1D Scheme Research Articles

Learned 1D Passive Scalar Advection to Accelerate Chemical Transport Modeling: A Case Study with GEOS-FP Horizontal Wind Fields

Abstract We developed and applied a machine-learned discretization for one-dimensional (1D) horizontal passive scalar advection, which is an operator component common to all chemical transport models (CTMs). Our learned advection scheme resembles a second-order accurate, three-stencil numerical solver but differs from a traditional solver in that coefficients for each equation term are output by a neural network rather than being theoretically derived constants. We subsampled higher-resolution simulation results—resulting in up to 16× larger grid size and 64× larger time step—and trained our neural-network-based scheme to match the subsampled integration data. In this way, we created an operator that has low resolution (in time or space) but can reproduce the behavior of a high-resolution traditional solver. Our model shows high fidelity in reproducing its training dataset (a single 10-day 1D simulation) and is similarly accurate in simulations with unseen initial conditions, wind fields, and grid spacing. In many cases, our learned solver is more accurate than a low-resolution version of the reference solver, but the low-resolution reference solver achieves greater computational speedup (500× acceleration) over the high-resolution simulation than the learned solver is able to (18× acceleration). Surprisingly, our learned 1D scheme—when combined with a splitting technique—can be used to predict 2D advection and is in some cases more stable and accurate than the low-resolution reference solver in 2D. Overall, our results suggest that learned advection operators may offer a higher-accuracy method for accelerating CTM simulations as compared to simply running a traditional integrator at low resolution. Significance Statement Chemical transport modeling (CTM) is an essential tool for studying air pollution. CTM simulations take a long computing time. Modeling pollutant transport (advection) is the second most computationally intensive part of the model. Decreasing the resolution not only reduces the advection computing time but also decreases accuracy. We employed machine learning to reduce the resolution of advection while keeping the accuracy. We verified the robustness of our solver with several generalization testing scenarios. In our 2D simulation, our solver showed up to 100 times faster simulation with fair accuracy. Integrating our approach to existing CTMs will allow broadened participation in the study of air pollution and related solutions.

An improved subgrid channel model with upwind-form artificial diffusion for river hydrodynamics and floodplain inundation simulation

Abstract. An accurate estimation of river channel conveyance capacity and the water exchange at the river–floodplain interfaces is pivotal for flood modelling. However, in large-scale models limited grid resolution often means that small-scale river channel features cannot be well-represented in traditional 1D and 2D schemes. As a result instability over river and floodplain boundaries can occur, and flow connectivity, which has a strong control on the floodplain hydraulics, is not well-approximated. A subgrid channel (SGC) model based on the local inertial form of the shallow water equations, which allows utilization of approximated subgrid-scale bathymetric information while performing very efficient computations, has been proposed as a solution, and it has been widely applied to calculate the wetting and drying dynamics in river–floodplain systems at regional scales. Unfortunately, SGC approaches to date have not included the latest developments in numerical solutions of the local inertial equations, and the original solution scheme was reported to suffer from numerical instability in low-friction regions such as urban areas. In this paper, for the first time, we implement a newly developed diffusion and explicit adaptive weighting factor in the SGC model. Adaptive artificial diffusion is explicitly included in the form of an upwind solution scheme based on the local flow status to improve the numerical flux estimation. A structured sequence of numerical experiments is performed, and the results confirm that the new SGC model improved the model performance in terms of water level and inundation extent, especially in urban areas where the Manning parameter is less than 0.03 m-1/3 s. By not compromising computational efficiency, this improved SGC model is a compelling alternative for river–floodplain modelling, particularly in large-scale applications.

Bounding the Round-Off Error of the Upwind Scheme for Advection

Numerical simulations are carefully-written programs, and their correctness is based on mathematical results. Nevertheless, those programs rely on floating-point arithmetic and the corresponding round-off errors are often ignored. This article deals with a specific simple scheme applied to advection, that is a particular equation from hydrodynamics dedicated to the transport of a substance. It shows a tight bound on the round-off error of the 1D and 2D upwind scheme, with an error roughly proportional to the number of steps. The error bounds are generic with respect to the format and exceptional behaviors are taken into account. Some experiments give an insight of the quality of the bounds.

