Effect of Time Step Size and Turbulence Model on the Open Water Hydrodynamic Performance Prediction of Contra-Rotating Propellers

A growing interest has been devoted to the contra-rotating propellers （CRPs） due to their high propulsive efficiency, torque balance, low fuel consumption, low cavitations, low noise performance and low hull vibration. Compared with the single-screw system, it is more difficult for the open water performance prediction because forward and aft propellers interact with each other and generate a more complicated flow field around the CRPs system. The current work focuses on the open water performance prediction of contra-rotating propellers by RANS and sliding mesh method considering the effect of computational time step size and turbulence model. The validation study has been performed on two sets of contra-rotating propellers developed by David W Taylor Naval Ship R ＆ D center. Compared with the experimental data, it shows that RANS with sliding mesh method and SST k-ω turbulence model has a good precision in the open water performance prediction of contra-rotating propellers, and small time step size can improve the level of accuracy for CRPs with the same blade number of forward and aft propellers, while a relatively large time step size is a better choice for CRPs with different blade numbers.

Modified precise time step integration method of structural dynamic analysis

The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.

On time-step in structural seismic response analysis under ground displacement/acceleration

There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.

A Proper Time Integration with Split Stepping for the Explicit Free-Surface Modeling

Errors due to split time stepping are discussed for an explicit free–surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with that of the baroclinic one. The baroclinic equation has three–time–level structure because of leapfrog scheme. The barotropic one, however, has two–time–level structure when represented in terms of the baroclinic time level, on which the baroclinic one is integrated. This incompatibility results in the splitting errors as shown in this paper. The proper split time stepping is therefore proposed in such a way that the compatibility is kept between the barotropic and baroclinic equations. Its splitting errors are shown extremely small, so that it is particularly relevant to long–term integration for climate studies. It is applied to a free–surface model for the North Pacific Ocean.

Multiple time step molecular dynamics simulation for interaction between dislocations and grain boundaries

A multiple time step algorithm, called reversible reference system propagator algorithm, is introduced for the long time molecular dynamics simulation. In contrast to the conventional algorithms, the multiple time method has better convergence, stability and efficiency. The method is validated by simulating free relaxation and the hypervelocity impact of nano-clusters. The time efficiency of the multiple time step method enables us to investigate the long time interaction between lattice dislocations and low-angle grain boundaries.

RETHINKING TO FINITE DIFFERENCE TIME-STEP INTEGRATIONS

The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and theschemes by the method employed in the present paper are made for diffusion andconvective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.

TIME ACCURATE 2D NAVIER-STOKES CALCULATIONS WITH A DUAL-TIME STEPPING METHOD

With the cell vertex finite volume discretization in space and second order backward implicit discretization in time, 2D unsteady Navier Stokes equations are solved by a dual time stepping method to simulate compressible viscous flow around rigid airfoils in arbitrary unsteady motion. The selection of physical time step is not restricted by stability condition any more, and most of the successful acceleration techniques used in steady calculations can be implemented to increase the computation efficiency.

Derivation and application of time step model in solidification process simulation

The heat transfer during the casting solidification process includes the heat radiation of the high temperature casting and the mold,the heat convection between the casting and the mold,and the heat conduction inside the casting and from the casting to the mold. In this paper,a formula of time step in simulation of solidification is derived,considering the heat radiation,convection and conduction based on the conservation of energy. The different heat transfer conditions between the conventional sand casting and the permanent mold casting are taken into account in this formula. The characteristics of heat transfer in the interior and surface of the casting are also considered. The numerical experiments show that this formula can avoid computational dispersion,and improve the computational efficiency by about 20% in the simulation of solidification process.

The Stable Explicit Time Stepping Analysis with a New Enrichment Scheme by XFEM

This paper focuses on the study of the stability of explicit time integration algorithm for dynamic problem by the Extended Finite Element Method(XFEM).A new enrichment scheme of crack tip is proposed within the framework of XFEM.Then the governing equations are derived and evolved into the discretized form.For dynamic problem,the lumped mass and the explicit time algorithm are applied.With different grid densities and different forms of Newmark scheme,the Dynamic Stress Intensity Factor(DSIF)is computed by using interaction integral approach to reflect the dynamic response.The effectiveness of the proposed scheme is demonstrated through the numerical examples,and the critical time stepping in different situations are listed and analyzed to illustrate the factors that affect the numerical stability.

