Nodal Correction Research Articles

Verification of tidal trends in Cananeia (SP) and Santos (SP)

Recent studies indicate an imminent global rise in mean sea level. However, comprehending variations in tidal patterns is imperative before analyzing the scenario of extreme events, typically associated with the combination of high tides and intense meteorological influences. This study presents local trends in sea level, amplitude, and phase of the two main tidal components in Cananeia (SP) and Santos (SP), utilizing tide gauge data from records of sufficient length to avoid the need for nodal correction in the tide components. Using more up-to-date tide gauge data allowed the investigation of observed trends. Long-term tidal data series revealed an upward trend in mean level of approximately 4,324 mm/year in Cananeia and 0,538 mm/year in Santos. Both locations were affected by human activities along their estuaries, with Santos experiencing significant variations in the amplitude and phase values of the tidal constituents annually.

Compression Behavior of Pilar Octahedral Lattice Structures

Lattice structures have a great potential in the fields like aerospace and biomedical, due to their outstanding properties like high strength, low mass, and good energy absorption capacity. With the development of the Additive Manufacturing technologies, there was an increasing attention towards these structures. The compressive behavior of the pilar octahedral lattice structure, which has the high strength to weight ratio was analyzed in this work. Lattice structures with three strut diameters of 1.5, 1.75, and 2 mm were built using Fused Filament Fabrication from Tough Polylactic Acid (PLA) plastic. Quasi-static compression tests were performed and two finite element models using beam elements with and without nodal beam diameter correction were proposed. It was found that as the diameter of the strut increases strength and elastic moduli are increased as well, while specific mechanical properties almost do not change. It was also confirmed from numerical and experimental results that lattice structure fails by forming a diagonal shear band. The relative error of the simulation without nodal correction in predicting the strength of the lattice with a 1.5 mm strut diameter was 1.58%. However, due to the inability of the beam element to model the behavior at the nodes properly its accuracy decreases for larger diameters. By modifying the model and using a nodal beam diameter correction, it has been possible to achieve a relative error of 0.58% and 12.15% for strut diameters of 1.75 and 2 mm respectively.

On the variation of LAT resulting from predictions computed using different tidal constituent sets

ABSTRACT While the Lowest Astronomical Tide (LAT) has a clear definition as the lowest water level caused by astronomical attractions at a water level station, there are variations in the implementation schemes for practically deriving LAT from a time series of tides. This article explores the variation resulting from different tide constituent sets, as named by the numbers, 25, 37, or 60 constituents. Hourly observations of 34 stations around Taiwan were examined in this study. Using LAT-60, the LAT with 60 constituents, as the reference, when the nodal correction is applied, the average deviation of LAT-25 is −2.12 cm, LAT-37 is 0.70 cm, and ISLW is 22.44 cm. Based on the experiments conducted, it is found that the difference between LAT-25 and LAT-60 is 1.18 cm as measured by the third quartile without nodal correction, and 0.89 cm with nodal correction. Nodal correction will lower the water level about 2 cm on average and maximum about 6.7 cm. ISLW is higher and has less influence by nodal correction than LAT so it is difficult to be regarded as a fairly stable water level for chart datum.

Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

A numerical procedure is presented to avoid the divergence problem during the iterative process in viscoelastic analyses. This problem is observed when the positional formulation of the finite element method is adopted in association with the finite difference method. To do this, the nonlinear positional formulation is presented considering plane frame elements with Bernoulli–Euler kinematics and viscoelastic behavior. The considered geometrical nonlinearity refers to the structural equilibrium analysis in the deformed position using the Newton–Raphson iterative method. However, the considered physical nonlinearity refers to the description of the viscoelastic behavior through the adoption of the stress-strain relation based on the Kelvin–Voigt rheological model. After the presentation of the formulation, a detailed analysis of the divergence problem in the iterative process is performed. Then, an original numerical procedure is presented to avoid the divergence problem based on the retardation time of the adopted rheological model and the penalization of the nodal position correction vector. Based on the developments and the obtained results, it is possible to conclude that the presented formulation is consistent and that the proposed procedure allows for obtaining the equilibrium positions for any time step value adopted without presenting divergence problems during the iterative process and without changing the analysis of the final results.