Modeling the Convective Boundary Layer in the Terra Incognita: Evaluation of Different Strategies with Real-Case Simulations

Abstract Modeling atmospheric turbulence in the convective boundary layer is challenging at kilometer and subkilometer resolutions, as the horizontal grid spacing approaches the size of the most energetic turbulent eddies. In this range of resolutions, termed terra incognita or gray zone, partially resolved convective structures are grid dependent and neither traditional 1D mesoscale parameterizations nor 3D large-eddy simulations closures are theoretically appropriate. Leveraging on a new set of one-way nested, full-physics multiscale numerical experiments, we quantify the magnitude of the errors introduced at gray zone resolutions in a real-case application and we provide new perspectives on recently proposed modeling approaches. The new set of experiments is forced by real-time-varying boundary conditions, spans a wide range of scales, and includes traditional 1D schemes, 3D closures, scale-aware parameterizations, and strategies to suppress resolved convection at gray zone resolutions. The study area is Riyadh (Saudi Arabia), where deep CBLs develop owing to strong convective conditions. Detailed analyses of our experiments, including validation with radiosonde data, calculations of spectral features, and partitioning of turbulent fluxes between resolved and subgrid scales, show that (i) grid-dependent convective structures entail minor impacts on the first-order characteristics of the fully developed boundary layer due to some degree of implicit scale awareness of 1D parameterizations and (ii) 3D closures and scale-aware schemes outperform traditional 1D schemes especially in the surface layer, among other findings. The new suite of experiments provides a benchmark of real simulations that can be extended to assess how new turbulence closures perform at gray zone resolutions. Significance Statement As recent advances in high-performance computing are leading to a new era in numerical simulations, regional atmospheric models can now increase their resolution to the widely unexplored kilometer and subkilometer range. While increasing the resolution of atmospheric models is desirable to (i) have more realistic weather and air quality predictions and (ii) better represent boundary conditions for microscale models, kilometer and subkilometer grid spacings pose some theoretical challenges that need to be addressed by the atmospheric modeling community. In this work we run a set of numerical experiments for a real case study that aim to offer new perspectives on recently developed modeling strategies and identify the most promising directions that should be investigated by follow-up studies.

Effects of Orifice Sizes for Uncontrolled Filling Processes in Water Pipelines

The sizing of air valves during the air expulsion phase in rapid filling processes is crucial for design purposes. Mathematical models have been developed to simulate the behaviour of air valves during filling processes for air expulsion, utilising 1D and 2D schemes. These transient events involve the presence of two fluids with different properties and behaviours (water and air). The effect of air valves under scenarios of controlled filling processes has been studied by various authors; however, the analysis of uncontrolled filling processes using air valves has not yet been considered. In this scenario, water columns reach high velocities, causing part of them to close air valves, which generates an additional peak in air pocket pressure patterns. In this research, a two-dimensional computational fluid dynamics model is developed in OpenFOAM software to simulate the studied situations.

Integration of 1D and 3D modeling schemes to establish the Farewell Formation as a self-sourced reservoir in Kupe Field, Taranaki Basin, New Zealand

Along with conventional methods, this paper proposed a method in which 1D and 3D models are integrated to identify the self-sourced reservoir potential of the Farewell Formation in the Kupe Gas Field within the Taranaki Basin, New Zealand. Source rock characteristics were evaluated at both field and basin scales by investigating source rock maturity, type of organic matter, and hydrocarbon generation potential by rock pyrolysis, using Rock-Eval 2 and 6. The 1D thermal and burial history model established the rate of sedimentation and thermal history of the Kupe 4 well. Reservoir characterization at field-scale was determined by seismic interpretation, well log analysis, and 3D structural and petrophysical models. The sediments of the Farewell Formation contain types II–III (oil/gas prone) and type III (gas prone) and have fair-to-excellent generation potential. The oxygen and hydrogen indices ranged from 3 to 476 mg CO2/g TOC and 26 to 356 mg HC/g TOC, respectively, whereas the thermal maturity determined by vitrinite reflectance values ranged between 0.3% and 0.72%, indicating that the Farewell Formation is in immature-to-mature hydrocarbon generation stage. Thus, Farewell Formation was verified to be a good source rock. Additionally, structural interpretations demonstrated the structural complexity of an extensional and contractional regime within the reservoir package. Multiple faults indicated a good reservoir property there with a trapping mechanism as well as migration paths. A well-log-based petrophysical analysis established the presence of up to 70% hydrocarbon saturation within the pore spaces of Farewell sandstones. The 3D models confirmed that the Farewell Formation has significant sand zones and hydrocarbon-saturated zones, thereby proving its very good reservoir characteristics. It has been proved that the 1D and 3D structural schemes, integrated with geological techniques, was vital in identifying the Kupe Field as a self-sourced reservoir.

