Temporal Scheme Research Articles

A second order accurate SAV numerical method for the nonlocal ternary conservative Allen-Cahn model

The nonlocal model has attracted a great attention in materials field for describing various types of material heterogeneities and defects. In this paper, we are concerned with construction of energy stability numerical methods for the nonlocal ternary conservative Allen-Cahn model, two different Lagrange multipliers to enforce conservation of mass are considered, respectively. By employing a stabilized scalar auxiliary variable (S-SAV) approach with second-order backward differentiation formula in temporal, two fast and effective schemes are established. The unconditional energy stability and mass conservation are rigorously derived. Numerical experiments are presented to verify theoretical results and to show the robustness and accuracy of the proposed method.

Predicting radiative intensity in transient radiative transfer with an inhomogeneous medium by spectral element discontinuous Galerkin method

Accurate prediction of the transient radiative intensity within an inhomogeneous medium is very useful in laser pulse technology. In the present work, a spectral element discontinuous Galerkin method (SEDGM) is proposed to solve transient radiative transfer with two kinds of boundary conditions, i.e., intense diffuse irradiation and short square laser irradiation. In the solving processing, the discontinuous elements are adopted to capture the large variety of radiative intensity on the element boundary. Then, the implicit temporal differencing scheme is introduced to deal with the time discretization. Several test cases are chosen to test the accuracy of the SEDGM. Results show that: (1) the SEDGM can provide good accuracy and efficiency for transient radiative transfer in an inhomogeneous medium; (2) the SEDGM has h-p convergence characteristics. Otherwise, the angle-time distributions of radiative intensities at boundaries are exhibited, and the influences of pulse duration and scattering phase function are investigated.

Pointwise error estimates of compact difference scheme for mixed-type time-fractional Burgers’ equation

In this paper, based on the developed nonlinear fourth-order operator and method of order reduction, a novel fourth-order compact difference scheme is constructed for the mixed-type time-fractional Burgers’ equation, from which L1-discretization formula is applied to deal with the terms of fractional derivative, and the nonlinear convection term is discretized by nonlinear compact difference operator. Then a fully discrete L1 compact difference scheme on uniform meshes can be established by approximating spatial second-order derivative with classic compact difference formula. The convergence and stability of the proposed scheme are rigorously proved in the L∞-norm by the energy argument and mathematical induction. We also establish a temporal second-order compact difference scheme on graded time meshes for solving the problem with weak initial singularity. Finally, several numerical experiments are provided to test the accuracy of two numerical schemes and verify the theoretical analysis.

High-fidelity video reversible data hiding using joint spatial and temporal prediction

An efficient predictor is essential in reversible data hiding methods. This paper proposes a video reversible data hiding method, where the correlations between pixels in both spatial and temporal domains are fully considered to improve prediction accuracy. In more detail, for each pixel, both intra prediction and inter prediction are implemented and the better prediction mode is selected according to intra or inter local complexity. A double-layered video partition scheme is applied so that the motion vectors generated during inter prediction are not necessarily embedded as additional information while reversibility is guaranteed. In addition, a cover pixel selection principle based on the probability distribution of the prediction errors is proposed, which prevents the pixels with large prediction errors from being modified. Experimental results demonstrate that the joint spatial and temporal prediction scheme offers satisfactory accuracy, and the proposed video reversible data hiding method can obtain high-quality stego videos.

Assessment of a new hybrid-SSOR implicit temporal scheme for turbulent flows across a wide range of Mach numbers

Assessment of a new hybrid-SSOR implicit temporal scheme for turbulent flows across a wide range of Mach numbers

A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel

A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with a weakly singular kernel is of concern in this paper. The scheme is targeted to reduce the computation time and to improve the accuracy of the scheme developed by Xu et al. (Appl Numer Math 152:169–184, 2020). The constructed scheme is armed by three steps: First, a small nonlinear system is solved on the coarse grid using a fix-point iteration. Second, Lagrange’s linear interpolation formula is used to arrive at some auxiliary values for the analysis of the fine grid. Finally, a linearized Crank–Nicolson finite difference system is solved on the fine grid. Moreover, the algorithm uses a central difference approximation for the spatial derivatives. In the time direction, the time derivative and integral term are approximated by the Crank–Nicolson technique and product integral rule, respectively. By means of the discrete energy method, stability and space-time second-order convergence of the proposed approach are obtained in $$L^2$$ -norm. Finally, the numerical verification is fulfilled as the numerical results of the given numerical experiments agree with the theoretical analysis and verify the effectiveness of the algorithm.