Comparison of Admiralty and Least Square Methods for Tidal Analysis in Mandangin Island, Sampang Regency, East Java

The existence of hydro-oceanographic information such as tides plays an essential role in supporting coastal areas' transportation. This study aims to compare the tidal analysis results in Mandangin Island, Sampang Regency, East Java using the Admiralty and Least Square methods. The data used in this study are tidal data for May and November 2020, which represent the dry and rainy seasons in Indonesia. Tide data are obtained from the Geospatial Information Agency (BIG) at one-hour intervals. From this research, it can be concluded that the tidal types generated from the Admiralty and Least Square methods in Mandangin Island, East Java, are mixed types with semidiurnal tendencies. The use of the Admiralty and Least Square methods results in the difference in the harmonic components' amplitude values. The M2 and O1 components have an enormous difference in May 2020, with amplitude values of 0.0003 and 0.0002, and the difference in the amplitude values of the harmonic components also occurred in November 2020. The M2 component has the most significant difference compar e to other components, namely 0.0011. The components O1, P1, and MS4 in the same month result in a relatively small difference in amplitude values with values of 0.0002, 0.0002, and 0.0001. For further tidal research, data corrections should be considered, a nodal correction to produce more accurate observational data. This correction can use the T_Tide program with constants obtained from the analysis process.

Prediction of elastic-plastic deformation of nanoporous metals by FEM beam modeling: A bottom-up approach from ligaments to real microstructures

For the prediction of elastic-plastic deformation behavior of nanoporous materials, a computationally efficient method is needed that integrates the complex 3D network structure and the large variation of ligament shapes in a representative volume element. Finite element simulations based on beam elements are most efficient, but for a quantitative prediction, a correction is required that accounts for the effects of the mass around the junctions. To this end, a nodal correction is presented that covers a wide range of parabolic-spherical ligament shapes. Smooth functions are provided that define the extension of the nodal corrected elements along the ligament axis, their radius and their yield stress as functions of the individual ligament shape. It is shown that the increase in radius of the nodal beam elements can be replaced by scaled material parameters. Simulations of randomized FEM beam networks revealed that, in relation to the randomization of the ligament axis, the distribution of the ligament shape has a stronger impact on the macroscopic stress–strain response and should thus receive particular attention during the characterization of nanoporous microstructures. This also emphasizes the importance of the thickness analysis via image processing. Combining a nodal corrected FEM beam model with geometry data derived from image multiplication of the skeleton and Euclidean distance transform of a nanoporous gold FIB-SEM tomography dataset significantly improves the prediction of the stress–strain curve. The remaining deviation is expected to stem from the known underestimation of the real ligament diameter by the Euclidean distance transform as well as local variations in the circularity of the ligaments.

Computation of Thickness and Mechanical Properties of Interconnected Structures: Accuracy, Deviations, and Approaches for Correction

Identifying local thickness information of fibrous or highly porous structures is challenging. The analysis of tomography data calls for computationally fast, robust and accurate algorithms. This work systematically investigates systematic errors in the thickness computation and the impact of observed deviations on the predicted mechanical properties using a set of 16 model structures with varying ligament shape and solid fraction. Strongly concave, cylindrical, and convex shaped ligaments organized in a diamond structure are analyzed. The predicted macroscopic mechanical properties represent a highly sensitive measure for systematic errors in the computed geometry. Therefore, the quality of proposed correction methods is assessed via FEM beam models that can be automatically generated from the measured data and allow an efficient prediction of the mechanical properties. The results show that low voxel resolutions can lead to an overprediction of up to 30% in the Young’s modulus. A model scanned with a resolution of 200 voxels per unit cell edge (8M voxels) reaches an accuracy of a few percent. Analyzing models of this resolution with the Euclidean distance transformation showed an underprediction of up to 20% for highly concave shapes whereas cylindrical and slightly convex shapes are determined at high accuracy. For the Thickness algorithm, the Young’s modulus and yield strength are overpredicted by up to 100% for highly concave ligament shapes. A proposed Smallest Ellipse approach corrects the Thickness data and reduces this error to 20%. It can be used as input for a further robust correction of the Thickness data using an artificial neural network. This approach is highly accurate with remnant errors in the predicted mechanical properties of only a few percent. Furthermore, the data from the FEM beam models are compared to results from FEM solid models providing deeper insights towards further developments on nodal corrections for FEM beam models. As expected, the FEM beam models show an increasing overprediction of the compliance with increasing solid fraction. As an unexpected result, the mechanical strength can however be underpredicted or overpredicted, depending on the ligament shape. Therefore, a nodal correction is needed that solves contradicting tasks in terms of stiffness and strength.

