Effect Of Time Step Size Research Articles

Spatiotemporal Patterns in a Space–Time Discrete SIRS Epidemic Model with Self- and Cross-Diffusion

In this work, a two-dimensional Coupled Map Lattice (CML) method is applied to a continuous Reaction–Diffusion (RD) SIRS epidemic model. The model involves a complex, nonlinear incidence rate and the spatially heterogeneous self- and cross-diffusion coefficients. The CML method applied here results in a space–time discrete counterpart of the model. The basic reproduction number is derived, and the local stability of the fixed points of the discrete model is established. The two typical bifurcations of codimension 1, such as the flip and the Neimark–Sacker (NS) bifurcations, are investigated by utilizing the center manifold theory and the normal form theorem. Furthermore, the codimension-2 fold–flip bifurcation about the endemic fixed point is discussed in detail. Turing instability criterion of the cross-diffusion epidemic model is established by utilizing the CML method under periodic boundary conditions. Finally, the numerical simulations clarify both the effectiveness of all theoretical findings and the effects of time step size and cross-diffusion on the spatiotemporal patterns. The main contribution of this work is the discovery of some interesting Turing and non-Turing patterns which may be induced by flip–Turing instability, NS–Turing instability or fold–flip–Turing instability. Concretely speaking, spiral patterns are observed near the flip bifurcation threshold value and ultimately evolve into an irregular defect pattern. Stripe pattern, labyrinth pattern and circular pattern are observed near the NS bifurcation threshold value. The disorderly interwoven ribbon pattern, mosaic pattern and some irregular oscillatory patterns are observed near the fold–flip bifurcation point. Our results greatly help in predicting the long-term behavior of the space–time discrete SIRS epidemic model under study.

Effect of Different Time Step Sizes on Pedestrian Evacuation Time under Emergencies Such as Fires Using an Extended Cellular Automata Model

The cellular automata (CA) model has been a meaningful way to study pedestrian evacuation during emergencies, such as fires, for many years. Although the time step used in the CA model is one of the most essential elements, there is a lack of research on its impact on evacuation time. In this paper, we set different time step sizes in an extended cellular automaton model and discuss the effect of time step size on the overall evacuation time under different emergency types and levels. For a fixed step time mode, the larger the time step, the longer the evacuation time. In each time step size, the evacuation time gradually increases with the increase of emergency level, and there is a sharp increase when the time for pedestrians to move one step is exactly an integer multiple of the time step. When there is no friction between pedestrians, the evacuation time at each time step first decreases slightly with the increase of emergency level and then remains unchanged; the larger the time step, when the evacuation time remains unchanged, the lower the emergency level and the greater the evacuation time. For the variable time step model, when the friction between pedestrians approaches infinity, the total evacuation time does not change with the emergency level; when the friction between pedestrians is reduced, the total evacuation time slightly decreases with the increase of the emergency level. The less friction there is, the more significant the reduction. The results of previous actual experiments are also reflected in the simulation at a lower emergency level. The result shows that the time step size significantly impacts the evacuation simulation results of the CA model, and researchers should choose carefully to obtain more realistic simulation results.

A Fully Explicit Lattice Spring Elastoplastic Solid Model for Fluid Structure Interaction Applications

The Fluid Structure Interaction (FSI) solver based on mesh-less methods developed at University of Nottingham Malaysia has been proven to be successful in solving hydroelastic problems involving elastic body. In this paper, the possibility of modelling elastocplastic material behaviour using mesh-less method is further explored. Elastoplastic material bahaviour is essential for modelling ductile fracture in a wide range of engineering problems. The use of a type of nonlocal lattice spring model (LSM) based on fully explicit integration scheme in modelling elastoplastic material behaviour is presented in this work. Specifically, the return mapping algorithm is incorporated in the solid solver for modelling J2 plasticity. The effect of time step size and particle spacing on the accuracy of the solver are investigated by checking the predicted strain against theoretical solution. It is found out that the strain results obtained by varying the time step size are somewhat consistent with the theoretical solution. The predicted strain also converges to the theoretical result as the particle spacing is refined.

Numerical analysis of the heat pump water heater with immersed helically coiled tubes

With the aim of increasing the accuracy of the numerical results and reduce the computational time of simulation, our work focuses on the study of a heat pump water heater with immersed helically coiled tubes. The effects of the storage tank dimension and the copper coil pitch on the heating process were investigated by considering the evolution of temperature and velocity field of the waterside at the axial centerline of cylindrical water tank. The effects of varying the time step on the evolution of the average water temperature and velocities during the heating process are analyzed using Computational fluid dynamics (CFD) software package. The results showed that the effects of time step size on the results and clearly led to less accuracy. The validation of the numerical solutions was performed by comparing the simulated average water temperature with the results reported from the literature [1,2].It was found that the simulation and experimental results are in good agreement.