Bounds preserving temporal integration methods for hyperbolic conservation laws

In this work, we present a modification of explicit Runge–Kutta temporal integration schemes that guarantees the preservation of any locally-defined quasiconvex set of bounds for the solution. These schemes operate on the basis of a bijective mapping between an admissible set of solutions and the real domain to strictly enforce bounds. Within this framework, we show that it is possible to recover a wide range of methods independently of the spatial discretization, including positivity preserving, discrete maximum principle satisfying, entropy dissipative, and invariant domain preserving schemes. Furthermore, these schemes are proven to recover the order of accuracy of the underlying Runge–Kutta method upon which they are built. The additional computational cost is the evaluation of two nonlinear mappings which generally have closed-form solutions. We show the utility of this approach in numerical experiments using a pseudospectral spatial discretization without any explicit shock capturing schemes for nonlinear hyperbolic problems with discontinuities.

Effects of Cover Crops and Soil Amendments on Soil CO2 Flux in a Mississippi Corn Cropping System on Upland Soil

Agroecosystems, accounting for more than one-third of arable land worldwide, play an essential role in the terrestrial carbon (C) cycle. The development of agricultural practices, which maximize soil C sequestration from the atmosphere, is receiving growing attention due to the recognition of agroecosystems’ great potential to serve as sinks of atmospheric carbon dioxide (CO2). In particular, cover crop and soil amendment applications are generating much interest in mitigating climate change and enhancing agricultural ecosystem services. The objective of this study was to evaluate the effects of winter cover crop and soil amendments, including broiler litter (BL), flue gas desulfurization (FGD) gypsum and lignite, on soil CO2 flux from cropping systems in southeastern USA, where related studies were limited. A field study was conducted from 2019 to 2021 in a Mississippi upland corn cropping system with measurements of soil CO2 flux, moisture and temperature during cash crop growing seasons. We observed high temporal variability in soil CO2 flux with flux peaks between late June and early July, which is likely due to the temporal changes in soil moisture. A significant increase in soil CO2 flux was found with BL application (p < 0.05). Co-application of FGD gypsum and lignite with BL-reduced soil CO2 flux by 15–23% but did not fully eliminate the rising effects. Significantly higher soil CO2 flux and lower soil temperature were observed from fields with cover crops than those without cover crops in the third year of this study (p < 0.05), which is likely attributed to the higher organic C content accumulated in soil with cover crops. Future research should assess year-round soil greenhouse gas fluxes in both cash crop and cover crop growing seasons using a high temporal resolution measurement scheme.

Three-dimensional elastic reverse-time migration using a high-order temporal and spatial staggered-grid finite-difference scheme

Three-dimensional (3D) elastic reverse-time migration (ERTM) can image the subsurface 3D seismic structures, and it is an important tool for the Earth’s interior imaging. A common simulation kernel used in 3D ERTM is the current staggered-grid finite-difference (SGFD) method of the first-order elastic wave equation. However, the mere second-order accuracy in time of the current SGFD method can bring non-negligible time dispersion, which reduces the simulation accuracy and further leads to the distortion of the imaging results. This paper proposes a vector-based 3D ERTM using the high-order accuracy SGFD method in time to obtain high-accuracy images. This approach is a new high-resolution ERTM workflow that improves the imaging accuracy of conventional ERTM from numerical simulation. The proposed ERTM workflow is established on a quasi-stress–velocity wave equation and its vector wavefield decomposition form. Advanced SGFD schemes and their corresponding coefficients with fourth-order temporal accuracy solve the quasi-linear wave equation system. The normalized dot product imaging condition produces high-quality images using high-accuracy vector wavefields solved using the SGFD method. Through the numerical examples, we test the simulation efficiency and analyze how temporal accuracy in numerical simulations affects migration imaging quality. We include that the proposed method obtains highly accurate images.

