instability even after one million time-steps. The grid construction is modified at the corner part of subgrid connection to improve the computational accuracy. The staircase-type grid relaxes the time-step restriction due to the CFL condition. [ABSTRACT FROM AUTHOR]

To improve the accuracy and the efficiency of morphodynamic simulations, we present a subgrid based approach for a morphodynamic model. This approach is well suited for areas characterized by sub-critical flow, like in estuaries, coastal areas and in low land rivers. This new method uses a different grid resolution to compute the hydrodynamics and the morphodynamics. The hydrodynamic computations are carried out with a subgrid based, two-dimensional, depth-averaged model. This model uses a coarse computational grid in combination with a subgrid. The subgrid contains high resolution bathymetry and roughness information to compute volumes, friction and advection. The morphodynamic computations are carried out entirely on a high resolution grid, the bed grid. It is key to find a link between the information defined on the different grids in order to guaranty the feedback between the hydrodynamics and the morphodynamics. This link is made by using a new physics-based interpolation method. The method interpolates water levels and velocities from the coarse grid to the high resolution bed grid. The morphodynamic solution improves significantly when using the subgrid based method compared to a full coarse grid approach. The Exner equation is discretised with an upwind method based on the direction of the bed celerity. This ensures a stable solution for the Exner equation. By means of three examples, it is shown that the subgrid based approach offers a significant improvement at a minimal computational cost. [ABSTRACT FROM AUTHOR]

A wide variety of coastal ocean models exist, each having attributes that reflect specific application areas. The model presented here is based on finite element methods with unstructured grids containing triangular and quadrilateral elements. The model optimizes robustness, accuracy, and efficiency by using semi-implicit methods in time in order to remove the most restrictive stability constraints, by using a semi-Lagrangian advection approximation to remove Courant number constraints, and by solving a wave equation at the discrete level for enhanced efficiency. An added feature is the approximation of the effects of subgrid objects. Here, the Reynolds-averaged Navier–Stokes equations and the incompressibility constraint are volume averaged over one or more computational cells. This procedure gives rise to new terms which must be approximated as a closure problem. A study of tidal power generation is presented as an example of this method. A problem that arises is specifying appropriate thrust and power coefficients for the volume averaged velocity when they are usually referenced to free stream velocity. A new contribution here is the evaluation of three approaches to this problem: an iteration procedure and two mapping formulations. All three sets of results for thrust (form drag) and power are in reasonable agreement. [ABSTRACT FROM AUTHOR]

We present the development of a high-efficiency and high-resolution subgrid model for simulating flooding and draining processes in salt marshes or tidal flats. The model integrates the concepts of Defina's (2000) subgrid model and the ideas of Volp et al. (2013) on treatment of the feedback of fine grid effects into coarse grid calculations. A pre-storage method is proposed to pre-calculate coarse cell-wise integrated variables associated with high resolution bathymetry data in order to further improve the model efficiency. Model validations are conducted in an idealized channel-flat system as well as a meso-tidal salt marsh. Results show that the subgrid model is capable of obtaining results which are comparable to those from the full grid model running directly on the high-resolution grid, but the computational cost can be orders of magnitude smaller than the full grid model due to the reduction in the number of computational cells and the increase in time-step size. Flows over subgrid micro-topography features like narrow channels and creeks can also be modeled, which is crucial for simulating flow routing in marsh networks. With the increasing availability of high-resolution coastal topographic data and the need for high-resolution modeling, the model is promising for applications to large-scale salt marsh modeling. [ABSTRACT FROM AUTHOR]

A common way of carrying out LES or RANS of premixed and partially premixed turbulent flames with tabulated combustion chemistry consists of using a presumed shape for the probability density function (PDF) of progress variable and mixture fraction in order to compute the reaction rates. Commonly utilized for this purpose is the β -function PDF. To the aim of clarifying the applicability of the presumed β -PDF approach to the modeling of methane and hydrogen turbulent premixed flames, in this paper an investigation of the probability density distribution is performed by processing three-dimensional DNS computational results performed with detailed chemistry. This analysis is performed by means of a detailed comparison between the DNS data and the corresponding a priori LES obtained with top-hat filters of various sizes. The analysis is conducted for hydrogen and methane turbulent flames, for comparison. In particular, it is assessed whether a lean premixed turbulent hydrogen-air flame can be well-represented in LES by a β -PDF approach as traditionally applied for methane in literature. It is shown that the presumed β -PDF model performs rather well for both hydrogen and methane. The total error between the real distribution and the presumed β -PDF is of comparable amount for the two fuels. However, the error shows a more consistent profile in methane flames. In addition, it is shown that mean and variance are not sufficient as control parameters for an improved modeling of hydrogen flames by means of presumed PDF, plausibly because of its strong differentially diffusive effects. [ABSTRACT FROM AUTHOR]