Analysis of the performance of a hybrid CPU/GPU 1D2D coupled model for real flood cases

Abstract Coupled 1D2D models emerged as an efficient solution for a two-dimensional (2D) representation of the floodplain combined with a fast one-dimensional (1D) schematization of the main channel. At the same time, high-performance computing (HPC) has appeared as an efficient tool for model acceleration. In this work, a previously validated 1D2D Central Processing Unit (CPU) model is combined with an HPC technique for fast and accurate flood simulation. Due to the speed of 1D schemes, a hybrid CPU/GPU model that runs the 1D main channel on CPU and accelerates the 2D floodplain with a Graphics Processing Unit (GPU) is presented. Since the data transfer between sub-domains and devices (CPU/GPU) may be the main potential drawback of this architecture, the test cases are selected to carry out a careful time analysis. The results reveal the speed-up dependency on the 2D mesh, the event to be solved and the 1D discretization of the main channel. Additionally, special attention must be paid to the time step size computation shared between sub-models. In spite of the use of a hybrid CPU/GPU implementation, high speed-ups are accomplished in some cases.

Optical absorption microscopy of localized atoms at microwave domain: two-dimensional localization based on the projection of three-dimensional localization

A new approach for achieving two – dimensional (2D) atom localization microscopy based on the projection of three – dimensional (3D) localization in the plane of the detector is described in the present work. Spatial variation of the position-dependent 2D-localization pattern in the xy-plane is obtained with the shifting of the position of the detector along the z-axis under the parallel- and cross- axis configurations of the standing-wave fields. An attempt is made to study the 2D-localization characteristics in the specific parametric conditions for which the localization structures evolve with different shapes eventually leading to 100% detection probability of the atom both in the sub-wavelength and sub-half-wavelength regimes. The scope of tuning the cross-axis configuration over a wide range adds novelty and robustness to this model. Apart from the 2D-localization, various localization patterns with eight- to single-peak structures appear as interesting outcomes through the efficient manipulation of control parameters in the study of one-dimensional (1D) atom localization. The application of the traveling-wave field or its equivalent appears to be unique in achieving high-precision localization with maximal probability (100%) in both the 1D and 2D field-configuration schemes. Proper tuning of the traveling wave accompanied by the standing wave in the 1D scheme results in the single-peak localization in the sub-half-wavelength range. As a whole, the present work seems to be very much efficient for high-precision optical lithography.

Improving Centrifugal Compressor Performance by Optimizing the Design of Impellers Using Genetic Algorithm and Computational Fluid Dynamics Methods

It has always been important to study the development and improvement of the design of turbomachines, owing to the numerous uses of turbomachines and their high energy consumption. Accordingly, optimizing turbomachine performance is crucial for sustainable development. The design of impellers significantly affects the performance of centrifugal compressors. Numerous models and design methods proposed for this subject area, however, old and based on the 1D scheme. The present article developed a hybrid optimization model based on genetic algorithms (GA) and a 3D simulation of compressors to examine the certain parameters such as blade angle at leading and trailing edges and the starting point of splitter blades. New impeller design is proposed to optimize the base compressor. The contribution of this paper includes the automatic creation of generations for achieving the optimal design and designing splitter blades using a novel method. The present study concludes with presenting a new, more efficient, and stable design.