S2 Stream Surface Approximation Approach for Quasi Three-Dimensional Turbine Time-Marching Design Method

A fast and reliable turbine design method is necessary in aeroengine development practice. As Q3D time-marching method iteration process can be time consuming and unstable, a novel S2 stream surface approximation approach coupled with flow tangential condition is proposed to reduce the computation requirement. The surface approximation uses a quadratic function of axial coordinate x to formulate distribution of circumferential coordinate θ . The flow tangential condition inherently represents inviscid blade force effect, and the formulation of inviscid blade force is not needed. A corresponding personal Q3D turbine computer code was developed, which was suitable for both design and analysis applications. The Q3D design method solves Euler’s equation through third-order Godunov’s scheme with TVD property in finite volume method. Semi-implicit Crank-Nicolson’s temporal scheme is implemented. Profile, secondary, and tip clearance energy loss models are added to predict viscous losses. Blade row exit swirl is required as the convergence target for Q3D design. A two-stage turbine and a single-stage high-pressure turbine were designed and analyzed by the Q3D method. Viscous 3D CFD was utilized to check design performances. The results showed that the Q3D method could finish a design case within 1 min. At design point, Q3D mass flow rate error was no more than 1.25%, expansion ratio error was no less than -0.022, and isentropic efficiency error was no more than 0.37 percentage points. The Q3D design method is fast and accurate. The stream surface approximation approach is suitable for Q3D design and analysis.

Fractional laplacians viscoelastic wave equation low-rank temporal extrapolation

The fractional Laplacians constant-Q (FLCQ) viscoelastic wave equation can describe seismic wave propagation accurately in attenuating media. A staggered-grid pseudo-spectral (SGPS) method is usually applied to solve this wave equation but it is of only second-order accuracy in time, due to a second-order finite-difference (FD) time differentiation. Visible time dispersion and numerical instability could appear in the case of a large timestepping size. To resolve this problem, we develop a more accurate low-rank temporal extrapolation scheme for the FLCQ viscoelastic wave equation. We realize this goal by deriving an analytical time-marching formula from the general solution of the FLCQ wave equation. Compressional (P) and shear (S) wave velocities dependent k-space operators are involved in the formula and they can compensate for the time dispersion errors caused by the FD time differentiation. To implement the k-space operators efficiently in heterogeneous media, we adopt a low-rank approximation of these operators, which reduces the computational cost at each time step to several fast Fourier transforms (FFTs). Another benefit of the low-rank extrapolation is explicit separation of P and S waves, which is helpful for further developing vector wavefield-based seismic migration methods. Several numerical examples are presented to verify the higher accuracy and the less restrictive stability condition of the low-rank temporal extrapolation than the traditional SGPS extrapolation.

Energy stability of a temporal variable-step difference scheme for time-fractional nonlinear fourth-order reaction-diffusion equation

In this paper, we propose a nonuniform numerical formula for the Caputo fractional derivative at the half-grid based on the piecewise linear interpolation and construct a difference scheme for the time-fractional nonlinear fourth-order reaction-diffusion equation. By virtue of two discrete tools: the discrete orthogonal convolution kernels and the discrete complementary convolution kernels, we obtain the positive definiteness of the discrete time-fractional derivative. Then a discrete variational energy dissipation law of the proposed difference scheme is established for the time-fractional nonlinear fourth-order reaction-diffusion equation, which is asymptotically compatible with the associated energy dissipation law for the classical equation as the value of fractional order approaches to one. Numerical experiments demonstrate the effectiveness and the energy dissipation of the proposed difference scheme with an adaptive time-stepping strategy.

Two SAV numerical methods for the nonlocal Cahn–Hilliard–Hele-Shaw system

The capability of nonlocal models in materials field has attracted the scientific community a great attention to characterize the effect of various types of material heterogeneities and defects. In this paper, we are concerned with construction of a energy stability method for the nonlocal Cahn–Hilliard–Hele-Shaw system under periodic boundary conditions. By employing the Fourier spectral method in spatial and the scalar auxiliary variable (SAV) approach with first/second-order backward differentiation formula in temporal, two fast and effective schemes are established. The unconditional energy stability analyses is rigorously derived. Numerical experiments are presented to verify our theoretical results and to show the robustness and accuracy of the proposed method.

