Grid Resolution Research Articles

Complete Dynamics from Ignition to Stabilization of a Lean Hydrogen Flame with Thickened Flame Model

Abstract In recent years, attention has been paid to hydrogen thanks to its carbon-free nature and its interesting characteristics as an energy vector. Despite the large number of numerical analyses regarding hydrocarbon combustion in all the steady and unsteady processes, few papers that cover all those aspects are available in the literature for hydrogen flames. Therefore, a numerical methodology to explore the complete ignition sequence from the spark release to the flame stabilization is validated on a single-sector hydrogen burner. In this context, a preliminary DNS investigation of laminar spherical expanding flames is performed using different diffusive transport models to isolate their impact. The present work, carried out within the European project HESTIA, investigates the atmospheric test rig installed at the Norwegian University of Science and Technology operating with a lean, perfectly premixed, hydrogen-air flame stabilized on a conical bluff body. Four simulations are performed adopting the Thickened Flame Model with an energy deposition strategy to assess the impact of preferential and thermal diffusion, as well as grid resolution, on flame dynamics. 3D flame structure visualization coupled with detailed PIV/OH-PLIF measurements allows the investigation of the key mechanisms involved during the ignition. The dynamic response of the flame through axial fluctuations once the ignition transient is concluded, is reconstructed by the numerical strategy employed. Although the overall behavior is almost unchanged by including or not thermal diffusion effects, their local impact on the flame is evident leading to a better agreement with experimental data.

Heat Distribution Simulation in a Square Aluminum 7075 Plate Using Laplace Equation and MATLAB

The efficient management of heat transfer from aircraft engines to the wings is vital for maintaining thermal efficiency and structural integrity in modern aircraft design. Excessive heating of the wings, caused by engine-generated heat, can negatively impact aerodynamic performance and safety. This study focuses on analyzing heat distribution in a square aluminum 7075 plate to better understand heat transfer mechanisms. Using the Laplace equation, implemented through MATLAB (2023 Online Version), we aim to simulate and analyze heat distribution on the plate. The numerical method employed in this research involves solving the Laplace equation with Neumann boundary conditions, which represent insulated edges. The Liebmann method is used to iteratively reduce error to less than 1%. Simulations are conducted on an aluminum 7075 plate of dimensions 4x10⁻² m x 4x10⁻² m under various temperature conditions at the edges. Numerical results show that at the 9th iteration, the error reaches 0.71%, while MATLAB simulations yield an error of 0.4681% at the same iteration. The heat distribution across the plate is clearly visualized, and the analysis indicates that increasing the number of grids improves both the clarity and accuracy of the simulation results. In conclusion, this study demonstrates that applying the Laplace equation via MATLAB is an effective approach for analyzing heat distribution in aluminum 7075 plates. The results show that a finer grid resolution enhances accuracy, with a 101-grid system providing particularly clear and precise heat distribution patterns. These findings contribute to the optimization of thermal system designs, especially in aviation-related applications.

GPU-enabled extreme-scale turbulence simulations: Fourier pseudo-spectral algorithms at the exascale using OpenMP offloading

