International Journal of Computational Methods

This research study aims to conduct the analysis and implementation of efficient algorithms for simulations of micro and nanoparticle transport models in porous media, coupled with the Darcy–Forchheimer fluid model, modified to include electromagnetic effects. The schemes developed were implemented via a parallel infrastructure for benchmark problems with a flexible algorithm that is efficient, robust, and stable. These improvements in the reliability and efficiency of simulations of nanoparticle transport in porous media contribute to the creation of an efficient method to counteract the contaminants in groundwater, and ultimately increase the availability of clean drinking water.

A straightforward implementation of the Multi-Block Lattice Boltzmann Method (MB-LBM) on a Graphics Processing Unit (GPU) is presented to accelerate the simulation of fluid flows in two-dimensional geometries. The algorithm is measured in terms of both accuracy and efficiency with the benchmark cases of the lid-driven cavity flow and the flow past a circular cylinder, and satisfactory results are obtained. The results show that the performance on GPU becomes even better with the amount of data increasing. Moreover, the arrangement of the computational domain has a significant effect on the efficiency. These results demonstrate the great potential of GPU on the MB-LBM, especially when dealing with massive data.

A cell-based smoothed finite element method (CS-FEM) is formulated for nonlinear free vibration analysis of a plate attached to a rigid rotating hub. The first-order shear deformation theory which is known as Mindlin plate theory is used to model the plate. In the process of formulating the system stiffness matrix, the discrete shear gap (DSG) method is used to construct the strains to overcome the shear locking issue. The effectiveness of the CS-FEM is first demonstrated in some static cases and then extended for free vibration analysis of a rotating plate considering the nonlinear effects arising from the coupling of vibration of the flexible structure with the undergoing large rotational motions. The nonlinear coupling dynamic equations of the system are derived via employing Lagrange’s equations of the second kind. The effects of different parameters including thickness ratio, aspect ratio, hub radius ratio and rotation speed on dimensionless natural frequencies are investigated. The dimensionless natural frequencies of CS-FEM are compared with those other existing method including the FEM and the assumed modes method (AMM). It is found that the CS-FEM based on Mindlin plate theory provides more accurate and “softer” solution compared with those of other methods even if using coarse meshes. In addition, the frequency loci veering phenomena associated with the mode shape interaction are examined in detail.

This paper presents a practical approach of model updating based on high-dimensional model representation (HDMR). The proposed methodology involves integrated finite element modeling, obtaining explicit relationships between the structural responses and parameters using HDMR and minimization of objective function developed using structural responses obtained from HDMR approximation functions using genetic algorithm. First, the efficiency of the proposed method is demonstrated by considering a simply supported beam example. Later model updating of an existing bridge is considered to check the adequacy of the proposed method.

Conventional methods for liquefaction assessment using engineering indices such as Factor of safety against Liquefaction (FL) tend to overestimate liquefaction hazards. The soil dynamics analysis-based assessment with automatic modeling is more rational and robust. Soil properties are known for large uncertainties. Rather than deterministic soil models, statistical models for soil parameters should be considered. With automatic modeling, a large number of statistic models can be generated without difficulty. The problem becomes how to assess liquefaction hazard with statistic models in an efficient way. Using high performance computing, we develop an efficient liquefaction assessment method for statistical modeling of soils. A high parallel efficiency can be achieved and a large number of statical models of the order of 10⁴ can be simulated within a reasonable time span. The method developed in this paper can be used as an efficient tool for unravelling critical parameters of soil liquefaction.

We have developped an original 2D modeling of bearings by Discrete Element Method (DEM). The mechanical behavior and the dynamic of a bearing is well reproduced. An electromechanical coupling is introduced to provide monitoring solutions. In practice, the mechanical state in real-time is usually unknown and existing numerical methods are restricted. Electromechanical coupling seems to be able to indirectly measure the dynamic loading of the bearing. This behavior leads to the development of a new monitoring method based on electrical signatures. The study proposes an original method of simulating the bearings to correlate dynamic mechanical state with electrical responses, over time. The bearing is seen as a polydisperse granular chain where rolling elements and cage components interact with a Hertzian contact model. Moreover, rings (and housing) are also taken into account using a cohesive model. Indeed, while many studies have been conducted on bearing simulation using FEM and multibody approaches, this discrete approach gives relevant informations on physical phenomena in the contact interface. One of our objectives is to investigate the sensitivity of the electrical measurement due to typical mounting. The ability of DEM to describe accurately the mechanical state of a bearing has been established by means of a comparison with FEM, of load distributions in a static case. In dynamic, the consequences associated with the flexibility of the bearing mounting (rigid and elastic rings) are studied with mechanical stresses acting in rings and with the load distribution. Also, by accessing dynamic stresses, this modeling opens certain possibilities on studies of damage and wear by providing the history of contact.

