Weiwu Jiang¹, Xiaowei Gao^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.1, pp. 41-76, 2024, DOI:10.32604/cmes.2024.048313

Abstract The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations. This paper provides a comprehensive review of collocation methods and their applications, focused on elasticity, heat conduction, electromagnetic field analysis, and fluid dynamics. The merits of the collocation method can be attributed to the need for element mesh, simple implementation, high computational efficiency, and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method. Beginning with the fundamental principles of the collocation method, the discretization process in the continuous domain is elucidated, and how… More >

Jinlong Yang, Kwang-Hee Lee, Chul-Hee Lee^*

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 2917-2946, 2024, DOI:10.32604/cmes.2024.046740

Abstract Cavitation is a common issue in pumps, causing a decrease in pump head, a fall in volumetric efficiency, and an intensification of outlet flow pulsation. It is one of the main hazards that affect the regular operation of the pump. Research on pump cavitation mainly focuses on mixed flow pumps, jet pumps, external spur gear pumps, etc. However, there are few cavitation studies on external herringbone gear pumps. In addition, pumps with different working principles significantly differ in the flow and complexity of the internal flow field. Therefore, it is urgent to study the cavitation characteristics of external herringbone gear… More >

Mingjing Li^1,*, Leiting Dong¹, Satya N. Atluri²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.4, pp. 1-2, 2023, DOI:10.32604/icces.2023.09689

Abstract The Fragile Points Method (FPM) is a discontinuous meshless method based on the Galerkin weak form [1]. In the FPM, the problem domain is discretized by spatial points and subdomains, and the displacement trial function of each subdomain is derived based on the points within the support domain. For this reason, the FPM doesn’t suffer from the mesh distortion and is suitable to model complex structural deformations. Furthermore, similar to the discontinuous Galerkin finite element method, the displacement trial functions used in the FPM is piece-wise continuous, and the numerical flux is introduced across each interior interface to guarantee the… More >

Jiaqun Wang^1,2, Guanxu Pan², Youhe Zhou², Xiaojing Liu^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.1, pp. 297-318, 2024, DOI:10.32604/cmes.2023.030622

Abstract In this study, a wavelet multi-resolution interpolation Galerkin method (WMIGM) is proposed to solve linear singularly perturbed boundary value problems. Unlike conventional wavelet schemes, the proposed algorithm can be readily extended to special node generation techniques, such as the Shishkin node. Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients. All the shape functions possess the Kronecker delta property, making the imposition of boundary conditions as easy as that in the finite element method. Four numerical examples are studied to demonstrate the validity and accuracy of the proposed… More >

Ziqiang Bai¹, Wenzhen Qu^2,*, Guanghua Wu^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.3, pp. 2955-2972, 2024, DOI:10.32604/cmes.2023.031474

Abstract In the past decade, notable progress has been achieved in the development of the generalized finite difference method (GFDM). The underlying principle of GFDM involves dividing the domain into multiple sub-domains. Within each sub-domain, explicit formulas for the necessary partial derivatives of the partial differential equations (PDEs) can be obtained through the application of Taylor series expansion and moving-least square approximation methods. Consequently, the method generates a sparse coefficient matrix, exhibiting a banded structure, making it highly advantageous for large-scale engineering computations. In this study, we present the application of the GFDM to numerically solve inverse Cauchy problems in two-… More >

Fabrizio Greco^*, Paolo Lonetti, Arturo Pascuzzo, Giulia Sansone

Structural Durability & Health Monitoring, Vol.17, No.6, pp. 457-483, 2023, DOI:10.32604/sdhm.2023.030075

Abstract This work proposes a numerical investigation on the effects of damage on the structural response of Reinforced Concrete (RC) bridge structures commonly adopted in highway and railway networks. An effective three-dimensional FE-based numerical model is developed to analyze the bridge’s structural response under several damage scenarios, including the effects of moving vehicle loads. In particular, the longitudinal and transversal beams are modeled through solid finite elements, while horizontal slabs are made of shell elements. Damage phenomena are also incorporated in the numerical model according to a smeared approach consistent with Continuum Damage Mechanics (CDM). In such a context, the proposed… More >

Tao Hu¹, Cheng Huang², Sergiy Reutskiy^3,*, Jun Lu⁴, Ji Lin^5,*

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1521-1548, 2024, DOI:10.32604/cmes.2023.030449

Abstract A novel accurate method is proposed to solve a broad variety of linear and nonlinear (1+1)-dimensional and (2+1)- dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic diffusivity. For (1+1)-dimensional problems, analytical solutions that satisfy the boundary requirements are derived. Such solutions are numerically calculated using the trigonometric basis approximation for (2+1)-dimensional problems. With the aid of these analytical or numerical approximations, the original problems can be converted into the fractional ordinary differential equations, and solutions to the fractional ordinary differential equations are approximated by modified radial basis functions with time-dependent coefficients. An efficient backward substitution strategy that… More >

Zhehan Ji¹, Tongqing Guo^1,*, Di Zhou¹, Zhiliang Lu¹, Binbin Lyu²

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 489-508, 2024, DOI:10.32604/cmes.2023.029088

Abstract The reduced weight and improved efficiency of modern aeronautical structures result in a decreasing separation of frequency ranges of rigid and elastic modes. Particularly, a high-aspect-ratio flexible flying wing is prone to body freedom flutter (BFF), which is a result of coupling of the rigid body short-period mode with 1^st wing bending mode. Accurate prediction of the BFF characteristics is helpful to reflect the attitude changes of the vehicle intuitively and design the active flutter suppression control law. Instead of using the rigid body mode, this work simulates the rigid body motion of the model by using the six-degree-of-freedom (6DOF)… More >

Jun Zeng¹, Fucheng Tian^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.2, pp. 1-1, 2023, DOI:10.32604/icces.2023.09636

Abstract Instability in dynamic fracture suppresses crack velocity from reaching theoretical limit predicted by the classical linear elastic fracture mechanics (LEFM). In thin systems, crack can accelerate to near the theoretical limiting velocity without micro-branching instability. A dynamic oscillatory instability is observed at such extreme crack speed. This sinusoidal oscillation was further found to be governed by intrinsic nonlinear scale. Using a dynamic phase-field model (PFM) with no attenuation of wave speed, we successfully reproduce the oscillations in the framework of non-linear deformation. The used PFM model based on Griffith's theory and derived from the nonconservative Lagrange's equation. To deal with… More >

Umut Hanoglu^1,2,*, Božidar Šarler^1,2

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.2, pp. 1-1, 2023, DOI:10.32604/icces.2023.09610

Abstract In this research, a rolling simulation system based on a novel meshless solution procedure is upgraded considering casting defects in the material model. The improved model can predict the final stage of the defects after multi-pass rolling. The casted steel billet that enters the rolling mill arrives with casting defects. Those defects may be porosity due to the shrinkage and cavity or micro-cracks near the surface due to hot tearing. In this work, porosity is considered the main defect source since it can easily be determined experimentally. The damage theory develops a damaged stiffness matrix with a scalar damage value.… More >