Time-stepping method for frictional contact of anisotropic viscoelastic solids

By the time-stepping method proposed in this paper, the basic equations for linear anisotropic viscoelasticity with small strains and quasi-static condition can be separated into two parts. One is an elastic system of the initial state, and the other is an elastic-like system related to the follow-up time step. Based upon this result, all the viscoelastic problems can be handled by two sets of elastic systems. Boundary element method and its associated constraint relations are then formulated for these two different elastic systems, which lead to a system of linear equations for each time step. To solve these systems of equations, in addition to the known boundary conditions for the non-contact portion, we need to pre-assume contact region and contact mode for each node pair as well as the possible slip direction, which should be checked later by contact criteria. Therefore, we further design an iteration procedure via time-stepping to solve the contact problems of anisotropic viscoelastic solids. The stability, accuracy, and generality of our proposed method are then demonstrated through three representative numerical examples. In these examples, the effects of time step size, material properties, friction coefficient, horizontal force as well as the presence of holes are all studied and discussed.

Development of stability maps for flashing-induced instability in a passive containment cooling system for iPOWER

Abstract A passive containment cooling system (PCCS) has been developed as advanced safety feature for innovative power reactor (iPOWER). Passive systems are inherently less stable than active systems and the PCCS encountered the flashing-induced instability previously identified. The objective of this study is to develop stability maps for flashing-induced instability using MARS (Multi-dimensional Analysis of Reactor Safety) code. Firstly, we conducted a series of sensitivity analysis to see the effects of time step size, nodalization, and alternative MARS user options on the onset of flashing-induced instability. The riser nodalization strongly affects the prediction of flashing in a long riser of the PCCS, while time step size and alternative user options do not. Based on the sensitivity analysis, a standard input and an analysis methodology were set up to develop the stability maps of PCCS. We found out that the calculated equilibrium quality at the exit of the riser as a stability boundary above 5 kW/m2 was approximately 1.2%, which was in good agreement with Furuya's results. However, in case of a very low heat flux condition, the onset of instability occurred at the lower equilibrium quality. In addition, it was confirmed that inlet throttling reduces the unstable region.

Implementation of a soil-structure interface constitutive model for application in geo-structures

In this paper, an implementation of an advanced two-surface plasticity interface constitutive model in a general-purpose finite element code ABAQUS for application in soil-structure interaction problems under static and dynamic loading conditions is presented. A recently developed constitutive model by the authors for gravelly soil-structure interface was improved to simulate the behavior of both gravelly and sandy soil-structure interfaces. A new failure surface was introduced into the model in order to simulate the softening behavior of interfaces under monotonic and cyclic loading. The constitutive model was then implemented in ABAQUS as a thin-layer interface element to demonstrate its capabilities in representing the complex behavior under different stress paths and normal stresses, including debonding and rebonding mechanisms at interface zones. The accuracy and robustness of the numerical implementation algorithm was examined by considering the effect of time step size, and by simulating different boundary value problems. The numerical predictions under different loading and boundary conditions were compared with experimental observations.

Effects of Turbulence Model and Numerical Time Steps on Von Karman Flow Behavior and Drag Accuracy of Circular Cylinder

The flow of air passing around a circular cylinder on the Reynolds number of 250,000 is to show Von Karman Vortex Street Phenomenon. This phenomenon was captured well by using a right turbulence model. In this study, some turbulence models available in software ANSYS Fluent 16.0 was tested to simulate Von Karman vortex street phenomenon, namely k- epsilon, SST k-omega and Reynolds Stress, Detached Eddy Simulation (DES), and Large Eddy Simulation (LES). In addition, it was examined the effect of time step size on the accuracy of CFD simulation. The simulations are carried out by using two-dimensional and three- dimensional models and then compared with experimental data. For two-dimensional model, Von Karman Vortex Street phenomenon was captured successfully by using the SST k-omega turbulence model. As for the three-dimensional model, Von Karman Vortex Street phenomenon was captured by using Reynolds Stress Turbulence Model. The time step size value affects the smoothness quality of curves of drag coefficient over time, as well as affecting the running time of the simulation. The smaller time step size, the better inherent drag coefficient curves produced. Smaller time step size also gives faster computation time.

