International Journal of Computational Methods

The wide range of requirements and constraints involved in the design of nuclear components for fusion reactors makes the development of multi-physics analysis procedures of utmost importance. In the framework of the European DEMO project, the Karlsruhe Institute of Technology (KIT) is dedicating several efforts to the development of a multi-physics analysis tool allowing the characterization of breeding blanket design points which are consistent from the neutronic, thermal-hydraulic and thermal-mechanical points of view. In particular, a procedure developed at KIT is characterized by the implementation of analysis software only. A preliminary step for the validation of such a procedure has been accomplished using a dedicated model of the DEMO Helium Cooled Pebble Bed Blanket 4th outboard module. A global model representative of nuclear irradiation in DEMO and two local models have been set up. Nuclear power deposition and the spatial distribution of its volumetric density have been calculated using Monte Carlo N-Particle transport code for the aforementioned models and compared in order to validate the procedure set up. The outcomes of this comparative study are herein presented and critically discussed.

A novel mathematical model and original numerical method for investigating time-dependent gas flows through a bed of granular phase change material (PCM) are proposed and described in detail. Such material is modeled as a porous medium, and continua mechanics method are used for constructing the mathematical model. The numerical method is based on a combination of explicit and implicit finite-difference schemes. Comparison of calculation results with known experimental data demonstrates a very good coincidence. The results of the study can be applied in modeling the thermal energy storage with granular PCM in advanced adiabatic compressed air energy storage and other heat storage devices.

This paper conducts a comparison analysis of high order central finite difference (HO-CFD) method and discrete singular convolution-regularized Shannon kernel (DSC-RSK) scheme with small computational bandwidths for solving some classes of boundary-value and eigenvalue problems. Second-, fourth- and sixth-order partial differential equations are taken into account. New strategies to generate parameters $r$ in DSC-RSK are proposed to ensure minimum errors for each case, and the influence of parameters $r$ with more decimal places is analyzed. Apart from the existing matched interface and boundary (MIB) scheme, a new double-parameter MIB scheme is also proposed. The influence of small computational bandwidths is discussed in detail. Numerical results by using HO-CFD and DSC-RSK are presented and compared to illustrate the performance of both methods in small bandwidth limit. Some remarkable conclusions have been drawn at the end of this study.

A coupled thermal–electrical–mechanical inhomogeneous cell-based smoothed finite element method (CICS-FEM) is presented for the multi-physics coupling problems, the displacements, the electrical potential and the temperature are obtained by combining the modified Wilson-$𝜃$ method. By introducing the gradient smoothing technique into the FE model, the system stiffness of the model is reduced. In addition, due to the absence of mapping, CICS-FEM is insensitive to mesh distortion. Curves and contour plots of displacements, electrical potential and temperature of three FGP structures are given in the article. The results shows that CICS-FEM possesses several advantages: (i) insensitive to mesh distortion; (ii) reduce the system stiffness; (iii) convergent and accuracy; (iv) efficient than FEM when the results are at the same accuracy.

In this paper, the base force element method (BFEM) for dynamic damage problems is proposed. And the BFEM model was applied to investigate the dynamic mechanical behavior of recycled aggregate concrete (RAC). Any convex polygon recycled aggregate was simulated. A constitutive relationship of dynamic damage was given. The compression test under dynamic loadings on the recycled concrete specimen was simulated. The stress–strain softening curve, variation law of dynamic enhancement coefficient and the damage pattern were researched under different strain rates. The dynamic properties of recycled concrete materials at high strain rate are also studied. The effect of different aggregate distribution on the mechanical properties of concrete was studied. The results of dynamic calculation of recycled concrete materials by this method are compared with the experimental results. The numerical simulation results are in good agreement with the experimental results. The comparative analysis on the dynamic mechanical properties of RAC and natural aggregate concrete (NAC) was also studied. The results show that the BFEM can be used to analyze the dynamic mechanical properties of RAC and NAC under high strain rate, and can be used for large-scale engineering calculations.