We perform an a priori analysis of the subfilter-scale ( SFS) conservation equations for the stably stratified atmospheric boundary layer ( ABL). Using data from the Horizontal Array Turbulence Studies ( HATS) experiment, we build on previous studies by exploring in greater detail the scale dependence of the mean and root-mean-square (r.m.s.) values of the production terms in the SFS stress and flux budgets. Our analysis shows production terms that are the dominant generation mechanisms for the SFS stresses and fluxes in conditions of under-resolved turbulence, also contribute significantly to their fluctuation levels. From the fluctuation levels of the production terms, we infer that fluctuations in terms other than the production terms (i.e. advection, transport and destruction) must be associated with strong auto-correlations or cross-correlations (with the production terms) for filter widths much finer than the length-scale for the most energetic eddies. For filter widths too coarse to resolve the most energetic eddies, we are unable either to confirm or rule out this possibility. The dominant production terms in the SFS stress budgets, upon suitable scaling, exhibit limiting values as we approach the Reynolds-averaged Navier-Stokes ( RANS) limit, i.e. when the turbulence resides entirely at the subfilter scales. The values in the RANS limit agree well with both existing analytical arguments and a previous LES study of the moderately convective ABL. The agreement between a priori and a posteriori statistics suggests consistency between the two methods is achievable in the RANS limit with the appropriate choice of scaling parameters. [ABSTRACT FROM AUTHOR]

This study presents a finite volume hydrodynamic model for shallow water flow that computes on a coarse grid, but accounts for high-resolution bathymetry and roughness variations on a subgrid. The detailed information can be incorporated by using the assumption of a uniform flow direction and a uniform friction slope within a part of a coarse-grid cell. It is shown in two examples that the results of coarse-grid simulations become as good as high-resolution results, but at much lower computational cost. [ABSTRACT FROM AUTHOR]

Abstract: The Huygens subgridding (HSG) is a subgridding technique developed for the numerical solution of the Maxwell equations. It relies on the theoretical equivalence of any physical volume with two or more fictitious volumes connected by equivalent currents. The application of this concept to the finite-difference time-domain (FDTD) method has been previously published in the one dimensional and two dimensional cases. In this paper the HSG is extended to the general three dimensional case, the exchange of the electromagnetic energy between the two FDTD grids is investigated theoretically, and some modifications to the HSG algorithm are presented with the objective of simplifying its implementation. [Copyright &y& Elsevier]

A subgrid-scale parameterization scheme motivated by statistical closure theory, but employing statistics obtained from high-resolution direct numerical simulations, is applied to large eddy simulations of two-level quasigeostrophic turbulence on the sphere. It is shown that these parameterizations are consistent with the phenomenology of quasigeostrophic turbulence. The parameterizations consist of 2 × 2 dissipation and stochastic forcing covariance matrices at each wavenumber, with the off-diagonal elements of the matrices representing vertical mixing. Two flow regimes, characterized by their deformation scales, are considered, namely atmospheric and oceanic. In the former, the deformation scale is fully resolved, and the truncation scale is within the enstrophy cascading interial range. In the latter, the deformation scale is not fully resolved, and the truncation scale is within the energy cascading inertial range. It is demonstrated through numerical experiments that both stochastic and deterministic variants of the scheme give comparable results for the energy spectra in the atmospheric regime. In the oceanic regime, the stochastic variant again gives excellent results, but the deterministic variant is found to be numerically unstable. [ABSTRACT FROM AUTHOR]

A wide range of wireless system developments require knowledge of the distribution of electromagnetic fields from various sources in humans. As experimental assessment is ethically unacceptable, high-resolution numerical dosimetry is needed. The finite-difference time-domain method is the most appropriate due to its simplicity and versatility. Reduction in demands on computational resources can be achieved using subgridding techniques. This paper rigorously introduces frequency dependency to one of the most promising subgridding techniques, Huygens subgridding. The validity of the Huygens surface in lossy media, as well as on the physical interface, is intensively studied. [ABSTRACT FROM AUTHOR]

This paper extends to two dimensions the finite-difference time-domain Huygens subgridding algorithm previously published in the one dimensional case. The algorithm is described in detail and several numerical experiments are provided to illustrate its possibilities and to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