Fourier pseudo-spectral methods for nonlinear partial differential equations are of wide interest in many areas of advanced computational science, including direct numerical simulation of three-dimensional (3-D) turbulence governed by the Navier-Stokes equations in fluid dynamics. This paper presents a new capability for simulating turbulence at a new record resolution up to 35 trillion grid points, on the world's first exascale computer, Frontier, comprising AMD MI250x GPUs with HPE's Slingshot interconnect and operated by the US Department of Energy's Oak Ridge Leadership Computing Facility (OLCF). Key programming strategies designed to take maximum advantage of the machine architecture involve performing almost all computations on the GPU which has the same memory capacity as the CPU, performing all-to-all communication among sets of parallel processes directly on the GPU, and targeting GPUs efficiently using OpenMP offloading for intensive number-crunching including 1-D Fast Fourier Transforms (FFT) performed using AMD ROCm library calls. With 99% of computing power on Frontier being on the GPU, leaving the CPU idle leads to a net performance gain via avoiding the overhead of data movement between host and device except when needed for some I/O purposes. Memory footprint including the size of communication buffers for MPI_ALLTOALL is managed carefully to maximize the largest problem size possible for a given node count.Detailed performance data including separate contributions from different categories of operations to the elapsed wall time per step are reported for five grid resolutions, from 20483 on a single node to 327683 on 4096 or 8192 nodes out of 9408 on the system. Both 1D and 2D domain decompositions which divide a 3D periodic domain into slabs and pencils respectively are implemented. The present code suite (labeled by the acronym GESTS, GPUs for Extreme Scale Turbulence Simulations) achieves a figure of merit (in grid points per second) exceeding goals set in the Center for Accelerated Application Readiness (CAAR) program for Frontier. The performance attained is highly favorable in both weak scaling and strong scaling, with notable departures only for 20483 where communication is entirely intra-node, and for 327683, where a challenge due to small message sizes does arise. Communication performance is addressed further using a lightweight test code that performs all-to-all communication in a manner matching the full turbulence simulation code. Performance at large problem sizes is affected by both small message size due to high node counts as well as dragonfly network topology features on the machine, but is consistent with official expectations of sustained performance on Frontier. Overall, although not perfect, the scalability achieved at the extreme problem size of 327683 (and up to 8192 nodes — which corresponds to hardware rated at just under 1 exaflop/sec of theoretical peak computational performance) is arguably better than the scalability observed using prior state-of-the-art algorithms on Frontier's predecessor machine (Summit) at OLCF. New science results for the study of intermittency in turbulence enabled by this code and its extensions are to be reported separately in the near future.

Effects of grid resolution on regional modelled groundwater salinity and salt fluxes to surface water

Coastal fresh groundwaters face growing threats from rising withdrawals and climate change, with salinization of surface and groundwater as notable impacts. Recent developments in parallel variable-density modelling enable studying these threats at unexplored resolutions and extents. To improve the understanding of ground- and surface water salinization processes, we designed an experiment to measure how spatial resolution affects both groundwater salinity distribution and salt loads to surface waters. An existing parallelized coupled variable-density groundwater flow and salt transport (VD-GWT) model is applied to a region in the Netherlands whereby the surface water drainage network is parameterized at grid resolutions between 10 and 250 m. The results show a strong dependency between resolution and the salinity distribution in shallow groundwater while simulated salt loads are affected by imperfect flux scaling. The computational resources needed for this test suggest that regional high-resolution VD-GWT models are feasible using HPC environments, albeit not practical.

Enhancing subsurface multiphase flow simulation with Fourier neural operator

Accurate numerical modeling of multiphase flow in subsurface oil and gas reservoirs is critical for optimizing hydrocarbon recovery. However, traditional physics-based algorithms face substantial computational hurdles due to the need for fine grid resolution and the inherent geological heterogeneity. To overcome these challenges, data-driven surrogate models solving the flow governing partial differential equations (PDEs) offer a promising alternative to enhance the efficiency of hydrocarbon production operations. In this study, we employ the Fourier Neural Operator (FNO) to extract spectral information from the reservoir properties, thereby facilitating the solution of coupled porous flow PDEs. Our focus is on two-phase flow dynamics, specifically exploring how water injection enhances reservoir pressure and displaces oil. This scenario involves solving a set of nonlinearly coupled PDEs with highly heterogeneous coefficients. Numerical results demonstrate that the developed FNO accurately predicts the reservoir pressure distributions. We further observe that the FNO's zero-shot super-resolution capability is sensitive to abrupt local changes in the reservoir pressure near injection and production wells. To enhance its accuracy, we propose a multi-fidelity FNO model that exhibits better adaptability across various grid configurations. After moderate training on graphics processing units (GPUs), the FNO achieves a speedup of three orders of magnitude compared to traditional numerical PDE solvers. Our experiments confirm the FNO's potential to replace repetitive physics-based simulations, significantly advancing computational efficiency in the uncertainty quantification of reservoir performance.