In this paper, a fitted finite difference method on Shishkin mesh is suggested to solve a class of third order singularly perturbed boundary value problems for ordinary delay differential equations of convection-diffusion type. Numerical solution converges uniformly to the exact solution. The order of convergence of the numerical method is almost first order. Numerical results are provided to illustrate the theoretical results.

In this study, we design a new efficient family of sixth-order iterative methods for solving scalar as well as system of nonlinear equations. The main beauty of the proposed family is that we have to calculate only one inverse of the Jacobian matrix in the case of nonlinear system which reduces the computational cost. The convergence properties are fully investigated along with two main theorems describing their order of convergence. By using complex dynamics tools, its stability is analyzed, showing stable members of the family. From this study, we intend to have more information about these methods in order to detect those with best stability properties. In addition, we also presented a numerical work which confirms the order of convergence of the proposed family is well deduced for scalar, as well as system of nonlinear equations. Further, we have also shown the implementation of the proposed techniques on real world problems like Van der Pol equation, Hammerstein integral equation, etc.

In this paper, we introduce a mesh-free computational model for the simulation of high-speed impact phenomena. Within the framework of particle dynamics simulations we model a macroscopic solid ceramic tile as a network of overlapping discrete particles of microscopic size. Using potentials of the Lennard–Jones type, we integrate the classical Newtonian equations of motion and perform uni-axial, quasi-static load simulations to customize our three model parameters to the typical tensile strength, Young’s modulus and the compressive strength of a ceramic. Subsequently we perform shock load simulations in a standard experimental setup, the edge-on impact (EOI) configuration. Our obtained results concerning crack initiation and propagation through the material agree well with corresponding high-speed EOI experiments with Aluminum Oxinitride (AlON), Aluminum Oxide $({\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3)$ and Silicon Carbide (SiC), performed at the Fraunhofer Ernst-Mach-Institute (EMI). Additionally, we present initial simulation results where we use our particle–based model to simulate a second type of high-speed impact experiments where an accelerated sphere strikes a thin aluminum plate. Such experiments are done at our institute to investigate the debris clouds arising from such impacts, which constitute a miniature model version of a generic satellite structure that is hit by debris in the earth’s orbit. Our findings are that a discrete particle based method leads to very stable, energy-conserving simulations of high–speed impact scenarios. Our chosen interaction model works particularly well in the velocity range where the local stresses caused by impact shock waves markedly exceed the ultimate material strength.

A new type of smoothed finite element method (S-FEM), F-barES-FEM-T4, is demonstrated in static large deformation elastoplastic cases. F-barES-FEM-T4 combines the edge-based S-FEM (ES-FEM) and the node-based S-FEM (NS-FEM) for 4-node tetrahedral (T4) elements with the aid of the F-bar method in order to resolve the major issues of Selective ES/NS-FEM-T4. As well as most of the other S-FEMs, F-barES-FEM-T4 inherits pure displacement-based formulation and thus has no increase in DOF. Moreover, the cyclic smoothing procedure introduced in F-barES-FEM-T4 is effective to adjust the smoothing level so that pressure checkerboarding (oscillation) is suppressed reasonably. Some examples of static large deformation analyses for elastoplastic materials proof the excellent performance of F-barES-FEM-T4 in contrast to the conventional hybrid T4 element formulation.

The desiccation cracks can be observed on dry-out soil fields or other various materials under desiccation. These cracks have a net-like structure and tessellate the surface of the materials into polygonal cells. The averaged cell size changes systematically depending on the size of the specimen. In spite of the varieties of the materials, these fundamental features of the cell topology are conserved. This implies the existence of the governing mechanism behind the desiccation crack phenomenon regardless of the materials. In this paper, the desiccation crack phenomenon is modeled by the coupling of desiccation, deformation, and fracture. We perform simulations for the reproduction of the desiccation cracking based on this coupling model. In the simulations, the finite element analysis for the desiccation problem and the analysis of particle discretization scheme finite element method for the deformation and the fracture problems are weakly coupled. The results of the simulations show the satisfactory agreements with the experimental observations in terms of the geometry of the crack pattern, the increase tendency of the averaged cell size depending on the size of the specimen, and the hierarchical sequence of the cell formation. These agreements indicate that the proposed model and method capture the fundamental features and the mechanism of the desiccation cracking.