We present an extension module for the D une system. This module, called dune-subgrid, allows to mark elements of another D une hierarchical grid. The set of marked elements can then be accessed as a D une grid in its own right. dune-subgrid is free software and is available for download (External D une Modules: ). We describe the functionality and use of dune-subgrid, comment on its implementation, and give two example applications. First, we show how dune-subgrid can be used for micro-FE simulations of trabecular bone. Then we present an algorithm that allows to use exact residuals for the adaptive solution of the spatial problems of time-discretized evolution equations. [ABSTRACT FROM AUTHOR]

Flow and transport in subsurface formations are affected by geological variability over multiple length scales. In this work, we develop a local-global two-phase upscaling approach to generate upscaled transport functions. The upscaling of multiphase flow parameters is challenging, due to their strong dependency on global flow effects. The local-global two-phase upscaling directly incorporates global coarse-scale two-phase solutions into local two-phase upscaling calculations. It effectively captures the impact of global flow, while avoiding global two-phase fine-scale simulations. The local boundary conditions are updated with time-dependent coarse-scale solutions. It therefore captures the global flow effects both spatially and temporally. The method is applied to permeability distributions with various correlation lengths and for different fluid-mobility ratios. Numerical results show that it consistently improves upon existing two-phase upscaling methods (e.g., upscaling with effective flux boundary conditions) and provides accurate coarse-scale solutions for both flow and transport. [ABSTRACT FROM AUTHOR]

Aiming at the better prediction of inertial particle dispersion in LES of turbulent shear flow, a stochastic diffusion process of the Langevin type is adopted to model the time increments of the fluid velocity seen by inertial particles. This modelling is particularly crucial for dispersion and deposition of inertial particles with small relaxation times compared to the smallest LES-resolved turbulence time scales. Simple closures for drift and diffusion terms are described. The effects of inertia and external forces on particle trajectories are modelled. To numerically validate the proposed model, LES calculations are performed to track solid particles (glass beads in air with different Stokes' numbers) in a high Reynolds number, equilibrium turbulent pipe flow (Re = 50 000 based on the maximum velocity and the pipe diameter). LES predictions are compared to RANS results and experimental observations. Simulation findings demonstrate the superiority of LES compared to RANS in predicting particle dispersion statistics. More importantly, the use of a stochastic approach to model the subgrid scale fluctuations has proven crucial for results concerning the small-Stokes-number particles. The influence of the model on particle deposition needs to be assessed and additional validation for non-equilibrium turbulent flows is required. [ABSTRACT FROM AUTHOR]

Abstract: Significant advances in flood inundation modelling have been made in the last decade through the use of a new generation of 2D hydraulic numerical models. These offer the potential to predict the local pattern and timing of flood depth and velocity, enabling informed flood risk zoning and improved emergency planning. With the availability of high resolution DEMs derived from airborne lidar, these models can theoretically now be routinely parameterized to represent considerable topographic complexity, even in urban areas where the potential exists to represent flows at the scale of individual buildings. Currently, however, computational constraints on conventional finite element and volume codes typically require model discretization at scales well below those achievable with lidar and are thus unable to make optimal use of this emerging data stream. In this paper we review two strategies that attempt to address this mismatch between model and data resolution in an effort to improve urban flood forecasts. The first of these strives for a solution by simplifying the mathematical formulation of the numerical model by using a computationally efficient 2D raster storage cell approach coupled to a 1D channel model. This parsimonious model structure enables simulations over large model domains offering the opportunity to employ a topographic discretization strategy which explicitly represents the built environment. The second approach seeks to further reduce the computational overhead of this raster method by employing a subgrid parameterization to represent the effect of buildings and micro-relief on flow pathways and floodplain storage. This multi-scale methodology enables highly efficient model applications at coarse spatial resolutions while retaining information about the complex geometry of the built environment. These two strategies are evaluated through numerical experiments designed to reconstruct a flood in the small town of Linton in southern England, which occurred in response to a 1 in 250 year rainfall event in October 2001. Results from both approaches are encouraging, with the spatial pattern of inundation and flood wave propagation matching observations well. Both show significant advantages over a coarse resolution model without subgrid parameterisation, particularly in terms of their ability to reproduce both hydrograph and inundation depth measurements simultaneously, without need for recalibration. The subgrid parameterization is shown to achieve this without contributing significant computational complexity and reduces model run-times by an order of magnitude. [Copyright &y& Elsevier]