On warm bias and mesoscale dynamics setting the Southern Ocean large-scale circulation mean state

A realistic representation of the Southern Ocean (SO) in climate models is critical for reliable global climate projections. However, many models are still facing severe biases in this region. Using a fully coupled global climate model at non-eddying (1/2∘) and strongly eddying (1/10∘) grid resolution in the SO, we investigate the effect of a 0.5 °C, 1.0 °C and 1.6 °C warmer than observed SO on i) the spin-up behaviour of the high-resolution simulation, and ii) the representation of main dynamical features, i.e., the Antarctic circumpolar current (ACC), the subpolar gyres, the overturning circulation and the Agulhas regime in a quasi-equilibrium state. The adjustment of SO dynamics and hydrography critically depends on the initial state and grid resolution. When initialised with an observed ocean state, only the non-eddying configuration quickly builds up a strong warm bias in the SO. The high-resolution configuration initialised with the biased non-eddying model state results in immense spurious open ocean deep convection, as the biased ocean state is not stable at eddying resolution, and thus causes an undesirable imprint on global circulation. The SO heat content also affects the large-scale dynamics in both low- and high-resolution configurations. A warmer SO is associated with a stronger Agulhas current and a temperature-driven reduction of the meridional density gradient at 45∘S to 65∘S and thus a weaker ACC. The eddying simulations have stronger subpolar gyres under warmer conditions while the response in the non-eddying simulations is inconsistent. In general, SO dynamics are more realistically represented in a mesoscale-resolving model at the cost of requiring an own spin-up.

Development of an Aerosol Assimilation System Using a Global Non‐Hydrostatic Model, a 2‐Dimensional Variational Method, and Multiple Satellite‐Based Aerosol Products

AbstractThe computational balance between the model grid resolution and the complexity of the data assimilation technique is essential for accurate aerosol forecasting and obtaining aerosol reanalysis data sets. This study aimed to develop a high‐resolution aerosol assimilation system. A 2‐dimensional variational method (2DVar) was implemented in a non‐hydrostatic icosahedral atmospheric model (NICAM). This new model (NICAM/2DVar), with a global grid size of 56 km, assimilated the observed aerosol optical depth (AOD) that is estimated by combining multiple products of geostationary and polar‐orbital satellites. The model results were evaluated against ground‐based AOD observations on a global scale. They exhibited higher correlations, lower uncertainties, and lower biases than those obtained without the 2DVar. The model also reproduced the observed surface aerosols (PM2.5) mass concentrations, especially in Kyushu, Japan. This occurred because the satellite‐estimated AODs over ocean close to air pollution sources were obtained for many occasions. The correlation coefficient values against the PM2.5 observations increased from 0.44 to 0.65 compared to the results without the 2DVar. The impact of the 2DVar on the forecast results was investigated, and the forecast values for 2–3 days were improved. Because satellite‐retrieved AODs are often lacking over land owing to retrieval difficulties, the use of ground‐based AODs in assimilations is essential for precise processing the of aerosol reanalysis data sets. The computational cost with the use of the 2DVar was only 0.6% more than that without its use. Thus, aerosol assimilation using the NICAM/2DVar can be realistically extended to finer grid sizes.

Exploring climate-change impacts on streamflow and hydropower potential: insights from CMIP6 multi-GCM analysis

ABSTRACT The generation of hydropower is profoundly influenced by shifts in streamflow patterns induced by climate change. This research examines changes in streamflow and the potential surge in hydropower generation over a span of 35 years (2015–2050) at the Bhakra Dam site within the Upper Sutlej River basin. Employing a deep learning methodology, particularly the long short-term memory (LSTM) model, in conjunction with Coupled Model Intercomparison Project (CMIP) 6 multi-global climate model (GCM), facilitates a thorough analysis of these dynamics. Six out of 14 bias-corrected statistically downscaled datasets (0.25° × 0.25° grid resolution) from CMIP6 multi-GCM were selected based on entropy and combined compromise solution techniques. This innovative approach is utilized to assess streamflows and project potential increases in hydropower at the Bhakra Dam site under shared socioeconomic pathways (SSP) scenarios, specifically SSP245 and SSP585. The results indicate a maximum increase of approximately 15% and 17% in mean monthly streamflow under SSP245 and SSP585, respectively. Moreover, dependability flows calculated at Q50, Q75, and Q90 show respective rises of 13%, 16%, and 17% under SSP245 and 21%, 17%, and 18% under SSP585. The projected hydropower potential exhibits an increase of up to 15.9% and 17.3% under SSP245 and SSP585, respectively.