A new flux‐limiting approach–based kinetic scheme for the Euler equations of gas dynamics

SummaryThis paper proposes a new kinetic‐theory‐based high‐resolution scheme for the Euler equations of gas dynamics. The scheme uses the well‐known connection that the Euler equations are suitable moments of the collisionless Boltzmann equation of kinetic theory. The collisionless Boltzmann equation is discretized using Sweby's flux‐limited method and the moment of this Boltzmann level formulation gives a Euler level scheme. It is demonstrated how conventional limiters and an extremum‐preserving limiter can be adapted for use in the scheme to achieve a desired effect. A simple total variation diminishing criteria relaxing parameter results in improving the resolution of the discontinuities in a significant way. A 1D scheme is formulated first and an extension to 2D on Cartesian meshes is carried out next. Accuracy analysis suggests that the scheme achieves between first‐ and second‐order accuracy as is expected for any second‐order flux‐limited method. The simplicity and the explicit form of the conservative numerical fluxes add to the efficiency of the scheme. Several standard 1D and 2D test problems are solved to demonstrate the robustness and accuracy.

Marine dipole–dipole controlled source electromagnetic and coincident-loop transient electromagnetic experiments to detect seafloor massive sulphides: effects of three-dimensional bathymetry

Seafloor massive sulphides (SMSs) are regarded as a potential future resource to satisfy the growing global demand of metals including copper, zinc and gold. Aside from mining and retrieving profitable amounts of massive sulphides from the seafloor, the present challenge is to detect and delineate significant SMS accumulations, which are generally located near mid-ocean ridges and along submarine volcanic arc and backarc spreading centres. Currently, several geophysical technologies are being developed to detect and quantify SMS occurrences that often exhibit measurable contrasts in their physical parameters compared to the surrounding host rock. Here, we use a short, fixed-offset controlled source electromagnetic (CSEM) system and a coincident-loop transient electromagnetic (TEM) system, which in theory allow the detection of SMS in the shallow seafloor due to a significant electrical conductivity contrast to their surroundings. In 2016, CSEM and TEM experiments were carried out at several locations near the Trans- Atlantic Geotraverse hydrothermal field to investigate shallow occurrences of massive sulphides below the seafloor. Measurements were conducted in an area that contains distinct SMS sites located several kilometres off-axis from the Mid-Atlantic ridge, some of which are still connected to hydrothermal activity and others where hydrothermal activity has ceased. Based on the quality of the acquired data, both experiments were operationally successful. However, the data analysis indicates bias caused by three-dimensional (3D) effects of the rough bathymetry in the study area and, thus, data interpretation remains challenging. Therefore, we study the influence of 3D bathymetry for marine CSEM and TEM experiments, focusing on shallow 3D conductors located beneath mound-like structures.We analyse synthetic inversion models for attributes associated with 3D distortions of CSEM and TEM data that are not sufficiently accounted for in conventional 1D (TEM) and 2D (CSEM) interpretation schemes. Before an adequate quantification of SMS in the region is feasible, these 3D effects need to be studied to avoid over/underestimation of SMS using the acquired EM data. The sensitivity of CSEM and TEM to bathymetry is investigated by means of 3D forward modelling, followed by 1D (TEM) and 2D (CSEM) inversion of the synthetic data using realistic error conditions. Subsequently, inversion models of the synthetic 3D data are analysed and compared to models derived from the measured data to illustrate that 3D distortions are evident in the recorded data sets.

Coupling simulation of the fast startup of a centrifugal pump with cavitation in a closed-loop pipeline system

PurposeCavitation inside pumps affects not only the steady state fluid flow, but also the unsteady or transient characteristic of the flow. However, cavitation inside pumps under transient processes is difficult to predict when the influence of the pipelines system is considered. In this paper we present a simulation method applied to a centrifugal pump and its related pipeline to analyze the induced unsteady cavitation phenomenon during the startup process.Design/methodology/approachIn order to effectively predict transient processes of a pump and its pipeline system, the simulation method uses a coupled 1D and 3D scheme, which reduces the simulation cost. The simulation of the startup process of a centrifugal pump in a closed-loop pipeline system with and without cavitation has been performed to verify the proposed method.FindingsThe evolution of the pressure and flow rate obtained with the simulation method agrees well with the experimental results. It is found that the mass flow rate at the pump inlet and outlet is highly related to the cavitation vapor volume and that the pressure at the outlet of the impeller is greatly influenced by the discharge.Originality/valueThe 1D-3D coupling simulation method used in this paper is proven to be highly accurate, efficient and can be used to solve transient processes combined with cavitation or other complex phenomena.