A class of super-linear stochastic delay differential equations (SDDEs) with variable delay and Markovian switching is considered. The main aim of this paper is to investigate the convergence and stability properties of partially truncated Euler–Maruyama (EM) method applied to the SDDEs with variable delay and Markovian switching under the generalized Khasminskii-type condition.

In the last decades, wavelets have become a dominant tool for having applications in almost all the areas of engineering and science such as numerical simulation of partial differential equations (PDEs). The performance of the conventional numerical methods has been found to involve some difficulty to observe fast convergence in low computational time. To overcome this difficulty, we presented wavelet-based full approximation scheme (WFAS) for the numerical solution of some class of nonlinear PDEs using Daubechies wavelet intergrid operators. The numerical results obtained by this scheme are compared with the exact solution to reveal the accuracy and also speed up convergence in lesser computational time as compared with the existing schemes. Some test problems are presented to show the applicability and attractiveness of WFAS.

This paper proposes an effective couple method for solving reliability-based multi-objective optimization problems of truss structures with static and dynamic constraints. The proposed coupling method integrates a single-loop deterministic method (SLDM) into the nondominated sorting genetic algorithm II (NSGA-II) algorithm to give the so-called SLDM-NSGA-II. Thanks to the advantage of SLDM, the probabilistic constraints are treated as approximating deterministic constraints. And therefore the reliability-based multi-objective optimization problems can be transformed into the deterministic multi-objective optimization problems of which the computational cost is reduced significantly. In these reliability-based multi-objective optimization problems, the conflicting objective functions are to minimize the weight and the displacements of the truss. The design variables are cross-section areas of the bars and contraints include static and dynamic constraints. For reliability analysis, the effect of uncertainty of parameters such as force, added mass in the nodes, material properties and cross-section areas of the bars are taken into account. The effectiveness and reliability of the proposed method are demonstrated through three benchmark-type truss structures including a 10-bar planar truss, a 72-bar spatial truss and a 200-bar planar truss. Moreover, the influence of parameters on the reliability-based Pareto optimal fronts is also carried out.

This paper presented a Gradient Weighted Finite Element Method (GW-FEM) for solving electromagnetic problems. First, the analysis domain is discretized into a set of triangular or tetrahedral elements which are easy to automatically generate. Then, Gradient Weighted influence domains are further constructed by the center element with all the adjacent elements. The Galerkin Weak form is evaluated based on these influence domains. The GW-FEM is employed here for the solution of static and quasi-static electromagnetic problems by using linear triangular or tetrahedral elements. All the properties of GW-FEM are proved theoretically and analyzed in detail. Consistency between four benchmark results is obtained by GW-FEM and analytical results verify the accuracy, stability, and potential of this method. It turns out that GW-FEM possesses potentials in the applications of electromagnetic problems.

Reliability-based design optimization (RBDO) has been widely used in mechanical design. However, the treatment of various uncertainties and associated computational burden are still the main obstacle of its application. A methodology of RBDO under random fuzzy and interval uncertainties (RFI-RBDO) is proposed in this paper. In the proposed methodology, two reliability analysis approaches, respectively named as FORM-$\alpha$-URA and interpolation-based sequential performance measurement approach (ISPMA), are developed for the mixed uncertainties assessment, and a parallel-computing-based SOMUA (PCSOMUA) method is proposed to reduce the computational cost of RFI-RBDO. Finally, two examples are provided to verify the validity of the methods.

The aim of the present paper was to explore the effect of initial lesions on the course of femoral head necrosis. A fracture mechanics model of the femoral head was developed and validated using the computed tomography (CT) scan images of a healthy volunteer and material mechanics test results of fresh femur samples. The dynamic development of stresses and fractures of the femoral head with various initial lesions were simulated under various loads. The results showed that the initial lesion of the femoral head spreads faster and collapses deeper as the load increases. The location of the initial lesion has a significant effect on the collapse of the femoral head. The lesions in the anterior and lateral areas of the femoral head are more likely to accelerate the collapse of the femoral head than the lesions in other areas. This study is helpful in predicting the collapse risk and guiding the daily activities of patients with femoral head necrosis. Additionally, this study helps doctors to make better decisions about treatment options.