Advection-based temporal reconstruction technique for turbulent velocity fields

The characterization of turbulent flows is challenging due to the interaction of widespread spatiotemporal scales. Experimental techniques such as particle image velocimetry can be used to obtain spatially resolved flow measurements; however, these systems often suffer from limited acquisition rates. The present work investigates the ability of an advection-based flow reconstruction technique to increase the temporal resolution of turbulent flow data without any prior knowledge of the flow physics. A semi-Lagrangian technique is suggested to obtain fluid trajectories through a forward and backward integration of the available spatiotemporal data. The estimates are then fused using a temporal weighting scheme to yield velocity fields at intermediate times. The performance of the method is verified against three-dimensional direct numerical simulation (DNS) data of a plane jet at Re = 10 000. Extracting time series data from the spatially and temporally resolved DNS results, five test cases with artificially lowered sampling frequencies were generated. Spectral analysis revealed that the characteristic frequency found in shear layer-dominated flows can be obtained even for the most extreme case. Additionally, spectral information up to two orders of magnitude beyond the Nyquist criteria is successfully recovered throughout the spatial domain—surpassing the performance of previously introduced methods. The maximum spectral reconstruction error of the suggested method, defined as net energy loss or gain, fell within the bounds of [−5, 3]%, with a corresponding global energy difference in the range of [−2, 1]%. Furthermore, the spatially averaged reconstruction error for the velocity fluctuations was bound by [6±6]%.

Transient analyses of wave propagations in nonhomogeneous media employing the novel finite element method with the appropriate enrichment function

An enriched finite element approach with appropriate enrichment function is proposed for the transient analyses of wave propagations in nonhomogeneous media. In present method, the traditional linear nodal interpolation functions for low order finite elements are enriched by the augmented enrichment function. For the purpose of improving the computation accuracy and reducing the numerical dispersion error, the polynomial bases and the trigonometric functions are utilized to form the enrichment functions. In addition, a simple and direct approach is introduced with the aim to tackle the possible linear dependence of the system equations. The numerical results show that the accuracy of the obtained numerical results can be markedly improved by the proposed method in comparison with the standard finite elements. What's more, it can be found that the calculated solutions from the proposed method with the appropriate temporal discretization scheme are able to monotonically converge to the exact solution in transient wave analysis. In consequence, it is possible to consistently increase the solution accuracy by directly decreasing temporal discretization step size. This valuable and important property enable the present approach to be particularly suitable to tackle the wave propagations in nonhomogeneous media.

A Novel Spatio–Temporal Deep Learning Vehicle Turns Detection Scheme Using GPS-Only Data

Whether the computer is driving your car or you are, advanced driver assistance systems (ADAS) come into play on all levels, from weather monitoring to safety. These modern-day ADASs use various assisting tools for drivers to keep the journey safe; these sophisticated tools provide early signals of numerous events, such as road conditions, emerging traffic scenarios, and weather warnings. Many urban applications, such as car-sharing and logistics, rely on accurate and up-to-date road map data. Map generation methods use a variety of data sources, including but not limited to global positioning systems (GPS). In this research we propose a GPS-only data trajectory analysis and a novel scheme to convert GPS trajectory data to image-based data to train a custom Convolutional Neural Network (CNN) model. The empirical results with an extensive 5-fold cross-validation show that the proposed scheme identifies turn and not turn with more than 94% recall. It outperforms the existing turn detection schemes on two major frontiers, the required data and the accuracy achieved in detecting different driving behaviors.

Numerical Study of Wax Deposition from Multiphase Flow in Oil Pipelines with Heat and Mass Transfer

Wax deposition in field‐scale crude oil pipelines poses a significant challenge to the oil and gas industry, leading to reduced flow rates, increased pressure drops, and potential blockages. Understanding the mechanisms governing wax deposition is crucial for developing effective mitigation strategies. This study investigates the impact of multiphase flow conditions, including water‐in‐oil emulsion, wax precipitation kinetics, shear dispersion, and molecular diffusion, on wax deposition in field‐scale crude oil pipelines. A numerical model is developed that employs second‐order semi‐implicit temporal discretization schemes, such as Crank–Nicolson and Adams–Bashforth methods, in conjunction with a bivariate spectral collocation scheme using Chebyshev–Gauss–Lobatto grid points. The impact of various flow parameters, including Reynolds number (Re), mass Grashof number (Gr), Schmidt number (Sc), and Weber number (We), on the flow variables, wall shear stress, and heat and mass fluxes are investigated. The numerical simulations demonstrate that flow parameters significantly influence the flow behavior, wall shear stress, wall heat flux, and wall mass flux in waxy crude oil pipelines. Specifically, the aggregation of wax crystals in the pipeline decreases by at most 2.5% with increasing Reynolds number from 2.2361 to 3.1361. Conversely, it increases by at most 3.4% with increasing mass Grashof number from 5 to 11 and by at most 4.8% with increasing Weber number from 1.0 to 2.5. Furthermore, the Nusselt number increases from 1.9907 to 4.9834 with increasing Reynolds number from 2.2361 to 5.2361 and from 1.9907 to 2.0225 with increasing mass Grashof number from 5 to 20. It also increases from 1.9907 to 2.0434 with increasing Weber number from 1.0 to 2.5. The insights gained from this study can be applied to optimize pipeline design, operational parameters, and wax deposition mitigation strategies, leading to enhanced pipeline performance and reduced operational costs. The numerical model developed in this work serves as a valuable tool for simulating and predicting wax deposition behavior under various operating conditions.