ENTROPY CONSISTENCY OF LARGE TIME STEP SCHEMES FOR ISENTROPIC EQUATIONS OF GAS DYNAMICS

In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.

LARGE TIME STEP GENERALIZATION OF RANDOM CHOICE FINITE DIFFERENCE SCHEME FOR HYPERBOLIC CONSERVATION LAWS

A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.

UTC TIME STEP on the 1st of July 1997

A positive leap second will be introduced in the UTC time scale UTC(JATC)、UTC (CSAO) and UTC time signals of BPL、BPM transmittings at the end of June 1997. The sequence of dates of the UTC second markers will be:

A Time Series Intrusion Detection Method Based on SSAE,TCN and Bi-LSTM

In the fast-evolving landscape of digital networks,the incidence of network intrusions has escalated alarmingly.Simultaneously,the crucial role of time series data in intrusion detection remains largely underappreciated,with most systems failing to capture the time-bound nuances of network traffic.This leads to compromised detection accuracy and overlooked temporal patterns.Addressing this gap,we introduce a novel SSAE-TCN-BiLSTM(STL)model that integrates time series analysis,significantly enhancing detection capabilities.Our approach reduces feature dimensionalitywith a Stacked Sparse Autoencoder(SSAE)and extracts temporally relevant features through a Temporal Convolutional Network(TCN)and Bidirectional Long Short-term Memory Network(Bi-LSTM).By meticulously adjusting time steps,we underscore the significance of temporal data in bolstering detection accuracy.On the UNSW-NB15 dataset,ourmodel achieved an F1-score of 99.49%,Accuracy of 99.43%,Precision of 99.38%,Recall of 99.60%,and an inference time of 4.24 s.For the CICDS2017 dataset,we recorded an F1-score of 99.53%,Accuracy of 99.62%,Precision of 99.27%,Recall of 99.79%,and an inference time of 5.72 s.These findings not only confirm the STL model’s superior performance but also its operational efficiency,underpinning its significance in real-world cybersecurity scenarios where rapid response is paramount.Our contribution represents a significant advance in cybersecurity,proposing a model that excels in accuracy and adaptability to the dynamic nature of network traffic,setting a new benchmark for intrusion detection systems.

Analytical study of subcritical crack growth under mode I loading to estimate the roof durability in underground excavation

The long-term stability of the roof is particularly important in designing underground rock structures.To estimate the durability of roof strata in underground excavation,a computation scheme of subcritical crack growth is proposed in this study.By adopting the proposed method,the potential collapse location of strata is derivable in accordance with a static model,the durability of roof strata can be estimated,a dynamic time step control strategy is achieved to balance the accuracy and speed of computing,and the initial crack size of rock can be estimated.In addition to the above,a mechanical model of underground excavation with non-uniformly distributed loads and partially yielded foundation is presented as the prototypical case.A set of case studies is carried out that showcase a power correlation between applied stress and roof durability.The allowable applied tensile stress for a 100-year life cycle is about 76%of the tensile strength.By using the proposed subcritical crack growth computation scheme,the roof stability in an underground excavation can be identified not only from the spatial view but also from the temporal perspective.

An improvement to the simulation of phase-change heat-transfer during soil freezing and thawing

A new variable time step method,which is called the backwards calculating time step method,is presented in this paper.It allows numerical simulation of soil freezing and thawing while avoiding "phase change missing and overflowing".A sensitive heat capacity model is introduced through which the calculation errors are analyzed.Then the equation using the self-adjusted time step is presented and solved using finite differences.Through this equation,the time needed for a space cell to reach the phase change point temperature is calculated.Using this time allows the time step to be adjusted so that errors caused by "phase change missing and overflowing" are successfully eliminated.Above all,the obvious features of this method are an accelerated rate for adjusting the time step and simplifing the computations.An actual example proves that this method can accurately calculate the temperature fields during soil freezing and thawing.It is an improvement over traditional methods and can be widely used on complicated multi-dimensional phase change problems.