A Framework for Iterative Phase Retrieval Technique Integration into Atmospheric Adaptive Optics—Part I: Wavefront Sensing in Strong Scintillations

The objective of this study, which is divided into two parts, is twofold: to address long-standing challenges in the sensing of atmospheric turbulence-induced wavefront aberrations under strong scintillation conditions via a comparative analysis of several basic scintillation-resistant wavefront sensing (SR-WFS) architectures and iterative phase retrieval (IPR) techniques (Part I, this paper), and to develop a framework for the potential integration of SR-WFS techniques into practical closed-loop non-astronomical atmospheric adaptive optics (AO) systems (Part II). In this paper, we consider basic SR-WFS mathematical models and phase retrieval algorithms, tradeoffs in sensor design and phase retrieval technique implementation, and methodologies for WFS parameter optimization and performance assessment. The analysis is based on wave-optics numerical simulations imitating realistic turbulence-induced phase aberrations and intensity scintillations, as well as optical field propagation inside the SR-WFSs. Several potential issues important for the practical implementation of SR-WFS and IPR techniques, such as the requirements for phase retrieval computational grid resolution, tolerance with respect to optical element misalignments, and the impact of camera noise and input light non-monochromaticity, are also considered. The results demonstrate that major wavefront sensing requirements desirable for AO operation under strong intensity scintillations can potentially be achieved by transitioning to novel SR-WFS architectures, based on iterative phase retrieval techniques.

Enhanced urban PM2.5 prediction: Applying quadtree division and time-series transformer with WRF-chem

Accurately predicting air quality levels in urban landscapes is a key environmental and public health challenge due to the complex interactions between pollutant emissions, atmospheric chemistry, and meteorological conditions. Chemical transport models such as Community Multiscale Air Quality (CMAQ) and Weather Research and Forecasting Modeling with Chemistry (WRF-Chem) provide fundamental insights into the behavior of atmospheric pollutants but face limitations in spatial resolution and prediction accuracy. Machine learning combined with low-cost sensors can improve prediction accuracy compared to numerical models, but uneven sensor distribution may result in biased prediction results. To address these limitations, this study introduces an innovative framework that leverages a quadtree space division to refine the numerical simulations of air pollutants into higher spatial resolutions by dynamically adjusting grid sizes based on the distribution of increased sensor deployments. Using a variable-resolution grid, the study first aggregates variables into a grid and then calculates spatial dependence based on grid cells. The deep-learning-based Time Series Transformer model is then used to perform detailed temporal predictions of PM2.5 concentration across the entire grid. The spatial and temporal modeling framework is designed to use the past 48 h' aggregated data, including meteorological variables from WRF-Chem numerical simulation and PM2.5 concentrations from ground monitoring stations and sensors, to predict future 48-h’ PM2.5 concentrations and tested across entire grids within Los Angeles County from January to June 2020. The results show that the performance of variable resolution grids is better than that of fixed grids regarding four metrics: minimum resolution, overall spatiotemporal RMSE, average bias, and prediction coverage. Among them, the variable resolution grids with up to 4 sensors showed the best performance, with an overall spatiotemporal RMSE of 1.12 μg/m3, which was about 40% lower than 2-sensor and 8-sensor variable resolution grids, a significant reduction of 55% compared to a 3 km fixed grid configuration. Future work will involve additional relevant factors such as emission sources and sinks to improve prediction accuracy.

