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 >

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 >

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 >

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 >

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 >

Qingguo Liu^1,2, 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.2023.09609

Abstract A simulation of reheating furnace in a steel production line where the steel billets are heated from room temperature up to 1200 ˚C, is carried out using a novel meshless solution procedure. The reheating of the steel billets before the continuous hot-rolling process should be employed to dissolve alloying elements as much as possible and redistribute the carbon. In this work, governing equations are solved by the local radial basis function collocation method (LRBFCM) in a strong form with explicit time-stepping. The solution of the diffusion equations for the temperature and carbon concentration fields is formulated on a twodimensional slice.… More >

Chengxin Zhang¹, Chao Wang¹, Shouhai Chen^2,*, Fajie Wang^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2407-2424, 2023, DOI:10.32604/cmes.2023.024884

Abstract This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method (LKM) with the dual reciprocity method (DRM). Firstly, the temporal derivative is discretized by a finite difference scheme, and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation. Secondly, the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution. And then, the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation, respectively.… More >

Muneerah Al Nuwairan^1,*, Elmiloud Chaabelasri²

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 133-154, 2023, DOI:10.32604/cmes.2022.022649

Abstract In this paper, natural heat convection inside square and equilateral triangular cavities was studied using a meshless method based on collocation local radial basis function (RBF). The nanofluids used were Cu-water or -water mixture with nanoparticle volume fractions range of . A system of continuity, momentum, and energy partial differential equations was used in modeling the flow and temperature behavior of the fluids. Partial derivatives in the governing equations were approximated using the RBF method. The artificial compressibility model was implemented to overcome the pressure velocity coupling problem that occurs in such equations. The main goal of this work was… More > Graphic Abstract

Zenglin Wang¹, Liaoyuan Zhang¹, Anhai Zhong², Ran Ding², Mingjing Lu^2,3,*

FDMP-Fluid Dynamics & Materials Processing, Vol.18, No.6, pp. 1795-1804, 2022, DOI:10.32604/fdmp.2022.020020

Abstract Due to the difficulties associated with preprocessing activities and poor grid convergence when simulating shale reservoirs in the context of traditional grid methods, in this study an innovative two-phase oil-water seepage model is elaborated. The modes is based on the radial basis meshless approach and is used to determine the pressure and water saturation in a sample reservoir. Two-dimensional examples demonstrate that, when compared to the finite difference method, the radial basis function method produces less errors and is more accurate in predicting daily oil production. The radial basis function and finite difference methods provide errors of 5.78 percent and… More >

Chih-Wen Chang^*

CMC-Computers, Materials & Continua, Vol.73, No.1, pp. 433-451, 2022, DOI:10.32604/cmc.2022.027021

Abstract We retrieve unknown nonlinear large space-time dependent forces burdened with the vibrating nonlinear Euler-Bernoulli beams under varied boundary data, comprising two-end fixed, cantilevered, clamped-hinged, and simply supported conditions in this study. Even though some researchers used several schemes to overcome these forward problems of Euler-Bernoulli beams; however, an effective numerical algorithm to solve these inverse problems is still not available. We cope with the homogeneous boundary conditions, initial data, and final time datum for each type of nonlinear beam by employing a variety of boundary shape functions. The unknown nonlinear large external force can be recuperated via back-substitution of the… More >