Accurate Numerical Simulations Research Articles

Ab initio approach to many-body quantum spin dynamics

A fundamental longstanding problem in studying spin models is the efficient and accurate numerical simulation of the long-time behavior of larger systems. The exponential growth of the Hilbert space and the entanglement accumulation at long times pose major challenges for current methods. To address these issues, we employ the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) framework to simulate the many-body spin dynamics of the Heisenberg model in various settings, including the Ising and XYZ limits with different interaction ranges and random couplings. Benchmarks with analytical and exact numerical approaches show that ML-MCTDH accurately captures the time evolution of one- and two-body observables in both one- and two-dimensional lattices. A comparison with the discrete truncated Wigner approximation (DTWA) highlights that ML-MCTDH is particularly well-suited for handling anisotropic models and provides more reliable results for two-point observables across all tested cases. The behavior of the corresponding entanglement dynamics is analyzed to reveal the complexity of the quantum states. Our findings indicate that the rate of entanglement growth strongly depends on the interaction range and the presence of disorder. This particular relationship is then used to examine the convergence behavior of ML-MCTDH. Our results indicate that the multilayer structure of ML-MCTDH is a promising numerical framework for handling the dynamics of generic many-body spin systems. Published by the American Physical Society 2025

A 2.5D Generalized Finite Difference Method for Elastic Wave Propagation Problems

The analysis of elastic wave propagation is a critical problem in both science and engineering, with applications in structural health monitoring and seismic wave analysis. However, the efficient and accurate numerical simulation of large-scale three-dimensional structures has posed significant challenges to traditional methods, which often struggle with high computational costs and limitations. This paper presents a novel two-and-a-half-dimensional generalized finite difference method (2.5D GFDM) for efficient simulation of elastic wave propagation in longitudinally invariant structures. The proposed scheme integrates GFDM with 2.5D technology, reducing 3D problems to a series of 2D problems in the wavenumber domain via Fourier transforms. Subsequently, the solutions to the original 3D problems can be recovered by performing inverse Fourier transforms on the solutions obtained from the 2D problems. The 2.5D GFDM avoids the inherent challenge of mesh generation in traditional methods like FEM and FVM, offering a meshless solution for complex 3D problems. By employing sparse coefficient matrices, it offers significantly improved computational efficiency. The new approach achieves significant computational advantages while maintaining high accuracy, as validated through three representative examples, making it a promising tool for solving large-scale elastic wave propagation problems in longitudinally invariant structures.

Understanding the influence of cage and instrumentation strategies with oblique lumbar interbody fusion for grade I spondylolisthesis - A comprehensive biomechanical modeling study.

Understanding the influence of cage and instrumentation strategies with oblique lumbar interbody fusion for grade I spondylolisthesis - A comprehensive biomechanical modeling study.

Accurate Simulations of EMAT Signal Amplitude and Shape Based on FEM Using a Coupled ECT-UT Formulation

Simulations of the EMAT signal, both in amplitude and shape, in metallic materials to detect defects located far from the EMAT area are performed using a FEM model based on a coupled eddy-current (ECT) and ultrasonic (UT) formulation. The paper presents the progress and achievements in performing very accurate numerical FEM simulations of the EMAT signal when using different numerical integration techniques such as Crank-Nicolson, Backward Euler and Newmark-beta method to avoid the large discrepancies in the EMAT signal shapes when using various models. The approach to obtain convergence in the simulated EMAT signal, not only of the burst amplitude of the defect but also of the time-transient shape of the signal, is based on the combination of high-order finite elements using triangular/rectangular meshes and advanced numerical time integration to obtain the converged EMAT signal in the shortest time while maintaining the same shape of the EMAT signal simulation.

Efficient Numerical Techniques for Investigating Chaotic Behavior in the Fractional-Order Inverted Rössler System