Effect of nodal mass on macroscopic mechanical properties of nanoporous metals

The current work investigates the effect of the nodal mass on the macroscopic mechanical behavior of nanoporous metals using the Finite Element Method. A nodal corrected beam modeling concept is introduced that allows local incorporation of the effective elastoplastic mechanical behavior of the nodal mass in the nodal area of a representative volume element (RVE). The calibration to the corresponding Finite Element solid model is achieved by integrating additional geometry and material parameters to the so-called nodal areas in the beam model. With this technique an excellent prediction can be achieved over a large range of deformation for different types of RVEs. From the results of the nodal corrected beam model, modified leading constants are determined in the scaling laws for Young's modulus and yield strength. The effect of the nodal correction is also studied with respect to various randomization levels. Finally, the ligament size dependent strength is analyzed by applying the proposed model to experimental data. It could be shown that the nodal correction improves the overall agreement with literature data, particularly for such data points that are related to samples with a high solid fraction.

The role of environmental forcing on tidal dynamics along complex near-shore waters off Bangladesh

In a geomorphic sense, the Bangladesh located in the head Bay region comprises of numerous tidal creeks, waterway inlets, and complex coastline geometry. This region encompassing the world׳s largest deltaic system is thickly populated and extremely low-lying, and therefore highly susceptible to coastal flooding and sea level rise. High tidal range existent in this region primarily governs the hydrodynamic behavior and coastal processes. The present study deals on a comprehensive tidal analysis, understanding the variations in tidal behavior over spatial and temporal scales in the near-shore region off Bangladesh. The harmonic tidal analysis using SLPR2 estimates the tidal constituents using linear least squares with respective nodal correction. Tide gauge observations from five different stations viz; Hiron Point, Khepupara, Charchanga, Khal No-10, and Cox׳s Bazaar were used for tidal analysis. The results from SLPR2 signify considerable seasonal variations in water level attributed due to meteorological factors and excess river discharge. Tidal pattern at all these five stations are primarily mixed semi-diurnal with M2 as the dominant constituent. The t-tide toolbox computed the equilibrium tidal amplitude for the study area. Some of the components known to be influenced by meteorological aspects such as Solar Annual component (Sa), Semi-Annual component (Ssa), and Solar Radiational component (S1) have higher amplitudes than expected, in the study area. The shallowness of the delta cause severe deviations in the tidal behavior from equilibrium tides. Interaction of tides with river discharge also dominant in this region indicates the role of hydrological forcing. Interestingly, the study also reveals the existence of compound tidal constituent Msf in this region. Monthly analysis of Msf component, using FFT, revealed peaks corresponding to the monsoon, Kal-Baisakhi months and to the seasonal changes in atmospheric pressure, thereby unfolding the seasonal influence on Msf. The funnel shaped head Bay plays an important role in amplification of tidal constituents, wherein the form factor and maximum tide levels showed an increasing trend. This study also demonstrates how tidal dynamics can be elucidated using location specific water-level observations. Investigations on the annual variations in observed and predicted water levels clearly signify the seasonal patterns. The correlation analysis show a reasonable match with skill level exceeding 93%, and the overall prediction by SLPR2 is highly satisfactory.

Harmonic Analysis in the Simulation of Multiple Constituents: Determination of the Optimum Length of Time Series

AbstractTo investigate the optimum length of time series (TS) for harmonic analysis (HA) in the simulation of multiple constituents, a two-dimensional tidal model is used to simulate the M2, S2, K1, and O1 constituents in the Bohai and Yellow Seas. By analyzing the HA results of several nonoverlapping TS of the same length, which varies from 15 to 365 days, a field-average deviation of HA results is calculated. A deviation that is sufficiently small means that HA results are independent of the choice of TS, and the corresponding TS length is regarded as the optimum. Results indicate that the range of 180–195 days is the optimum length of TS for HA in the simulation of the four principal constituents. To investigate what determines the optimum length, experiments with different computed area and model settings are carried out. Results indicate that the optimum length is independent of advection, nodal corrections, and computed area, and only depends on bottom friction. Nonlinear bottom friction results in the appearance of higher harmonics and explains why the optimum length of TS for HA is 180–195 days.

Harmonic Decomposition Tidal Analysis and Prediction Based on Astronomical Arguments and Nodal Corrections in Persian Gulf, Iran

The establishment and maintenance of marine structures and near-shore constructions together require having sufficient and accurate information about sea level variations not only in the present time but also in the near future as a reliable prediction. It is therefore necessary to analyze and predict Mean Sea Level (MSL) for a specific time considering all possible effects which may modify the accuracy and precision of the results. This study presents tidal harmonic decomposition solutions based on the first and second method of solving the Fourier series to analyze of the tides in January 2010 hourly and predict for the whole days of 2012 year considering the astronomical arguments and nodal corrections in Bandar-e-Abbas, Kangan Port and Bushehr Port tide gauge stations located in the Persian Gulf at the South of Iran. Moreover the accurate predictions of Mean Tide Level (MTL) are provided for the entire of 2012 year in each tide gauge station by excluding the effects of astronomical arguments and nodal corrections due to their unreasonable destroying effects. The MTL's fluctuations derived from the predicted results during 2012 year and different phases of the Moon show a very good agreement together according to tide- generating forces theories.