This paper deals with numerical linear analyses of laminated composite plate/shell structures. The method is based on a four-node quadrilateral element, namely, SQ4T, within the framework of the first-order shear deformation theory (FSDT). This element is established by incorporating the twice interpolation strategy (TIS) into a traditional four-node finite element to build the membrane, bending and shear stiffness matrices. Many desirable characteristics of this efficient numerical method are shown as continuous nodal gradients, higher-order polynomial basis, no increase in number of the degree of freedom of the system. The performance of the proposed element is validated and demonstrated through several numerical benchmark problems. Convergence studies and comparison with other existing solutions in the literature suggest that the present element is efficient, accurate and free of lockings.

In this paper, we present a new method to derive transparent boundary conditions for the Regularized Long Wave equation and its linearized equation. These boundary conditions have the advantage of being exact for both linearized and nonlinear equations. The resulting problems supplemented with initial data are approximated numerically using finite difference method in space discretization and Crank–Nicolson scheme in time for the linearized equation, while implicit scheme in time is used for the Regularized Long Wave equation. Numerical experiments are made for solitary initial data and various source terms to illustrate the transparency of the introduced boundary conditions. Results are compared with the use of usual boundary conditions, namely, Dirichlet and Neumann via infinite norm error on the boundary and also by displaying geophones and instantaneous figures.

In this study, we present a fourth-order and a sixth-order blended compact difference (BCD) schemes for approximating the three-dimensional (3D) convection–diffusion equation with variable convective coefficients. The proposed schemes, where transport variable, its first and second derivatives are carried as the unknowns, combine virtues of compact discretization, fourth-order Padé scheme and sixth-order combined compact difference (CCD) scheme for spatial derivatives and can efficiently capture numerical solutions of linear and nonlinear convection–diffusion equations with Dirichlet boundary conditions. The fourth-order scheme requires only 7 grid points and the sixth-order scheme requires 19 grid points. The distinguishing feature of the present method is that methodologies of explicit compact difference and implicit compact difference are blended together. The truncation errors of the two difference schemes are analyzed for the interior grid points, respectively. Simultaneously, a sixth-order accuracy scheme is proposed to compute the first and second derivatives of the grid points on boundaries. Finally, the presented methods are applied to several test problems from the literature including linear and nonlinear problems. It is found that the presented schemes exhibit good performance.

Rackwitz–Fiessler (RF) method is well accepted as an efficient way to solve the uncorrelated non-Normal reliability problems by transforming original non-Normal variables into equivalent Normal variables based on the equivalent Normal conditions. However, this traditional RF method is often abandoned when correlated reliability problems are involved, because the point-by-point implementation property of equivalent Normal conditions makes the RF method hard to clearly describe the correlations of transformed variables. To this end, some improvements on the traditional RF method are presented from the isoprobabilistic transformation and copula theory viewpoints. First of all, the forward transformation process of RF method from the original space to the standard Normal space is interpreted as the isoprobabilistic transformation from the geometric point of view. This viewpoint makes us reasonably describe the stochastic dependence of transformed variables same as that in Nataf transformation (NATAF). Thus, a corresponding enhanced RF (EnRF) method is proposed to deal with the correlated reliability problems described by Pearson linear correlation. Further, we uncover the implicit Gaussian copula hypothesis of RF method according to the invariant theorem of copula and the strictly increasing isoprobabilistic transformation. Meanwhile, based on the copula-only rank correlations such as the Spearman and Kendall correlations, two improved RF (IRF) methods are introduced to overcome the potential pitfalls of Pearson correlation in EnRF. Later, taking NATAF as a reference, the computational cost and efficiency of above three proposed RF methods are also discussed in Hasofer–Lind reliability algorithm. Finally, four illustrative structure reliability examples are demonstrated to validate the availability and advantages of the new proposed RF methods.