In this study, the numerical scheme for the Caputo fractional derivative (NCFD) method and the He–Laplace method (H-LM) are two powerful methods used for analyzing fractional-order systems. These two approaches are used in the study of the complex dynamics of the fractional-order inverted Rössler system, particularly for the detection of chaotic behavior. The enhanced NCFD method is used for reliable and accurate numerical simulations by capturing the intricate dynamics of chaotic systems. Further, analytical solutions are obtained using the H-LM for the fractional-order inverted Rössler system. This method is popular due to its simplicity, numerical stability, and ability to handle most initial values, yielding very accurate results. Combining analytical insights from the H-LM with the robust numerical accuracy of the NCFD approach yields a comprehensive understanding of this system’s dynamics. The advantages of the NCFD method include its high numerical accuracy and ability to capture complex chaotic dynamics. The H-LM offers simplicity and stability. The proposed methods prove to be capable of detecting chaotic attractors, estimating their behavior correctly, and finding accurate solutions. These findings confirm that NCFD- and H-LM-based approaches are promising methods for the modeling and solution of complex systems. Since these results provide improved numerical simulations and solutions for a broad class of fractional-order models, they will thus be of greatest use in forthcoming applications in engineering and science.

Inverse Properties Estimation of Methanol Adsorption in Activated Carbon to Utilise in Adsorption Cooling Applications: An Experimental and Numerical Study

The precise estimation of influential parameters in adsorption is a key point in conducting simulations for the sensitivity analysis and optimal design of cooling systems. This study explores the critical role of a new type of granular activated carbon (GAC-208C) in adsorption refrigeration systems. By fitting experimental and numerical models to the thermophysical properties of GAC/methanol as a working pair, an advanced methodology is established for the thermal analysis of the adsorption bed, addressing the various operating conditions overlooked in prior studies. The physical properties of the studied carbon sample are determined in a laboratory using surface area and pore volume tests, thermal adsorption analysis, and weight loss. To determine the thermal properties of GAC/methanol, the adsorption process is experimentally tested inside an isolated heat exchanger. A three-dimensional (3D) model is created to simulate the procedure and then coupled with the particle swarm optimisation (PSO) algorithm in MATLAB. The optimal thermal parameters for adsorption are determined by minimising the mean square error (MSE) of the adsorption bed temperature between the numerical and experimental data. The laboratory studies yielded accurate results for the physical properties of GAC, including adsorption capacity, porosity, permeability, specific heat capacity, density, activation energy, and the heat of adsorption. The thermal analysis of the adsorption process identified the ideal values for the Dubinin–Astakhov equation constants, diffusion coefficients, heat transfer coefficients, and contact resistance. The numerical model demonstrated strong agreement with the experimental results, and the dynamic behaviour of pressure and uptake distribution showed good agreement with 1.2% relative error. This research study contributes to the improved estimation of adsorption parameters to conduct more accurate numerical simulations and design new adsorption systems with enhanced performance under different operating conditions.

Optimization design of welding parameters of key components of car body based on finite element

Abstract The characteristics of the welding heat source, the morphology of the molten pool, the formation mechanism of the weld, and the amount of heat input have an important and direct influence on the welding quality and performance of the joint. At present, the empirical curve that depends on the experimental results or the calculation formula of statistics cannot comprehensively evaluate the impact of welding on the mechanical properties of the whole structure. Therefore, this research is based on the finite element analysis technique of Simufact Welding software and analyzes the evolution of the temperature field, stress field, and the deformation of the residual stress in the welding process, and provides a powerful tool and a lot of support for welding technology. The aim of the study is to develop an accurate numerical simulation method for the weld temperature field and a dynamic simulation analysis system for the weld stress field and deformation.

Accurate Cerebral Blood Flow Simulations Compared to Real Data

In this work, we develop models of cerebral venous blood flows in realistic 3D geometries and run accurate numerical 3D simulations leveraging real data. These data come from Magnetic Resonance Imaging measures and provide both morphological and physiological information on the same subject. It allows to calibrate a subject specific simulation and improve its reliability. We present the complete pipeline going from data pre-processing to the integration in the simulation framework. The 3D Finite Element simulations in the main cerebral venous vessels are coupled with Windkessel reduced models, whose parameters are chosen according to the data, to take into account the neglected network. First results are discussed and compared with literature data, opening the way to obtain reliable information difficult or even impossible to obtain in vivo in a non-invasive way. All codes are in-house openly developed ones to ensure reproducibility. p { line-height: 115%; margin-bottom: 0.1in; background: transparent

Assessment of RANS Models for Milli-Channel Turbulent Flow in Drip Irrigation Emitter