NUMERICAL ANALYSIS AND EXPERI-MENT OF UNSTEADY THERMAL FIELD OF ROTOR PLATE FOR EDDY CURRENT RETARDER

The physical model based on heat transfer theory and virtual boundary method for analyzing unsteady thermal field of rotor plate for eddy current retarder used in automobile is established and boundary conditions are also defined. The finite element governing equation is derived by Galerkin method. The time differential item is discrete based on Galerkin format that is stable at any condition. And a new style of varying time step method is used in iteration process. The thermal field on the rotor plate at the radial and axle directions is analyzed and varying temperature at appointed points on two side-surfaces is measured. The testing and analytical data are uniform approximately. Finite element method can be used for estimating thermal field of the rotor plate at initial design stage of eddy current retarder.

Lagrangian model of zooplankton dispersion:numerical schemes comparisons and parameter sensitivity tests

This paper presents two comparisons or tests for a Lagrangian model of zooplankton dispersion:numerical schemes and time steps.Firstly,we compared three numerical schemes using idealized circulations.Results show that the precisions of the advanced Adams-Bashfold-Moulton(ABM) method and the Runge-Kutta(RK) method were in the same order and both were much higher than that of the Euler method.Furthermore,the advanced ABM method is more efficient than the RK method in computational memory requirements and time consumption.We therefore chose the advanced ABM method as the Lagrangian particle-tracking algorithm.Secondly,we performed a sensitivity test for time steps,using outputs of the hydrodynamic model,Symphonie.Results show that the time step choices depend on the fluid response time that is related to the spatial resolution of velocity fields.The method introduced by Oliveira et al.in 2002 is suitable for choosing time steps of Lagrangian particle-tracking models,at least when only considering advection.

A new simple method of implicit time integration for dynamic problems of engineering structures

This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.

Non Linear Electrodynamics Contributing to a Minimum Vacuum Energy (“Cosmological Constant”) Allowed in Early Universe Cosmology

This article poses the question of a minimum cosmological constant, i.e. vacuum energy at the start of the cosmological evolution from a near singularity. We pose this comparing formalism as given by Berry (1976) as to a small time length, and compare that in its entirety to compare this value given by Berry (1976) with a minimum time length at the start of cosmological space-time evolution. Using the methodology of Zeldovich (1972) as to a problem with electron-positron pair production we also propose another upper bound to the problem of minimum time length which may be accessible to experimental inquiry. This then makes the problem of minimum time length a way of specifying a magnetic field dependence of the cosmological constant, which has major implications to answering if quintessence, i.e. a changing cosmological vacuum energy, or a constant for the “cosmological constant” problem. Our answer is an initial value for the cosmological vacuum energy 1010 - 1020 times greater than today which suggests either Quintessence, or if still a constant, a much better value for this parameter than what is suggested by traditional field theory methods. In closing we review how our construct supports work done by Corda, as to early universe models and what the implications are, as to the choices we have made.

Effect of Bed Vicinity on Vortex Shedding and Force Coefficients of Fluid Flow on an Offshore Pipeline

The effect of rigid bed proximity on flow parameters and hydrodynamic loads in offshore pipelines exposed to turbulent flow is investigated numerically. The Galerkin finite volume method is employed to solve the unsteady incompressible 2D Navier–Stokes equations. The large eddy simulation turbulence model is solved using the artificial compressibility method and dual time-stepping approach. The proposed algorithm is developed for a wide range of turbulent flows with Reynolds numbers of 9500 to 1.5×10^4.Evaluation of the developed numerical model shows that the proposed technique is capable of properly predicting hydrodynamic forces and simulating the flow pattern. The obtained results show that the lift and drag coefficients are strongly affected by the gap ratio. The mean drag coefficient slightly increases as the gap ratio increases, although the mean lift coefficient rapidly decreases. The vortex shedding suppression happen at the gap ratio of less than 0.2.