Trend and inter-annual variability in regional climate models – Validation and hydrological implications in southeast Australia

We assessed the ability of Regional Climate Models (RCMs) to reproduce observed means, inter-annual variance and trends for rainfall indices that were important for runoff generation over southeast Australia. To establish the benefit of the RCM without being penalized or rewarded by the performance of the forcing GCM, we used ECMWF Re-Analysis-interim (ERA-Interim) to force the Weather Research and Forecasting model (WRF) and the Conformal Cubic Atmospheric Model (CCAM). The performance of two different configurations of each RCM was evaluated against an observational dataset (Australian Gridded Climate Data, AGCD) and compared with that of ERA-Interim. The assessments were carried out at both observational and ERA-Interim grid resolutions: ∼5 km and ∼80 km, respectively. As hypothesised, the RCMs outperformed ERA-Interim in representing spatial patterns and magnitude of mean rainfall, because of higher spatial resolution. RCMs also accurately represented the general spatial patterns of variance, but systematically underestimated the inter-annual variability over much of the domain. RCMs performed better than ERA-Interim in reproducing the magnitude of trends in some cases, especially in the decline of cool season rainfall in southeast Australia, which has had significant impacts on water resources. One of the two CCAM runs generally performed best across all rainfall indices, in part because of atmospheric spectral nudging and an improved land-surface model. Based on the findings, we have provided suggestions on where new research on the development of RCMs could be focused and recommendations relevant to the next generation of Australian hydro-climate projections generated from the sixth phase of the Coupled Model Intercomparison Project (CMIP6).

Efficient Path Planning Algorithm Based on Laser SLAM and an Optimized Visibility Graph for Robots

Mobile robots’ efficient path planning has long been a challenging task due to the complexity and dynamism of environments. If an occupancy grid map is used in path planning, the number of grids is determined by grid resolution and the size of the actual environment. Excessively high resolution increases the number of traversed grid nodes and thus prolongs path planning time. To address this challenge, this paper proposes an efficient path planning algorithm based on laser SLAM and an optimized visibility graph for mobile robots, which achieves faster computation of the shortest path using the optimized visibility graph. Firstly, the laser SLAM algorithm is used to acquire the undistorted LiDAR point cloud data, which are converted into a visibility graph. Secondly, a bidirectional A* path search algorithm is combined with the Minimal Construct algorithm, enabling the robot to only compute heuristic paths to the target node during path planning in order to reduce search time. Thirdly, a filtering method based on edge length and the number of vertices of obstacles is proposed to reduce redundant vertices and edges in the visibility graph. Additionally, the bidirectional A* search method is implemented for pathfinding in the efficient path planning algorithm proposed in this paper to reduce unnecessary space searches. Finally, simulation and field tests are conducted to validate the algorithm and compare its performance with classic algorithms. The test results indicate that the method proposed in this paper exhibits superior performance in terms of path search time, navigation time, and distance compared to D* Lite, FAR, and FPS algorithms.

Numerical simulation of deep-water wave breaking using RANS: Comparison with experiments

Wave breaking is a multifaceted physical phenomenon that is not fully understood and remains challenging to model. An effective method for investigating wave breaking involves utilising the two-phase Reynolds-averaged Navier–Stokes (RANS) equations to directly simulate breaking waves. In this study, we apply a RANS model with an adaptively refined mesh to simulate breaking waves in deep water using the stabilised RANS model proposed by Larsen and Fuhrman. This approach enables a more efficient simulation of the physics of breaking waves compared to Direct Numerical Simulations, as it places less stringent demands on grid resolution. Our findings demonstrate that the RANS model compares well with deep water wave breaking experiments in terms of surface elevation. We also give estimates of the breaking strength parameter of our RANS simulations and compared them with the literature.