Accurate numerical simulation of turbulent flow within the milli-channels of drip irrigation emitters has long been a significant challenge. This paper presents a comprehensive Reynolds-Averaged Navier–Stokes (RANS) modeling-based analysis of the flow dynamics within the labyrinth milli-channel of a tooth-shaped emitter, with partial experimental validation. The objective was to assess the performances of four RANS turbulence models: RNG k-ε (RNG), Realizable k-ε (RKE), SST k-ω (SST), and baseline k-ω (BSL), alongside three near-wall treatments: scalable wall function (SWF), enhanced wall treatment (EWT), and y+-insensitive wall treatment (YIWT) for emitter flow analysis. The results showed that the RNG and RKE, coupled with EWT, are preferred options for predicting the flow rate—pressure loss relationship of the emitter, with relative errors of 2.08% and 1.02% in the discharge exponent and 5.66% and 7.58% in the flow rate coefficient, respectively. Although both RNG and RKE using SWF are viable for hydraulic performance prediction under high-flow rate conditions, the deviation of predicted flow rate reaches up to 25.46% under low-flow rate conditions. The SST and BSL models, utilizing YIWT effectively, captured induced vortices at channel corners; however, they underestimated emitter flow rates. Furthermore, computations using SWF failed to capture the asymptotic characteristics of flow parameters in the near-wall region, resulting in an overestimation of turbulent kinetic energy and turbulence intensity. Additionally, the magnitude of wall shear stress in the channel corners fell below the threshold required for self-cleaning, underscoring the necessity for optimizing channel structures to enhance the anti-clogging performance of the emitter.

Regional-Scale Equidistance Optimizing Method Considering the Equidistance Patterns of Discrete Global Grid Systems

The Discrete Global Grid System (DGGS) provides a foundational framework for the digital Earth, where uniform intercell distances are essential for accurate numerical simulations. However, due to the spherical topology, achieving strictly equidistant spherical grid cells is impractical. Most existing studies have focused on regional scales, which are constrained by data acquisition limitations and render global equidistant optimization algorithms economically infeasible. The equidistant characteristics of cells are influenced by map projections and often exhibit regional variations. In this paper, we analyze these equidistant characteristics and construct an equidistant pattern for an icosahedral hexagonal DGGS. By integrating this pattern into the icosahedral orientation method, we develop a regional-scale equidistant optimization method for DGGS. Experiments on river network extraction in the Yangtze River Basin demonstrate significant improvements: the equidistance of grid cells covering the region increased by over 34.2%, while the accuracy of river network extraction improved by 51.41%. Moreover, this method is extensible to other grid models, enhancing the broader applicability of DGGS.

Accurate numerical simulations of open quantum systems using spectral tensor trains.

Decoherence between qubits is a major bottleneck in quantum computations. Decoherence results from intrinsic quantum and thermal fluctuations as well as noise in the external fields that perform the measurement and preparation processes. With prescribed colored noise spectra for intrinsic and extrinsic noise, we present a numerical method, Quantum Accelerated Stochastic Propagator Evaluation (Q-ASPEN), to solve the time-dependent noise-averaged reduced density matrix in the presence of intrinsic and extrinsic noise. Q-ASPEN is arbitrarily accurate and can be applied to provide estimates for the resources needed to error-correct quantum computations. We employ spectral tensor trains, which combine the advantages of tensor networks and pseudospectral methods, as a variational ansatz to the quantum relaxation problem and optimize the ansatz using methods typically used to train neural networks. The spectral tensor trains in Q-ASPEN make accurate calculations with tens of quantum levels feasible. We present benchmarks for Q-ASPEN on the spin-boson model in the presence of intrinsic noise and on a quantum chain of up to 32 sites in the presence of extrinsic noise. In our benchmark, the memory cost of Q-ASPEN scales as a low-order polynomial in the size of the system once the number of system states surpasses the number of basis functions used in the spectral expansion.

Automated Gold Nanorod Spectral Morphology Analysis Pipeline.