Effect of time step size on configurational temperature accuracy in dissipative particle dynamics simulation of complex fluids

Effect of time step size on configurational temperature accuracy in dissipative particle dynamics simulation of complex fluids

On the efficiency of a matrix-free linearly implicit time integration strategy for high-order Discontinuous Galerkin solutions of incompressible turbulent flows

The paper aims at investigating and comparing the efficiency of matrix-based and matrix-free implementations of implicit time integration strategies, here linearly implicit Rosenbrock-type Runge–Kutta schemes, in the context of a high order Discontinous Galerkin space discretization applied to DNS/ILES of turbulent flows. In particular, the effects of time step size, GMRES solution tolerance and preconditioner, mesh size, order of polynomial approximation of the solution and parallel efficiency are here considered. The performance of the solvers have been compared though the solution of the two-dimensional laminar traveling waves test case, the ILES of the Rayleigh–Bénard natural convection up to Ra=108, and the channel flow up to Reτ=950. The results highlight that while matrix-based strategies are the most adequate for low-order polynomial approximations, considerable improvements in computational efficiency can be achieved, both in terms of CPU time and memory footprint, by a proper use of the matrix-free solver for three-dimensional test cases and very high-order accurate DG space discretizations.

A numerical model for transient simulation of borehole heat exchangers

A numerical model is developed to simulate the borehole heat exchanger both in the short and long time. In this regard, the computational domain is divided into the inside and outside borehole regions. A two-dimensional finite volume method is implemented in a cylindrical coordinate system for modeling of the outside borehole. Also, a thermal resistance-capacity model is presented for the borehole cross section. This model is extended to take into account the fluid transport through the U-tube and the temperature variation of the borehole components with depth. The governing equations of the two regions are solved iteratively in each time step. The proposed model is verified with the previously reported numerical, experimental and analytical results. Furthermore, the ability of the model in predicting the short-time response is evaluated in comparison with a three-dimensional computational fluid dynamics (CFD) model with a fine grid. The results show that the proposed model has a good performance in the prediction of the thermal response of the borehole in a wide time interval from 1 min to over 10 years. Moreover, the effects of time step size and number of capacity nodes on the results are investigated.

Quantitative photoacoustic image reconstruction improves accuracy in deep tissue structures.

Photoacoustic imaging (PAI) is emerging as a potentially powerful imaging tool with multiple applications. Image reconstruction for PAI has been relatively limited because of limited or no modeling of light delivery to deep tissues. This work demonstrates a numerical approach to quantitative photoacoustic image reconstruction that minimizes depth and spectrally derived artifacts. We present the first time-domain quantitative photoacoustic image reconstruction algorithm that models optical sources through acoustic data to create quantitative images of absorption coefficients. We demonstrate quantitative accuracy of less than 5% error in large 3 cm diameter 2D geometries with multiple targets and within 22% error in the largest size quantitative photoacoustic studies to date (6cm diameter). We extend the algorithm to spectral data, reconstructing 6 varying chromophores to within 17% of the true values. This quantitiative PA tomography method was able to improve considerably on filtered-back projection from the standpoint of image quality, absolute, and relative quantification in all our simulation geometries. We characterize the effects of time step size, initial guess, and source configuration on final accuracy. This work could help to generate accurate quantitative images from both endogenous absorbers and exogenous photoacoustic dyes in both preclinical and clinical work, thereby increasing the information content obtained especially from deep-tissue photoacoustic imaging studies.

Effect of time step size on stress relaxation

Effect of time step size on stress relaxation

The effect of time step, thermostat, and strain rate on ReaxFF simulations of mechanical failure in diamond, graphene, and carbon nanotube.

As the sophistication of reactive force fields for molecular modeling continues to increase, their use and applicability has also expanded, sometimes beyond the scope of their original development. Reax Force Field (ReaxFF), for example, was originally developed to model chemical reactions, but is a promising candidate for modeling fracture because of its ability to treat covalent bond cleavage. Performing reliable simulations of a complex process like fracture, however, requires an understanding of the effects that various modeling parameters have on the behavior of the system. This work assesses the effects of time step size, thermostat algorithm and coupling coefficient, and strain rate on the fracture behavior of three carbon-based materials: graphene, diamond, and a carbon nanotube. It is determined that the simulated stress-strain behavior is relatively independent of the thermostat algorithm, so long as coupling coefficients are kept above a certain threshold. Likewise, the stress-strain response of the materials was also independent of the strain rate, if it is kept below a maximum strain rate. Finally, the mechanical properties of the materials predicted by the Chenoweth C/H/O parameterization for ReaxFF are compared with literature values. Some deficiencies in the Chenoweth C/H/O parameterization for predicting mechanical properties of carbon materials are observed.

