Fluid–structure interaction approaches on fixed grids based on two different domain decomposition ideas

This paper presents two domain decomposition techniques for fixed grid fluid–structure interaction simulations that can be applied to the interaction of general structures with incompressible flows. One approach is based on an overlapping domain decomposition idea while the other uses non-overlapping domains. The first technique combines a fixed grid Chimera approach with arbitrary Lagrangean Eulerian based methods, the second one is based on an eXtended Finite Element Method (XFEM) strategy. Both techniques are used in a partitioned and strong coupling fluid–structure framework. The usage of such fixed-grid methods considerably increases the range of possible applications. Several test examples demonstrate key features of both methods.     

Measurement on particle rotation speed in gas–solid flow based on identification of particle rotation axis

When a two-dimensional (2D) imaging system is used to visualize particle motion in a 3D gas–solid flow, the particle rotation speed was found extremely difficult to be accurately measured due to the fact that the direction of rotation axis was usually random and hard to be distinguished. The paper presents a method to calculate the particle rotation speed from particle images based on the identification of its rotation axis using two or more characteristic points on its surface. The idea was analyzed and realized in a mathematical way and based on which a calculation program was given. The measurement method was verified with an experiment using a small sphere with known rotation axis and rotation speed. The effects of several factors, including the direction of the particle rotation axis, the particle image resolution, the types and positions of characteristic points, etc., on the measurement error are discussed. The error is found to be acceptable for most cases. The measurement method was finally applied to those small glass beads in a real 3D gas–solid flow inside a cold circulating fluidized bed (CFB) riser, which indicates that the problems of 2D imaging system applying to 3D particulate system could be solved by using this mathematical method.     

Acoustoelastic effect simulation by time–space finite element formulation based on quadratic interpolation of the acceleration

Acoustoelastic effect describes the change of ultrasound velocity due to the initial stress. Its simulation involves a numerical analysis of nonlinear elastodynamics and requires high accuracy in the time domain. A time–space finite element formulation, derived from the quadratic interpolation of the acceleration within a time segment, is proposed for an accurate simulation of the acoustoelastic effect in the present study. Ten different integration schemes are generated based on this formulation and nine of them are found to be conditionally stable. Among the nine stable schemes, one is found to obtain a spectral radius of one when the normalized step ratio is less than 5.477, indicating no numerical dissipation or numerical divergence. Compared with integration schemes from previous studies, this integration scheme demonstrates better performance in calculation accuracy and energy conservation. A two-stage approach, namely the static stage and the dynamic stage, has been employed in the simulation of the acoustoelastic effect. The former stage is adopted to obtain the initial stress and the latter stage, where the proposed integration scheme is implemented, is adopted to simulate the ultrasound propagation in an initial stress state. The simulation results of the dynamic stage show that the ultrasound velocity increases in a compression stress state and decreases in a tension stress state for aluminum alloy, which is in good agreement with previous experimental studies. Together with the simulation result of the static stage, it is conjectured that the acoustoelastic effect results from the stress-dependent elastic modulus.     

Generalized Swift–Hohenberg and phase-field-crystal equations based on a second-gradient phase-field theory

Meccanica - The principle of virtual power is used derive a microforce balance for a second-gradient phase-field theory. In conjunction with constitutive relations consistent with a free-energy...     

Algorithm and implementation of soil–tire contact analysis code based on dynamic FE–DE method

One of the fundamental problems in terramechanics is soil–tire system. Past achievements on this topic can be observed in various literatures. Fast development on CPU power of PC system enables us to apply numerical methods to this basic subject. Among others, finite element method (FEM) has been applied to simple problems of soil–tire system not only in 2D but also in 3D approach. However, it is noted that the current FEM technology cannot handle “singular” boundary conditions with sufficient accuracy of analysis. Typical example of this limitation can be seen in an application to traction tire–soil contact problems, where the contact point of tire lug tip behaves as the singular point of stress field. On the other hand, distinct or discrete element method (DEM) has in essence the capability of analyze microscopic deformation (or flow) of soil as many researchers have already been demonstrated. It is noted that DEM suffers large calculation time that is consumed not only at contact check between particulate elements but also at incremental time step. In our present study, we try to combine both merit of FEM and DEM together in order to analyze the soil–tire system interaction, where, for example, a tire and deep soil layer are modeled as FEM and soil surface layer as DEM. We propose simple algorithm of this FE–DE coupled method and sample program is developed that can solve some basic terramechanics problems in order to verify our idea. The obtained result shows qualitatively sufficient accuracy.     