The development of a colloidal synthesis procedure to produce nanomaterials with high shape and size purity is often a time-consuming, iterative process. This is often due to quantitative uncertainties in the required reaction conditions and the time, resources, and expertise intensive characterization methods required for quantitative determination of nanomaterial size and shape. Absorption spectroscopy is often the easiest method for colloidal nanomaterial characterization. However, due to the lack of a reliable method to extract nanoparticle shapes from absorption spectroscopy, it is generally treated as a more qualitative measure for metal nanoparticles. This work demonstrates a gold nanorod (AuNR) spectral morphology analysis tool, called AuNR-SMA, which is a fast and accurate method to extract quantitative structural information from colloidal AuNR absorption spectra. To demonstrate the practical utility of this model, we apply it to three distinct applications. First, we demonstrate this model's utility as an automated analysis tool in a high-throughput AuNR synthesis procedure by generating quantitative size information from optical spectra. Second, we use the predictions generated by this model to train a machine learning model to predict the resulting AuNR size distributions under specified reaction conditions. Third, we apply this model to spectra extracted from the literature where no size distributions are reported and impute unreported quantitative information on AuNR synthesis. This approach can potentially be extended to any other nanocrystal system where absorption spectra are size dependent, and accurate numerical simulation of absorption spectra is possible. In addition, this pipeline could be integrated into automated synthesis apparatuses to provide interpretable data from simple measurements, help explore the synthesis science of nanoparticles in a rational manner, or facilitate closed-loop workflows.

Locally-Verifiable Sufficient Conditions for Exactness of the Hierarchical B-spline Discrete de Rham Complex in $$\mathbb {R}^n$$

AbstractGiven a domain $$\Omega \subset \mathbb {R}^n$$ Ω ⊂ R n , the de Rham complex of differential forms arises naturally in the study of problems in electromagnetism and fluid mechanics defined on $$\Omega $$ Ω , and its discretization helps build stable numerical methods for such problems. For constructing such stable methods, one critical requirement is ensuring that the discrete subcomplex is cohomologically equivalent to the continuous complex. When $$\Omega $$ Ω is a hypercube, we thus require that the discrete subcomplex be exact. Focusing on such $$\Omega $$ Ω , we theoretically analyze the discrete de Rham complex built from hierarchical B-spline differential forms, i.e., the discrete differential forms are smooth splines and support adaptive refinements—these properties are key to enabling accurate and efficient numerical simulations. We provide locally-verifiable sufficient conditions that ensure that the discrete spline complex is exact. Numerical tests are presented to support the theoretical results, and the examples discussed include complexes that satisfy our prescribed conditions as well as those that violate them.

Influence of side channel inlet angle on energy conversion of a side channel pump

The side channel pump generates several disadvantage vortices due to abrupt structural changes at the junction of the impeller and side channel, leading to unstable flow, which may induce severe vortex cavitation at the inlet section of the side channel, its impact on the pump's unstable flow mechanism and on the energy conversion characteristics has yet to be thoroughly investigated. This paper explores the effect of backflow vortex on pump performance through optimizing side channel inlet angles by combining the Ω criterion, helicity, and entropy production methods. The computational fluid dynamics numerical simulation's accuracy has been experimentally verified. It was found that increasing the side channel inlet angle could improve internal flow, thereby suppressing backflow vortices and promoting dynamic vortices formation in the inlet section. The backflow vortex is the primary source of high localized energy loss in the inlet section, significantly influencing the reduction of flow loss. It also reduces low pressure areas caused by backflow vortices, thus, restricting cavitation origin. In addition, within a certain range, the flat side channel pump enhances its hydraulic performance, exhibiting the best performance at a 60° inlet angle with an efficiency improvement of 4.6% at the Best Efficiency Flow Point (BEP), which has the most effective backflow vortex suppression, and therefore, lowest flow losses. However, the head improvement was negligible. The performance improvement is due to complete energy conversion within the inlet section. This paper offers new insights into the mechanisms underlying internal energy loss and cavitation characteristics in refining side channel pumps.

Accurate and Efficient Numerical Simulation of Land Models Using SUMMA With SUNDIALS.

Numerical simulation of land models without error control can be highly inaccurate. We present the incorporation of the Suite of Nonlinear and Differential-Algebraic Equation Solvers (SUNDIALS) package to solve the equations that simulate thermodynamics and hydrologic processes in the Structure for Unifying Multiple Modeling Alternatives (SUMMA) land model. The algorithmic features of SUNDIALS, such as error estimation and adaptive order and step-size control, result in a SUMMA-SUNDIALS model that delivers substantially improved accuracy and relative computational efficiency compared to integration with the previous SUMMA model, which uses the low-order backward Euler method with no rigorous error control. The results are demonstrated through simulations over the North American continent with more than 500,000 spatial elements. Compared to the previous SUMMA model, we find that the simulations produced by the SUMMA-SUNDIALS model are orders of magnitude closer to converged solutions for the same computational cost. Being able to efficiently perform more reliable simulations makes the SUMMA-SUNDIALS model a powerful tool for improving our understanding of the terrestrial component of the Earth System.