Residue selective 15N CEST and CPMG experiments for studies of millisecond timescale protein dynamics

Proteins are intrinsically dynamic molecules and undergo exchanges among multiple conformations to perform biological functions. The CPMG relaxation dispersion and CEST experiments are two important solution NMR techniques for characterizing the conformational exchange processes on the millisecond timescale. Traditional pseudo 3D 15N CEST and CPMG experiments have certain limitations in their applications. For example, both experiments have low sensitivity for broadened resonances, and the process of optimizing sample conditions and experimental parameters are often time consuming. To overcome these limitations, we herein present a new set of residue selective 15N CEST and CPMG pulse sequences by employing the Hartmann-Hahn cross-polarization transfer of magnetization in both 1D and 2D schemes. Combined with frequency labeling in the indirect dimension using only a small number of increments, the pulse sequences in the 2D scheme can be applied on resonances in overlapped regions of the 1H-15N HSQC spectrum. The pulse sequences were further applied on several proteins, demonstrating their advantages over the traditional CEST and CPMG experiments under specific circumstances.

Prediction of the 21-cm signal from reionization: comparison between 3D and 1D radiative transfer schemes

Three-dimensional radiative transfer simulations of the epoch of reionization can produce realistic results, but are computationally expensive. On the other hand, simulations relying on one-dimensional radiative transfer solutions are faster but limited in accuracy due to their more approximate nature. Here, we compare the performance of the reionization simulation codes grizzly and C2-ray which use 1D and 3D radiative transfer schemes respectively. The comparison is performed using the same cosmological density fields, halo catalogues and source properties. We find that the ionization maps, as well as the 21-cm signal maps from these two simulations are very similar even for complex scenarios which include thermal feedback on low mass halos. The comparison between the schemes in terms of the statistical quantities such as the power spectrum of the brightness temperature fluctuation agree with each other within 10% error throughout the entire reionization history. grizzly seems to perform slightly better than the semi-numerical approaches considered in Majumdar et al. (2014) which are based on the excursion set principle. We argue that grizzly can be efficiently used for exploring parameter space, establishing observations strategies and estimating parameters from 21-cm observations.

Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations

This paper first studies the admissible state set [Formula: see text] of relativistic magnetohydrodynamics (RMHD). It paves a way for developing physical-constraints-preserving (PCP) schemes for the RMHD equations with the solutions in [Formula: see text]. To overcome the difficulties arising from the extremely strong nonlinearities and no explicit formulas of the primitive variables and the flux vectors with respect to the conservative vector, two equivalent forms of [Formula: see text] with explicit constraints on the conservative vector are skillfully discovered. The first is derived by analyzing roots of several polynomials and transferring successively them, and further used to prove the convexity of [Formula: see text] with the aid of semi-positive definiteness of the second fundamental form of a hypersurface. While the second is derived based on the convexity, and then used to show the orthogonal invariance of [Formula: see text]. The Lax–Friedrichs (LxF) splitting property does not hold generally for the nonzero magnetic field, but by a constructive inequality and pivotal techniques, we discover the generalized LxF splitting properties, combining the convex combination of some LxF splitting terms with a discrete divergence-free condition of the magnetic field. Based on the above analyses, several 1D and 2D PCP schemes are then studied. In the 1D case, a first-order accurate LxF-type scheme is first proved to be PCP under the Courant–Friedrichs–Lewy (CFL) condition, and then the high-order accurate PCP schemes are proposed via a PCP limiter. In the 2D case, the discrete divergence-free condition and PCP property are analyzed for a first-order accurate LxF-type scheme, and two sufficient conditions are derived for high-order accurate PCP schemes. Our analysis reveals in theory for the first time that the discrete divergence-free condition is closely connected with the PCP property. Several numerical examples demonstrate the theoretical findings and the performance of numerical schemes.

A 1D–2D Shallow Water Equations solver for discontinuous porosity field based on a Generalized Riemann Problem

A novel augmented Riemann Solver capable of handling porosity discontinuities in 1D and 2D Shallow Water Equation (SWE) models is presented. With the aim of accurately approximating the porosity source term, a Generalized Riemann Problem is derived by adding an additional fictitious equation to the SWEs system and imposing mass and momentum conservation across the porosity discontinuity. The modified Shallow Water Equations are theoretically investigated, and the implementation of an augmented Roe Solver in a 1D Godunov-type finite volume scheme is presented. Robust treatment of transonic flows is ensured by introducing an entropy fix based on the wave pattern of the Generalized Riemann Problem. An Exact Riemann Solver is also derived in order to validate the numerical model. As an extension of the 1D scheme, an analogous 2D numerical model is also derived and validated through test cases with radial symmetry. The capability of the 1D and 2D numerical models to capture different wave patterns is assessed against several Riemann Problems with different wave patterns.