Rankine–Hugoniot conditions for fluids whose energy depends on space and time derivatives of density

By using the Hamilton principle of stationary action, we derive the governing equations and Rankine–Hugoniot conditions for continuous media where the specific energy depends on the space and time density derivatives. The governing system of equations is a time reversible dispersive system of conservation laws for the mass, momentum and energy. We obtain additional relations to the Rankine–Hugoniot conditions coming from the conservation laws and discuss the well-founded of shock wave discontinuities for dispersive systems.     

Efficient cryptosystem approaches: S-boxes and permutation–substitution-based encryption

Nonlinear Dynamics - In this paper, two efficient cryptosystem schemes in the form of permutation–substitution based on chaotic systems are proposed. Firstly, a simple and efficient S-box...     

Spectral method and Bayesian parameter estimation for the space fractional coupled nonlinear Schrödinger equations

Nonlinear Dynamics - In a lot of dynamic processes, the fractional differential operators not only appear as discrete fractional, but they also have a continuous nature in some sense. In the...     

A novel method for designing S-box based on chaotic map and Teaching–Learning-Based Optimization

A new method for obtaining strong S-boxes based on chaotic map and Teaching–Learning-Based Optimization (TLBO) is presented in this paper. Our method presents eight rounds; each round contains two transformations: row left shifting and columnwise rotation. The vectors for the transformations are different from one round to another, and they are controlled by two keys to the logistic map. These two keys are optimized by using TLBO which aims to construct a strong S-box that satisfies to the criteria set in advance. Test for the following criteria such as bijectivity, nonlinearity, strict avalanche criteria, equiprobable inputs/outputs XOR distribution is analyzed. Additionally, we will provide many comparisons with other S-boxes and test of the sensitivity to keys. The results of performance test show that the proposed design S-boxes presents good cryptography proprieties and can resist to several attacks.     

Development and elaboration of numerical method for simulating gas–liquid–solid three-phase flows based on particle method

A numerical method for simulating gas–liquid–solid three-phase flows based on the moving particle semi-implicit (MPS) approach was developed in this study. Computational instability often occurs in multiphase flow simulations if the deformations of the free surfaces between different phases are large, among other reasons. To avoid this instability, this paper proposes an improved coupling procedure between different phases in which the physical quantities of particles in different phases are calculated independently. We performed numerical tests on two illustrative problems: a dam-break problem and a solid-sphere impingement problem. The former problem is a gas–liquid two-phase problem, and the latter is a gas–liquid–solid three-phase problem. The computational results agree reasonably well with the experimental results. Thus, we confirmed that the proposed MPS method reproduces the interaction between different phases without inducing numerical instability.     

Hopf–Hopf bifurcation analysis based on resonance and non-resonance in a simplified railway wheelset model

Nonlinear Dynamics - This paper mainly investigates the dynamics of the non-resonant and near-resonant Hopf–Hopf bifurcations caused by the interaction of the lateral and yaw motion in a...     