This paper conducts time history analysis to explore the influence of spatially varying earthquake ground motion (SVEGM) on seismic responses of the long immersed tunnel. Incoherence effect and wave passage effect are mainly focused here. Moreover, three coherency models are adopted to investigate the sensitivity of the computed responses to the models. The calculation results show that SVEGM enlarges seismic responses of the immersed tunnel significantly than uniform excitation. Considering wave passage effect and incoherence effect simultaneously makes the seismic responses increase more sharply than considering the latter only. The deformation of Gina gasket is barely sensitive to coherency model, while the axial compression force is sensitive to coherency model. It indicates suppressing that the fundamental mode and dominating higher-mode response are the hallmark of multi-support excitation. The great differences of three models decay with separation at low frequencies and their coherency in frequency domain are the main reasons that cause the variations of the axial compression forces.

This paper presents a novel equilibrium formulation, that uses the cell-based smoothed method and conic programming, for limit and shakedown analysis of structures. The virtual strains are computed using straining cell-based smoothing technique based on elements of discretized mesh. Fictitious elastic stresses are also determined within the framework of finite element method (CS-FEM)-based Galerkin procedure, and equilibrium equations for residual stresses are satisfied in an average sense at every cell-based smoothing cell. All constrains are imposed at only one point in the smoothing domains, instead of Gauss points as in a standard FEM-based procedure. The resulting optimization problem is then handled using the highly efficient solvers. Various numerical examples are investigated, and obtained solutions are compared with available results in the literature.

Fluid–Structure Interaction (FSI) is an important phenomenon in many fields. In this study, the Moving Particle Simulation (MPS) along with Finite Element Method (FEM) are coupled together. MPS-FEM coupled method is used as the numerical simulators to estimate the effects for structures by the fluid pressure of the tsunami. This simulator consists of two solvers: fluid analysis and structure analysis. The fluid analysis is based on MPS and the structural part is analyzed by using FEM. In this paper, for verification of the MPS-FEM coupled method, the problem of hydrostatic pressure on a structure is calculated. The results are compared with the theoretical values and the results obtained by the original FEM analysis. We confirmed that the MPS-FEM coupling method can achieve adequate accuracy. Furthermore, the MPS-FEM coupled simulation for the turbine building of Fukushima Dai-ichi Nuclear Power Station Unit 1 has been done.

With the great progress in supercomputers and numerical methods, the applications of computational fluid dynamics are advancing rapidly in the field of ship hydrodynamics. And the dynamic overset grid method makes it possible for computing complex ship motions. In the present work, CFD-based method coupling with dynamic overset grid technique is applied to investigate the hydrodynamic performance of the fully appended ONR Tumblehome ship model during self-propulsion condition. Open water performance of propeller and towing condition of bare hull are computed before the self-propulsion simulation. The ship model is fitted with twin rotating propellers and twin static rudders, achieving self-propulsion model point at $Fr=0.20$ and $Fr=0.30$, respectively. All the computations are carried out by our in-house CFD solver naoe-FOAM-SJTU, which solves the Navier–Stokes equations for unsteady turbulent flows with VOF method capturing free surface around the complex geometry models. During the self-propulsion simulation, a feedback controller is used to update the rotational speed of the propeller to achieve the target ship speed. Detailed information of the flow field during the self-propulsion condition is presented and analyzed. In addition, predicted results, i.e. self-propulsion model point, ship motions and force coefficients, are also presented and compared with the available experimental data. Good agreements are achieved, which indicates that the present approach is applicable for the self-propulsion simulation.

The present work demonstrates an efficient method for reliability analysis using sequential development of the stochastic response surface. Here, orthogonal Hermite polynomials are used whose unknown coefficients are evaluated using moving least square technique. To do so, collocation points in the conventional stochastic response surface method (SRSM) are replaced by the sparse grid scheme so as to reduce the number of function evaluations. Moreover, the domain is populated sequentially by the sparse grid based on the outcome of the optimization to find out the most probable failure point. Hence, the support points are generated based on a coupled effect of the optimization for failure region and the sub-grids hierarchy. Continuous and differentiable penalty function is imposed to determine multiple failure points, if any, by repeating the optimization. Once the response surface is developed, reliability analysis is carried out using importance sampling. Five different benchmark examples are presented in this study to validate the performance of the proposed modeling. As the accuracy of the method is established, two reliability-based design examples involving nonlinear finite element (FE) analysis of plates are demonstrated. Numerical study shows the efficiency of the proposed sequential SRSM in terms of accuracy and number of time-exhaustive evaluation of the original performance function, as compared to other methods available in the literature. Based on these results, it may be concluded that the proposed method works satisfactorily for a large class of reliability-based design problems.