Validation study of cross-ventilation in a realistic building geometry: RANS, SAS and LES

The validation of computational fluid dynamics (CFD) simulations of natural cross-ventilation flow with wind tunnel (WT) measurements is important in view of accurate and reliable numerical simulations. A review of the literature indicates that the majority of previous CFD and WT measurement studies employed a simplified generic single-zone building with a prismatic shape. The objective of this study is the validation of isothermal CFD simulations of two different realistic building models resembling a pitched roof single-story house, both without (case 1) and with internal partition (case 2). The CFD simulations were conducted using the 3D steady Reynolds-averaged Navier-Stokes (RANS) approach with the SST k-ω, RLZ k-ε and RNG k-ε turbulence models, scale-adaptive simulations (SAS) with the SST k-ω model, and large eddy simulations (LES) with the Smagorinsky-Lilly subgrid-scale model. The evaluation was performed in two parts: impact of turbulence model and impact of internal partition. The results show that LES and SAS exhibit a good agreement with WT results, outperforming RANS for the two cases. When considering only indoor streamwise mean velocity, for case 1, 97 % and 73 % of the sampled LES and SAS velocities fall with the uncertainty band of the WT measurements. For case 2, these values are 92 % and 75 % for LES and SAS, respectively. Steady RANS provides an agreement of only 56 % and 63 % for case 1 and case 2, respectively.

A data-free Kolmogorov–Arnold Network-based method for structured mesh generation

Mesh generation is a critical but time-consuming process for stable and accurate numerical simulations. Although multi-layer perceptron-based meshing methods can be effective, they suffer from slow training convergence and heavy reliance on prior datasets. To overcome these problems, we propose the Kolmogorov–Arnold Network-based meshing network, an efficient data-free method for structured mesh generation. The proposed method takes the meshing task as an optimization problem and embeds meshing-related differential equations into the loss function of Kolmogorov–Arnold Networks. It employs two parts to generate meshes efficiently. The Kolmogorov–Arnold Network part introduces learnable activation functions on the edges of the network, which enables the network to learn meshing rules between parametric and computational domains. The physics-informed learning part provides meshing-related information to guide the network training. Finally, the proposed method can produce high-quality structured meshes with a user-defined number of quadrilateral or hexahedral cells through feed-forward prediction. Experiments on different geometries show that the proposed method achieves up to three orders of magnitude improvement in meshing efficiency compared to traditional methods. It also outperforms state-of-the-art multi-layer perceptron-based methods, yielding high-quality meshes in both two-dimensional and three-dimensional cases without prepared data.

Mechanical performance analysis method for ribbed H-section aluminum alloy members with initial curvature and torsion angle

Mechanical performance analysis method for ribbed H-section aluminum alloy members with initial curvature and torsion angle

Advancing superconductivity research: Insights from numerical simulations of potassium fullerenide-60 and gold and with Ginzburg-Landau theory

Advancing superconductivity research: Insights from numerical simulations of potassium fullerenide-60 and gold and with Ginzburg-Landau theory

Research on the Hydrodynamic Characteristics of a Rectangular Otter Board in Different Work Postures Based on a Dynamic Model

This paper investigates the hydrodynamic characteristics of a rectangular otter board in different working postures by using a dynamic model. Dynamic models are mainly based on dynamic mesh techniques. The results of the dynamic model are, compared to the model test, carried out in a flume tank. Furthermore, different rotation speeds of dynamic model were analyzed. The research results are as follows: compared to flume tank results, the maximum error of the dynamic model is 23.77%. Moreover, the influence of rotation speed on the hydrodynamic board is not obvious, and 2 deg./s was chosen as the rotation speed. When the board is tilted slightly (including four working postures), its lift-to-drag ratio first increases slightly and then gradually decreases. Compared with the other three working postures, the pressure center coefficient of the board does not change significantly when it is tilted inward. When studying different working angles (including AOA and tilt angle) of the otter board, the numerical dynamic model significantly reduces repetitive setup work, making simulations more efficient. Its ability to provide continuous curves and a large volume of results offers researchers a more detailed and comprehensive understanding of the board’s hydrodynamics. Additionally, the dynamic model supports innovative fishery equipment development by allowing more accurate and continuous numerical simulations.