Junsong Xiong¹, Zhen Wang², Shaofan Li³, Xin Lai^1,*, Lisheng Liu^2,*, Xiang Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 151-169, 2024, DOI:10.32604/cmes.2024.053078 - 20 August 2024

Abstract Natural convection is a heat transfer mechanism driven by temperature or density differences, leading to fluid motion without external influence. It occurs in various natural and engineering phenomena, influencing heat transfer, climate, and fluid mixing in industrial processes. This work aims to use the Updated Lagrangian Particle Hydrodynamics (ULPH) theory to address natural convection problems. The Navier-Stokes equation is discretized using second-order nonlocal differential operators, allowing a direct solution of the Laplace operator for temperature in the energy equation. Various numerical simulations, including cases such as natural convection in square cavities and two concentric cylinders, More >

Chih-Ping Wu^*, Ruei-Syuan Chang

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 917-949, 2024, DOI:10.32604/cmes.2024.052307 - 20 August 2024

Abstract This work develops a Hermitian C differential reproducing kernel interpolation meshless (DRKIM) method within the consistent couple stress theory (CCST) framework to study the three-dimensional (3D) microstructure-dependent static flexural behavior of a functionally graded (FG) microplate subjected to mechanical loads and placed under full simple supports. In the formulation, we select the transverse stress and displacement components and their first- and second-order derivatives as primary variables. Then, we set up the differential reproducing conditions (DRCs) to obtain the shape functions of the Hermitian C differential reproducing kernel (DRK) interpolant’s derivatives without using direct differentiation. The interpolant’s… More >

Xin Liu^1,*, Kai Yan², Bo Fang³, Xiaoyu Sun³, Daqiang Feng⁴, Li Yin⁵

FDMP-Fluid Dynamics & Materials Processing, Vol.20, No.7, pp. 1539-1552, 2024, DOI:10.32604/fdmp.2024.047922 - 23 July 2024

Abstract In response to the complex characteristics of actual low-permeability tight reservoirs, this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs, considering complex boundary shapes. Utilizing radial basis function point interpolation, the method approximates shape functions for unknown functions within the nodal influence domain. The shape functions constructed by the aforementioned meshless interpolation method have δ-function properties, which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells. Moreover, the meshless method offers greater flexibility and freedom compared to grid cell discretization, making it simpler… More >

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 - 16 April 2024

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… 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 - 15 December 2023

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 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 - 17 November 2023

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 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… 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… 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… 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 - 23 November 2022

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 More >