A simple finite-difference scheme for handling topography with the second-order wave equation

ABSTRACTThe presence of topography poses a challenge for seismic modeling with finite-difference codes. The representation of topography by means of an air layer or vacuum often leads to a substantial loss of numerical accuracy. A suitable modification of the finite-difference weights near the free surface can decrease that error. An existing approach requires extrapolation of interior solution values to the exterior while using the boundary condition at the free surface. However, schemes of this type occasionally become unstable and may be impossible to implement with highly irregular topography. One-dimensional extrapolation along coordinate lines results in a simple and efficient scheme. The stability of the 1D scheme is improved by ignoring the interior point nearest to the boundary during extrapolation in case its distance to the boundary is less than half a grid spacing. The generalization of the 1D scheme to more than one dimension requires a modification if the boundary intersects the finite-difference stencil on both sides of the central evaluation point and if there are not enough interior points to build the finite-difference stencil. Examples for the 2D constant-density acoustic case with a fourth-order finite-difference scheme demonstrate the method’s capability. Because the 1D assumption is not valid in two dimensions if the boundary does not follow grid lines, the formal numerical accuracy is not always obtained, but the method can handle highly irregular topography.

Flow and Sediment Transport with Non-Submerged Riparian Vegetation in 1D Scheme

ABSTRACT Jeon, H.S.; Obana, M.; Kim, K.H., and Tsujimoto, T., 2017. Flow and sediment transport with non-submerged riparian vegetation in 1D scheme. In: Lee, J.L.; Griffiths, T.; Lotan, A.; Suh, K.-S., and Lee, J. (eds.), The 2nd International Water Safety Symposium. Journal of Coastal Research, Special Issue No. 79, pp. 329–333. Coconut Creek (Florida), ISSN 0749-0208. Recently depth averaged analysis has become popular and powerful even in a stream with vegetation by taking account of form drag due to vegetation. A number of studies about the drag force related with various vegetation configuration were also carried out and focus on determining the drag coefficients and empirical formulas. However, there must be some restriction for application in depth averaged model for flow with vegetation. When it is applied to a stream with vegetation, form drag due to vegetation is taken into account, but the shear stress is not properly described because the frictional resistance law due to bed roughness is not m...

Evaluation of Fast Flood Diffusion through a Drainage Channel: A Flood Disaster Case Study of Japan’s Kinugawa River, September 10, 2015

On September 10, 2015, unprecedented flood was occurred in Kinugawa River basin located on eastern Japan. It inundated 40 km2 of flood plain in Joso city, Ibaraki Prefecture, and more than 4000 people there called for help despite supposedly having sufficient time to evacuate. Some said that small initial flood before main severe flood arrived made them make a mistake in deciding whether to evacuate or stay there, despite having to actually evacuate in reality. This study focused on flood behaviour in this area, in particular, the effect of a small drainage channel lying on the flood plain which caused fast flood diffusion in case of occurring huge overflowing. Field investigations starting on time of the disaster with high-resolution positioning system were conducted to obtain spatial maps of flood depth and height. For appropriate modelling of the effect of small channel, we applied simulation model coupling 1-dimensional (1D) and 2-dimensional (2D) hydraulic scheme on the field and compared results from the 1D/2D coupled model and model without 1D scheme. The models provided information that the flood could reach 4 hours earlier to the city central of Joso city comparing in case of model without 1D scheme. The water depth rose irregularly and it was more confusing and difficult for the victims to make appropriate evacuation act.

Proof of uniform convergence for a cell-centered AP discretization of the hyperbolic heat equation on general meshes

We prove the uniform AP convergence on unstructured meshes in 2D of a generalization, of the Gosse-Toscani 1D scheme for the hyperbolic heat equation. This scheme is also a nodal extension in 2D of the Jin-Levermore scheme described in [18] for the 1D case. In 2D, the proof is performed using a new diffusion scheme.