On detailed representation of flood defences and flow-wave coupling in coastal flood modelling

Coastal flooding is projected to become more severe over the 21st century, necessitating effective adaptation, which in turn requires detailed local scale information that can only be provided by detailed numerical modelling. The current lack of information on flood protection measures and the high resource requirements of traditional hydrodynamic models presents concurrent challenges for detailed coastal flood modelling. But how comprehensive do the representation of coastal flood defences and hydrodynamic forcing need to be for adequately accurate modelling of coastal flooding? Here, we attempt to answer this question through strategic numerical simulations of the flooding that occurred at Île de Ré (France) during the Xynthia storm (2010), using the flexible mesh model Delft3D FM, with an over-land grid resolution of ~10 m. The model is validated against the flood extents observed in Île de Ré during Xynthia. We use three levels of detail in flood defence representation: a 5 m resolution DEM (i.e. base case DEM), the same 5 m DEM augmented with defences extracted from a 1 m DEM and Google Earth images (i.e. moderately augmented DEM), and the moderately augmented DEM further augmented with in-situ measurements of flood defences (i.e. highly augmented DEM). Simulations with these three DEMs are performed with and without flow-wave coupling (thus, 6 simulations in total), and results are analysed in terms of four flood indicators: maximum flood depths, flood extents, flood current velocities and flood damages. Our analysis indicates that both detailed representation of flood defences and the inclusion of waves have substantial effects on coastal flood modelling at local scale, with the former having a more pronounced effect. The return on the investment in implementing highly detailed in-situ measurements to represent flood defences appears to be low in this case, and adequately accurate results are obtained with a moderately augmented DEM. The combined effect of using the moderately augmented DEM together with waves, relative to using the base case DEM without waves, is to decrease maximum flood depths (up to 2 m), flood extent (by ~10%), maximum current velocities (in ~50% flooded area) and total flood damage (by ~27% or ~€ 188 million).

Wall Modeling of Turbulent Flows with Varying Pressure Gradients Using Multi-Agent Reinforcement Learning

We propose a framework for developing wall models for large-eddy simulation that is able to capture pressure-gradient effects using multi-agent reinforcement learning. Within this framework, the distributed reinforcement learning agents receive off-wall environmental states, including pressure gradient and turbulence strain rate, ensuring adaptability to a wide range of flows characterized by pressure-gradient effects and separations. Based on these states, the agents determine an action to adjust the wall eddy viscosity and, consequently, the wall-shear stress. The model training is in situ with wall-modeled large-eddy simulation grid resolutions and does not rely on the instantaneous velocity fields from high-fidelity simulations. Throughout the training, the agents compute rewards from the relative error in the estimated wall-shear stress, which allows them to refine an optimal control policy that minimizes prediction errors. Employing this framework, wall models are trained for two distinct subgrid-scale models using low-Reynolds-number flow over periodic hills. These models are validated through simulations of flows over periodic hills at higher Reynolds numbers and flows over the Boeing Gaussian bump. The developed wall models successfully capture the acceleration and deceleration of wall-bounded turbulent flows under pressure gradients and outperform the equilibrium wall model in predicting skin friction.

Bayesian inversion of HFC-134a emissions in southern China from a new AGAGE site: Results from an observing system simulation experiment

The abundance of hydrofluorocarbons (HFCs) in the atmosphere is increasing and is of significant importance to the Earth's system. It is thus crucial to investigate the spatial distribution of HFC emissions. However, inversion modeling, a commonly used approach, is susceptible to errors from a-priori emissions, inversion grids, observations, and other parameters. In this study, we conduct Observing System Simulation Experiment (OSSE) to evaluate the impact of inversion parameters on HFC emission estimates, focusing on HFC-134a at the newly established Xichong (XCG) AGAGE site in Shenzhen, China. We regard the EDGAR (v7) dataset as a reference for “true” emissions and simulate the “true” atmosphere using the GEOS-Chem model. Our OSSE indicates that conducting inversions in the medium-sensitivity region with source-receptor sensitivity larger than 6.0 (nmol mol−1)/(mol m−2 s−1) minimizes the bias between a-posteriori and “true” total emissions to 0.58 %–1.88 %. In the high-sensitivity region, enhancing the spatial resolution of inversion grids lowers this error from −27.07 % to +0.36 %. The accuracy of a-priori spatial distribution crucially influences that of the a-posteriori: the higher correlation coefficient between a-priori and “true” emissions, the better a-posteriori agree with the “true” emissions, as evidenced by a reduced root mean square error (RMSE) of the a-posteriori vs. “true” emissions from 1.44 × 10−9 g m−2 s−1 (GDP-based) to 8.78 × 10−10 g m−2 s−1 (VIIRS-based). Furthermore, selecting regularization parameters and balancing instrumental and a-priori errors are also important. Our OSSE setups allow for parameter testing during the inversion, offering a framework to assess the regional representativeness of future HFC measurement sites.