Temporal Upscaling of MODIS 1-km Instantaneous Land Surface Temperature to Monthly Mean Value: Method Evaluation and Product Generation

The monthly mean land surface temperature (MMLST) reflects more stable intra- and inter-annual temperature variations, and therefore, it has a wider range of applications than instantaneous land surface temperature (LST). This study aimed to generate a high-resolution global MMLST product by temporally upscaling the Moderate Resolution Imaging Spectroradiometer (MODIS) 1-km instantaneous LST. First, six current methods were comprehensively evaluated using cross-validation technology. These six methods are the cross combinations of two temporal aggregation schemes: the average by observations (ABO) and by days (ABD), and three conversion models: the diurnal temperature cycle model (DTC), a simple average model for two instantaneous LSTs (TSA), and a weighted average model for multiple instantaneous LSTs (MWA). The analysis with measurements from 235 flux stations worldwide revealed that the choice of conversion model considerably affected the overall retrieval accuracy whereas the influence of the aggregation scheme was minor. From the conversion model standpoint, MWA performed best, followed by DTC, and finally TSA; this order remained the same even if DTC and TSA were improved with mean bias correction. Notably, the errors of ABD <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MWA</sub> decreased as the number of daily mean LST (NOD) increased, whereas the errors of ABO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MWA</sub> were not related to NOD. Accordingly, we deduced that the optimal strategy for estimating MMLST is using ABO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MWA</sub> when NOD is <20 and ABD <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MWA</sub> when NOD is ≥20. Subsequently, we adopted this combination method to process MODIS instantaneous LSTs and produced a global 1-km MMLST dataset for the years 2003–2020. The validation showed a satisfactory accuracy with a root mean square error of 1.6 K. The intercomparison with MMLSTs from geostationary satellites (containing complete LST daily cycle) presented a good agreement (biases < 0.3 K and STDs < 2 K). Compared with AIRS3STM product which had the same temporal span, the newly generated product exhibited a high consistency in reflecting temporal variations of global temperature. Most importantly, it had a prominently better ability to retrieve spatial details of temperature variations due to its higher resolution. Our new method and product show promising prospects for applications in global change studies where accurate spatially resolved MMLST data are one of the fundamental geophysical variables required.

Attribute-Aware RBFs: Interactive Visualization of Time Series Particle Volumes Using RT Core Range Queries.

Smoothed-particle hydrodynamics (SPH) is a mesh-free method used to simulate volumetric media in fluids, astrophysics, and solid mechanics. Visualizing these simulations is problematic because these datasets often contain millions, if not billions of particles carrying physical attributes and moving over time. Radial basis functions (RBFs) are used to model particles, and overlapping particles are interpolated to reconstruct a high-quality volumetric field; however, this interpolation process is expensive and makes interactive visualization difficult. Existing RBF interpolation schemes do not account for color-mapped attributes and are instead constrained to visualizing just the density field. To address these challenges, we exploit ray tracing cores in modern GPU architectures to accelerate scalar field reconstruction. We use a novel RBF interpolation scheme to integrate per-particle colors and densities, and leverage GPU-parallel tree construction and refitting to quickly update the tree as the simulation animates over time or when the user manipulates particle radii. We also propose a Hilbert reordering scheme to cluster particles together at the leaves of the tree to reduce tree memory consumption. Finally, we reduce the noise of volumetric shadows by adopting a spatially temporal blue noise sampling scheme. Our method can provide a more detailed and interactive view of these large, volumetric, time-series particle datasets than traditional methods, leading to new insights into these physics simulations.

Temporal second-order finite difference schemes for variable-order time-fractional generalized Oldroyd-B fluid model

In this paper, we study the variable-order generalized time fractional Oldroyd-B fluid model, use the reduced order method and the L2-1? method to establish the differential format with second-order accuracy, prove the stability and convergence of the format, and give numerical examples to illustrate the effectiveness of the differential format.