A finite-different time-domain subgrid algorithm locally refines the mesh at regions requiring higher resolution. A novel separation of spatial and temporal subgridding interfaces is presented that allows implementing a novel spatial subgridding method and investigating the stability of each subalgorithm individually. Details are given for a spatial subgridding algorithm having a 1:3 mesh ratio. In the spatial subgridding algorithm, the fine-mesh is constructed with a recessed interface and the interpolation scheme is designed to be symmetric to maintain the stability of the update process. The stability of the spatial subgridding algorithm is analyzed with a matrix method. Numerical examples showing stability and accuracy are provided. [ABSTRACT FROM AUTHOR]

Abstract: Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine scale permeability variations through the calculation of specialized coarse scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. This can be accomplished using global fine scale simulations, but this may be computationally expensive. In this paper an adaptive local–global technique, originally developed within the context of upscaling, is applied for the computation of multiscale basis functions. The procedure enables the efficient incorporation of approximate global information, determined via coarse scale simulations, into the multiscale basis functions. The resulting procedure is formulated as a finite volume element method and is applied for a number of single- and two-phase flow simulations of channelized two-dimensional systems. Both conforming and nonconforming procedures are considered. The level of accuracy of the resulting method is shown to be consistently higher than that of the standard finite volume element multiscale technique based on localized basis functions determined using linear pressure boundary conditions. [Copyright &y& Elsevier]

To dynamically improve system selections of the waiting jobs under de-centralized scheduling frameworks, each computation system together with its neighbors is assumed to compose a subgrid, and distributed backfilling is proposed as the scheduling strategy in each subgrid. Whenever a job terminates, distributed backfilling is triggered to re-backfill all waiting jobs on the corresponding subgrid in order of their submittal. Each subgrid is overlapped with another, so the waiting jobs may be migrated around the Grid. To evaluate distributed backfilling, Grid resources and scheduling framework are configured, the model of Grid workload is constructed by extending the workload models of parallel systems and the Job Scheduling Simulation System is designed to simulate the process of de-centralized job scheduling. In addition, job speedup is presented as performance metrics of scheduling strategies. Results show the dynamic optimization of system selections brought by distributed backfilling is Grid-wide, and can improve scheduling performance remarkably as long as Grid load is not too light and the job migration costs are not too high. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A new subgridding technique is presented for the finite-difference time-domain (FDTD) method. The connection between the grid and the subgrid is realized by means of equivalent currents. The ratio of the steps of the grids can be arbitrarily large, and no significant reflection is produced from the grids interface. The principle of the method is presented in the continuous three dimensional space. The FDTD algorithm is described in detail in the one dimensional case. [ABSTRACT FROM AUTHOR]

Geological variability occurring over multiple length scales can significantly affect fluid flow in subsurface formations. In this paper we explore the impact of large scale (global) information on the accuracy of coarse scale models for two-phase flow and transport. Based on these findings, a new methodology for generating coarse models is introduced. This approach, which avoids any global fine scale calculations, entails adaptive local-global single-phase parameter upscaling coupled with subgrid models for two-phase parameters. Two related subgrid treatments for two-phase flow effects-a pseudorelative permeability model and a generalized convection-diffusion model-are investigated and applied. The upscaled single-phase parameters (transmissibilities), computed using the adaptive local-global procedure, account explicitly for global boundary conditions as they are adapted for a specific flow scenario. The two-phase coarse scale functions are computed from local simulations using effective flux boundary conditions (EFBCs), which account approximately for global effects in the local computations. The advantages of the adaptive local-global upscaled single-phase parameters, as well as the superior accuracy of EFBCs relative to standard treatments for two-phase parameters, are demonstrated for several challenging two-dimensional example cases. The overall method is also applied to highly heterogeneous systems with global boundary conditions that vary in time. Using standard upscaling methods, errors for some of these cases are very large, though the new methodology is shown to consistently provide reasonably accurate coarse models. [ABSTRACT FROM AUTHOR]