Influence of Grid Resolution and Assimilation Window Size on Simulating Storm Surge Levels

Grid resolution and assimilation window size play significant roles in storm surge models. In the Bohai Sea, Yellow Sea, and East China Sea, the influence of grid resolution and assimilation window size on simulating storm surge levels was investigated during Typhoon 7203. In order to employ a more realistic wind stress drag coefficient that varies with time and space, we corrected the storm surge model using the spatial distribution of the wind stress drag coefficient, which was inverted using the data assimilation method based on the linear expression Cd = (a + b × U10) × 10−3. Initially, two grid resolutions of 5′ × 5′ and 10′ × 10′ were applied to the numerical storm surge model and adjoint assimilation model. It was found that the influence of different grid resolutions on the numerical model is almost negligible. But in the adjoint assimilation model, the root mean square (RMS) errors between the simulated and observed storm surge levels under 5′ × 5′ and 10′ × 10′ grid resolutions were 11.6 cm and 15.6 cm, and the average PCC and WSS values for 10 tidal stations changed from 89% and 92% in E3 to 93% and 96% in E4, respectively. The results indicate that the finer grid resolution can yield a closer consistency between the simulation and observations. Subsequently, the effects of assimilation window sizes of 6 h, 3 h, 2 h, and 1 h on simulated storm surge levels were evaluated in an adjoint assimilation model with a 5′ × 5′ grid resolution. The results show that the average RMS errors were 11.6 cm, 10.6 cm, 9.6 cm, and 9.3 cm under four assimilation window sizes. In particular, the RMS errors for the assimilation window sizes of 1 h and 6 h at RuShan station were 3.9 cm and 10.2 cm, a reduction of 61.76%. The PCC and WSS values from RuShan station in E4 and E7 separately showed significant increases, from 85% to 98% and from 92% to 99%. These results demonstrate that when the assimilation window size is smaller, the simulated storm surge level is closer to the observation. Further, the results show that the simulated storm surge levels are closer to the observation when using the wind stress drag coefficient with a finer grid resolution and smaller temporal resolution.

Diagnosis of The State and Changes in The Ecosystem of Lake Onego and Watershed Based on The Information-Analytical System

The results of the diagnosis of the state and changes in the ecosystem of Onegskoe Lake (Lake Onego) and the watershed are presented using the developed information and analytical system “Lake Onego-watershed” (IAS), consisting of a comprehensive database (DB), a combined database of Roshydromet and Northern water problems institute/Karelian Research Center of the Russian Academy of Sciences on the nutrient load for the modern period 1995–2022, the ILLM mathematical model for assessing the removal of nutrients from the watershed and the formation of the nutrient load on the lake and the 3D-mathematical model SPLEM, developed for Lake Onego. Information was collected on the main sources of nutrient load in the Lake Onego catchment area, as well as available field observation data on the flow of nitrogen and phosphorus into the lake. The contribution of different nutrient sources coming from river runoff, diffuse sources, urban discharges and from trout farms was calculated for the lake and the main limnic areas. Based on data from field observations over the past 30 years and the results of numerical experiments using the SPLEM model with a grid resolution of 1 km it is shown that the ecosystem of the lake not only did not restored after the reduction in anthropogenic load after 1991, but eutrophication of waters in the lips and bays continues due to the influence of industrial and agricultural enterprises, trout farms and noticeable climate warming. Functional for the IAS “Lake Onego-catchment” to visualize the main modeling results on a 1 km grid was developed, and a web application interface has been created.