Hybrid LES–RANS technique based on a one-equation near-wall model

In order to reduce the high computational effort of wall-resolved large-eddy simulations (LES), the present paper suggests a hybrid LES–RANS approach which splits up the simulation into a near-wall RANS part and an outer LES part. Generally, RANS is adequate for attached boundary layers requiring reasonable CPU-time and memory, where LES can also be applied but demands extremely large resources. Contrarily, RANS often fails in flows with massive separation or large-scale vortical structures. Here, LES is without a doubt the best choice. The basic concept of hybrid methods is to combine the advantages of both approaches yielding a prediction method, which, on the one hand, assures reliable results for complex turbulent flows, including large-scale flow phenomena and massive separation, but, on the other hand, consumes much fewer resources than LES, especially for high Reynolds number flows encountered in technical applications. In the present study, a non-zonal hybrid technique is considered (according to the signification retained by the authors concerning the terms zonal and non-zonal), which leads to an approach where the suitable simulation technique is chosen more or less automatically. For this purpose the hybrid approach proposed relies on a unique modeling concept. In the LES mode a subgrid-scale model based on a one-equation model for the subgrid-scale turbulent kinetic energy is applied, where the length scale is defined by the filter width. For the viscosity-affected near-wall RANS mode the one-equation model proposed by Rodi et al. (J Fluids Eng 115:196–205, 1993) is used, which is based on the wall-normal velocity fluctuations as the velocity scale and algebraic relations for the length scales. Although the idea of combined LES–RANS methods is not new, a variety of open questions still has to be answered. This includes, in particular, the demand for appropriate coupling techniques between LES and RANS, adaptive control mechanisms, and proper subgrid-scale and RANS models. Here, in addition to the study on the behavior of the suggested hybrid LES–RANS approach, special emphasis is put on the investigation of suitable interface criteria and the adjustment of the RANS model. To investigate these issues, two different test cases are considered. Besides the standard plane channel flow test case, the flow over a periodic arrangement of hills is studied in detail. This test case includes a pressure-induced flow separation and subsequent reattachment. In comparison with a wall-resolved LES prediction encouraging results are achieved.      

Love–Bishop rod solution based on strain gradient elasticity theory

In the present work, the propagation of longitudinal stress waves is investigated with a strain gradient elasticity theory given by Lam et al. In principle, the analysis of wave motion is based on the Love rod model including the lateral deformation effects, but in the same time is also taken into account the shear strain effects with Bishop?s correction. By applying Hamilton?s principle, a general explicit strain gradient elasticity solution is developed for the longitudinal stress waves, and it is compared with the special solutions based on the modified couple stress and classical theories. This work gives useful information with regard to the meaning of the three scale parameters in the strain gradient elasticity theory used here.     

Effect of promoters on dynamics of gas-solid fluidized bed Statistical and ANN approaches

In this study, a bubbling fluidized bed column, 99 mm in inside diameter and 960 mm in height, was used to investigate the effect of rod and disc promoters on fluctuation and expansion ratios. Factorial design （statistical approach） and artificial neural network （ANN） models were developed to predict the fluctuation and expansion ratios in this gas-solid fluidized bed with varying gas flow rates, bed heights, particle sizes and densities. The fluctuation and expansion predicted using these statistical and ANN models, for beds with and without promoters, were found to agree well with corresponding experiments. The statistical model was found to be superior to the ANN model due to its ability to take into account both individual and interactive effects. The rod promoters were found to be more effective in reducing bed fluctuation, and in increasing bed expansion at high gas mass velocities.     

Computing flow-induced stresses of injection molding based on the Phan–Thien–Tanner model

A numerical approach is introduced to solve the viscoelastic flow problem of filling and post-filling in injection molding. The governing equations are in terms of compressible, non-isothermal fluid, and the constitutive equation is based on the Phan–Thien–Tanner model. By introducing some hypotheses according to the characteristics of injection molding, a quasi-Poisson type equation about pressure is derived with part integration. Besides, an analytical form of flow-induced stress is also generalized by using the undermined coefficient method. The conventional Galerkin approach is employed to solve the derived pressure equation, and the ‘upwind’ difference scheme is used to discrete the energy equation. Coupling is achieved between velocity and stress by super relax iteration method. The flow in the test mold is investigated by comparing the numerical results and photoelastic photos for polystyrene, showing flow-induced stresses are closely related to melt temperatures. The filling of a two-cavity box is also studied to investigate the viscoelastic effects on real injection molding.     

A modified beam model based on Gurtin–Murdoch surface elasticity theory

In this work, a modified surface-effect incorporated beam model based on Gurtin and Murdoch (GM) surface elasticity theory is established by satisfying the required balance equations on surfaces, which is often overlooked by researchers in this field. With the refinement, the proposed model is more rigorous in mathematics and mechanics compared with GM theory-based beam models in literature. To demonstrate the model, the problem for static bending of simply supported beam considering surface effects is solved by applying the general equations derived, and numerical results are obtained and discussed.