For flow problems, turbulence models and numerical methods can be thought of as model reductions. Herein we consider reduction imposed as a constraint using Lagrange multipliers. Development of this last method recovers the subgrid eddy viscosity method and a new stabilization of the incompressibilty constraint. Analysis of the new incompressibility stabilization reveals that stabilization is only really needed for the finest pressure scales. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a two-scale theoretical framework for approximating the solution of a second order elliptic problem. The elliptic coefficient is assumed to vary on a scale that can be resolved on a fine numerical grid, but limits on computational power require that computations be performed on a coarse grid. We consider the elliptic problem in mixed variational form over W × V ⊂ L² × H(div). We base our scale expansion on local mass conservation over the coarse grid. It is used to define a direct sum decomposition of W × V into coarse and "subgrid" subspaces Wc × Vc and δW × δV such that (1) ∇ · Vc = Wc and ∇ · δV = δW, and (2) the space δV is locally supported over the coarse mesh. We then explicitly decompose the variational problem into coarse and subgrid scale problems. The subgrid problem gives a well-defined operator taking Wc × Vc to δW × δV, which is localized in space, and it is used to upscale, that is, to remove the subgrid from the coarse-scale problem. Using standard mixed finite element spaces, two-scale mixed spaces are defined. A mixed approximation is defined, which can be viewed as a type of variational multiscale method or a residual-free bubble technique. A numerical Green's function approach is used to make the approximation to the subgrid operator efficient to compute. A mixed method π-operator is defined for the two-scale approximation spaces and used to show optimal order error estimates. [ABSTRACT FROM AUTHOR]

Subgrid models for the reaction terms in Large Eddy Simulation of turbulent flows are studied. The subgrid density is commonly approximated by a beta law. The optimal estimates for this problem are investigated. This shows that the choice of beta distributions is well founded. The largest error comes from the choice of the fundamental parameters of the model and not from the shape of the distribution itself. It is thus shown that the optimal estimates are a relevant tool for the investigation of subgrid modelling and the identification of directions for future improvements. To cite this article: A. Moreau et al., C. R. Mecanique 332 (2004). [Copyright &y& Elsevier]

A new technique for generating coarse scale models of highly heterogeneous subsurface formations is developed and applied. The method uses generic global coarse scale simulations to determine the boundary conditions for the local calculation of upscaled properties (permeability or transmissibility). An iteration procedure assures consistency between the local and global calculations. Transport processes are simulated using a subgrid velocity reconstruction technique applied in conjunction with the local–global upscaling procedure. For highly heterogeneous (e.g., channelized) systems, the new method is shown to provide considerably more accurate coarse scale models for flow and transport, relative to reference fine scale results, than do existing local (and extended local) upscaling techniques. The applicability of the upscaled models for different global boundary conditions is also considered. [Copyright &y& Elsevier]

We present a locally mass conservative scheme for the approximation of two-phase flow in a porous medium that allows us to obtain detailed fine scale solutions on relatively coarse meshes. The permeability is assumed to be resolvable on a fine numerical grid, but limits on computational power require that computations be performed on a coarse grid. We define a two-scale mixed finite element space and resulting method, and describe in detail the solution algorithm. It involves a coarse scale operator coupled to a subgrid scale operator localized in space to each coarse grid element. An influence function (numerical Greens function) technique allows us to solve these subgrid scale problems independently of the coarse grid approximation. The coarse grid problem is modified to take into account the subgrid scale solution and solved as a large linear system of equations posed over a coarse grid. Finally, the coarse scale solution is corrected on the subgrid scale, providing a fine grid representation of the solution. Numerical examples are presented, which show that near-well behavior and even extremely heterogeneous permeability barriers and streaks are upscaled well by the technique. [ABSTRACT FROM AUTHOR]

Coastal flooding models are used to predict the timing and magnitude of inundation during storms, both for real-time forecasting and long-term design. However, there is a need for faster flooding predictions that also represent flow pathways and barriers at the scales of critical infrastructure. This need can be addressed via subgrid corrections, which use information at smaller scales to 'correct' the flow variables (water levels, current velocities) averaged over the mesh scale. Recent studies have shown a decrease in run time by 1 to 2 orders of magnitude, with the ability to decrease further if the model time step is also increased. In this study, subgrid corrections are added to a widely used, finite-element-based, shallow water model to better understand how they can improve the accuracy and efficiency of inundation predictions. The performance of the model, with and without subgrid corrections, is evaluated on scenarios of tidal flooding in a synthetic domain and a small bay in Massachusetts, as well as a scenario with a real atmospheric forcing and storm surge in southwest Louisiana. In these tests we observed that the subgrid corrections can increase model speed by 10 to 50 times, while still representing flow through channels below the mesh scale to inland locations. • Coastal flooding may be controlled by flow channels and barriers at very small scales. • These flow features can be represented at the mesh scale with subgrid corrections. • ADCIRC model was corrected for subgrid flows in tide and storm surge predictions. • Close matches to peak water levels with models that are 65 times coarser than before. • Significant speed-ups will allow for faster predictions and ensemble forecasts. [ABSTRACT FROM AUTHOR]