Versatile Harmonic Tidal Analysis: Improvements and Applications

Abstract New computer software that permits more versatility in the harmonic analysis of tidal time series is described and tested. Specific improvements to traditional methods include the analysis of randomly sampled and/or multiyear data; more accurate nodal correction, inference, and astronomical argument adjustments through direct incorporation in the least squares matrix; multiconstituent inferences from a single reference constituent; correlation matrices and error estimates that facilitate decisions on the selection of constituents for the analysis; and a single program that analyzes one- or two-dimensional time series. This new methodology is evaluated through comparisons with results from old techniques and then applied to two problems that could not have been accurately solved with older software. They are (i) the analysis of ocean station temperature time series spanning 25 yr, and (ii) the analysis of satellite altimetry from a ground track whose proximity to land has led to significant data dropout. This new software is free as part of the Institute of Ocean Sciences (IOS) Tidal Package and can be downloaded, along with sample input data and an explanatory readme file.

Efficient solution techniques for implicit finite element schemes with flux limiters

AbstractThe algebraic flux correction (AFC) paradigm is equipped with efficient solution strategies for implicit time‐stepping schemes. It is shown that Newton‐like techniques can be applied to the nonlinear systems of equations resulting from the application of high‐resolution flux limiting schemes. To this end, the Jacobian matrix is approximated by means of first‐ or second‐order finite differences. The edge‐based formulation of AFC schemes can be exploited to devise an efficient assembly procedure for the Jacobian. Each matrix entry is constructed from a differential and an average contribution edge by edge. The perturbation of solution values affects the nodal correction factors at neighbouring vertices so that the stencil for each individual node needs to be extended. Two alternative strategies for constructing the corresponding sparsity pattern of the resulting Jacobian are proposed. For nonlinear governing equations, the contribution to the Newton matrix which is associated with the discrete transport operator is approximated by means of divided differences and assembled edge by edge. Numerical examples for both linear and nonlinear benchmark problems are presented to illustrate the superiority of Newton methods as compared to the standard defect correction approach. Copyright © 2007 John Wiley & Sons, Ltd.

Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE

A standard part of any oceanic pressure gauge or current meter analysis is the separation of tidal from non-tidal components of the signal. The tidal signal can either be discarded, or its characteristics described in some fashion useful for further analysis. Although tidal signals can be removed by standard high or bandpass filtering techniques, their relatively deterministic character and large amplitude make special techniques more effective. In classical harmonic analysis, the tidal signal is modelled as the sum of a finite set of sinusoids at specific frequencies related to astronomical parameters. A set of programs has been written in MATLAB to (a) perform classical harmonic analysis for periods of about 1 year or shorter, (b) account for (some) unresolved constituents using nodal corrections, and (c) compute confidence intervals for the analyzed components.

Possibility of rapid changes in the tide of the Bay of Fundy, based on a scrutiny of the records from Saint John

The tide gauge at Saint John Harbour (45°19′N, 65°59′W), in the Bay of Fundy, has functioned almost continuously since 1894. The data scrutinized by Doodson (1924) as well as that covering 1947–1979, reveals that the amplitude of the major component of the tide, M 2, has been increasing since the beginning of the observations. The amplification is of the order of 10–15 cm century −1 and shows signs of accelerating, The solar component S 2, on the other hand, is diminishing at the rate of 4–5 cm century −1. Since the conventional nodal corrections fail to stabilize the M 2 component, Doodson developed a formula to reproduce its local 19 year modulations. The formula took account of the effects of quadratic friction and revealed the phase discontinuity between M 2 and its satellites, but it overlooked the reduction in the size of the nodal modulations. A least square fit over a set of M 2 samples, derived from the later years, gives an actual range of modulation of ±2.8% with a possible error of at least ±0.7%, compared with the theoretical ±3.7%. Consequently the tide in the Bay of Fundy, known to be strongly affected by frictional effects, is also evolving rapidly, probably because of the continuous increase in sea level and a redistribution of the sediments in Minas and Cumberland Basins.

Third order effects in the tide of the Pacific, near Acapulco

Vertical oscillations, attributable to the third order term of the potential of the tide-generating forces, are conspicuous in the semidiurnal band, near the frequency of L 2, in water level records from Acapulco on the Pacific coast of Mexico and at other sites. Since the relative magnitude of the third order contribution can only be derived from similar observations at any gauging site, it is not possible to take into account third order inputs in conventional nodal corrections.