Performance analysis and feasibility study of ant colony optimization, particle swarm optimization and cuckoo search algorithms for inverse heat transfer problems

In the present work, three recently developed metaheuristic algorithms (ant colony optimization, cuckoo search and particle swarm optimization) are examined for a class of heat transfer problems. Unknown boundary heat fluxes are estimated for conduction, convection and coupled conduction–radiation problems. Direct problems are solved to determine temperature distribution assuming known boundary heat flux. Inverse method is then used to estimate boundary heat flux with the help of the temperature previously determined from the direct problem. To replicate experimental error, effect of noise on temperature data is introduced to examine the robustness of all the algorithms. Effect of time step size and regularization are studied. It is found that all the algorithms are promising and can be used for this class of inverse heat transfer problems. Performance of all the algorithms is comparable. Efficiency of the three algorithms is compared in terms of CPU time. Ant colony optimization algorithm is found to be most efficient followed by particle swarm optimization and cuckoo search algorithms for all the considered heat transfer problems. All the algorithms are also applied to estimate diffusion coefficient of a food material (mushroom) using experimental data.

Time dependent adjoint-based optimization for coupled fluid–structure problems

A formulation for sensitivity analysis of fully coupled time-dependent aeroelastic problems is given in this paper. Both forward sensitivity and adjoint sensitivity formulations are derived that correspond to analogues of the fully coupled non-linear aeroelastic analysis problem. Both sensitivity analysis formulations make use of the same iterative disciplinary solution techniques used for analysis, and make use of an analogous coupling strategy. The information passed between fluid and structural solvers is dimensionally equivalent in all cases, enabling the use of the same data structures for analysis, forward and adjoint problems. The fully coupled adjoint formulation is then used to perform rotor blade design optimization for a four bladed HART2 rotor in hover conditions started impulsively from rest. The effect of time step size and mesh resolution on optimization results is investigated.

Accuracy of dynamic disk-based DDA with respect to a single sliding disk cluster

Disk clusters are developed to represent the shape of granular materials more precisely (compared to circular particles) and to minimise excessive rolling. Investigating the behaviour of dynamic disk-based discontinuous deformation analysis (DDA) with disk clusters is very important to evaluate the applicability of disk-based DDA to dynamic problems in geomechanics. In this paper, the accuracy of disk-based DDA under dynamic conditions is studied by a comprehensive sensitivity analysis. The results obtained by disk-based DDA are compared with the analytical solutions of a disk cluster on an incline subjected to gravitational force only, and three different accelerations of increasing complexity with sinusoidal input functions as well as gravitational load. In this research, the effects of time step size and interface friction angles on the results are studied. Overall, most of the error for both velocity and displacement occurs at the beginning of the solution. With increasing friction angle, the initial perturbation of the solution increases in the case of sliding under gravitational force only, and decreases in the case of sliding under dynamic loads. This study shows that disk-based DDA predicts accurately the velocities and displacements derived with respect to the frictional resistance offered by the inclines.

Effects of mesh refinement, time step size and numerical scheme on the computational modeling of temperature evolution during natural-convection heating

A computational fluid dynamics (CFD) analysis includes creating geometry, dividing it into elements, discretizing governing equations and solving with suitable numerical schemes. Refining mesh and lowering time step size increase accuracy. However, this may not always give the best result since convergence depends upon parameters of time step size, mesh resolution and numerical scheme. Therefore, the objective of this study was to determine the effects of these on the accuracy of a CFD solution. For this purpose, canning example was used, and results obtained with ANSYS CFX (v12.1.) were experimentally validated. Effects of time step size, mesh resolution and numerical scheme on temperature and velocity field evolution were determined. Mesh refinement affected temperature distribution significantly and surprisingly led to less accuracy. The reasons for this behavior were presented and explained comprehensively.

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.

Effects of time step size on the simulation of tropical climate in NCAR-CAM3

This paper describes the effects of time step on the simulation of tropical climate in the NCAR-Community Atmosphere Model version 3 (CAM3). A set of multi-year integrations are carried out in a real-planet framework using actual land–ocean distribution and observed sea surface temperature. Over the tropics there is an increase in total rainfall with a decrease in time step size. Using a lower time step, there is a decrease in the convective component of rainfall, however, the stratiform component increases, and more than compensates the decrease in the former, thus leading to a higher total rainfall. A decrease in time step leads to an increase in the frequencies of moderate, and heavy rainfall categories, which is responsible for the increase in time mean total rainfall over the tropics. Also, the spatial distribution of rainfall becomes more realistic during both summer and winter seasons. In regard to the simulation of equatorial waves, it is found that a lower time step leads to a reduction in the speed of Kelvin waves. The latent heating profile becomes more bottom-heavy with a reduction in time step size, which potentially leads to slower Kelvin waves. Finally, additional experiments conducted in an aqua-planet framework show a consistent and systematic change in the analyzed variables with change in time step, and hence confirm the robustness of the results across modeling frameworks.