Variational Feature Extraction in Scientific Visualization

Across many scientific disciplines, the pursuit of even higher grid resolutions leads to a severe scalability problem in scientific computing. Feature extraction is a commonly chosen approach to reduce the amount of information from dense fields down to geometric primitives that further enable a quantitative analysis. Examples of common features are isolines, extremal lines, or vortex corelines. Due to the rising complexity of the observed phenomena, or in the event of discretization issues with the data, a straightforward application of textbook feature definitions is unfortunately insufficient. Thus, feature extraction from spatial data often requires substantial pre- or post-processing to either clean up the results or to include additional domain knowledge about the feature in question. Such a separate pre- or post-processing of features not only leads to suboptimal and incomparable solutions, it also results in many specialized feature extraction algorithms arising in the different application domains. In this paper, we establish a mathematical language that not only encompasses commonly used feature definitions, it also provides a set of regularizers that can be applied across the bounds of individual application domains. By using the language of variational calculus, we treat features as variational minimizers, which can be combined and regularized as needed. Our formulation not only encompasses existing feature definitions as special case, it also opens the path to novel feature definitions. This work lays the foundations for many new research directions regarding formal definitions, data representations, and numerical extraction algorithms.

Evaluation of the non-Newtonian lattice Boltzmann model coupled with off-grid bounce-back scheme: Wall shear stress distributions in Ostwald-de Waele fluids flow.

We present a comprehensive analysis of the non-Newtonian lattice Boltzmann method (LBM) when it is used to simulate the distribution of wall shear stress (WSS). We systematically identify sources of numerical errors associated with non-Newtonian rheological behavior of fluids in off-grid geometries. We implement the single relaxation time, Bhatnagar-Gross-Krook (BGK), and multiple relaxation time (MRT) collision operators and investigate flow in a two-dimensional channel aligned with lattice directions and off-grid Hagen-Poiseuille flow of Ostwald-de Waele (power-law) fluids. As for boundary conditions, we implement constant body force-driven and pressure-driven flows. These two boundary conditions have different numerical challenges, which include numerical stability, accuracy, mass conservation, and compressibility effects, which are inherent in the LBM method. Our results indicate that MRT, when the relaxation times are adequately tuned in the non-Newtonian case, significantly improves the WSS distribution accuracy and the numerical stability of the LBM. MRT also enhances the stability and accuracy for non-Newtonian fluids compared with the Newtonian case, meaning that it is questionable if a BGK collision operator is appropriate to use in a non-Newtonian case with off-grid boundaries. When analyzing the non-Newtonian LBM in the context of staircase walls and interpolated bounce-back (IBB) walls, a MRT collision operator with the appropriate choice of tunable relaxation times makes it possible to achieve numerically accurate results without a significant increase in grid resolution for matching to the analytical solution of WSS distributions. In analyzing the non-Newtonian flows, we show that the viscosity dependency of bounce-back walls in the BGK-LBM deviates from the results obtained under Newtonian assumptions. The power-law index further influences these discrepancies, and errors caused by the viscosity dependency of the bounce-back boundary conditions can be effectively mitigated by implementing the MRT procedure. Results show that non-Newtonian fluids, in contrast with the Newtonian assumption, encounter a greater mass imbalance when flowing through a periodic system with IBB walls. MRT can address this challenge, as it allows for independent adjustments of physical relaxation times and enhances mass conservation in the case of non-Newtonian fluids. In pressure-driven non-Newtonian flows, there is a significant impact of bulk viscosity. This aspect is often overlooked in Newtonian simulations but can significantly impact fluid adapting to rapid changes in local effective viscosity. One of our main conclusions is that the MRT collision operator with tuned relaxation times can effectively resolve numerical problems caused by non-Newtonian rheological properties and off-grid geometries. We also provide practical guidelines for selecting the most suitable simulation approach.