Chunlei Ruan^1,2,*, Cengceng Dong¹, Zeyue Zhang¹, Boyu Chen¹, Zhijun Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.3, pp. 2707-2728, 2024, DOI:10.32604/cmes.2024.050003

Abstract Transient heat conduction problems widely exist in engineering. In previous work on the peridynamic differential operator (PDDO) method for solving such problems, both time and spatial derivatives were discretized using the PDDO method, resulting in increased complexity and programming difficulty. In this work, the forward difference formula, the backward difference formula, and the centered difference formula are used to discretize the time derivative, while the PDDO method is used to discretize the spatial derivative. Three new schemes for solving transient heat conduction equations have been developed, namely, the forward-in-time and PDDO in space (FT-PDDO) scheme,… 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 More >

Hongfen Gao¹, Gaofeng Wei^2,3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.3, pp. 1793-1814, 2022, DOI:10.32604/cmes.2022.019687

Abstract By introducing the radial basis functions (RBFs) into the reproducing kernel particle method (RKPM), the calculating accuracy and stability of the RKPM can be improved, and a novel meshfree method of the radial basis RKPM (meshfree RRKPM) is proposed. Meanwhile, the meshfree RRKPM is applied to transient heat conduction problems (THCP), and the corresponding equations of the meshfree RRKPM for the THCP are derived. The two-point time difference scheme is selected to discretize the time of the THCP. Finally, the numerical results illustrate the effectiveness of the meshfree RRKPM for the THCP. More >

Leilei Chen¹, Kunpeng Li¹, Xuan Peng², Haojie Lian^3,4,*, Xiao Lin⁵, Zhuojia Fu⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 125-146, 2021, DOI:10.32604/cmes.2021.012821

Abstract This paper presents an isogeometric boundary element method (IGABEM) for transient heat conduction analysis. The Non-Uniform Rational B-spline (NURBS) basis functions, which are used to construct the geometry of the structures, are employed to discretize the physical unknowns in the boundary integral formulations of the governing equations. B´ezier extraction technique is employed to accelerate the evaluation of NURBS basis functions. We adopt a radial integration method to address the additional domain integrals. The numerical examples demonstrate the advantage of IGABEM in dimension reduction and the seamless connection between CAD and numerical analysis. More >

Yiqiang Li¹, Liang Ma², Zhiqiang Yang³, Xiaofei Guan⁴, Yufeng Nie¹, Zihao Yang^{1, 2}

CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.1, pp. 1-24, 2018, DOI:10.3970/cmes.2018.115.001

Abstract This paper is devoted to the homogenization and statistical multiscale analysis of a transient heat conduction problem in random porous materials with a nonlinear radiation boundary condition. A novel statistical multiscale analysis method based on the two-scale asymptotic expansion is proposed. In the statistical multiscale formulations, a unified linear homogenization procedure is established and the second-order correctors are introduced for modeling the nonlinear radiative heat transfer in random perforations, which are our main contributions. Besides, a numerical algorithm based on the statistical multiscale method is given in details. Numerical results prove the accuracy and efficiency More >

D. Mirzaei¹, M. Dehghan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.3, pp. 185-210, 2011, DOI:10.3970/cmes.2011.072.185

Abstract The meshless local Petrov-Galerkin (MLPG) method with an efficient technique to deal with the time variable are used to solve the heat conduction problem in this paper. The MLPG is a meshless method which is (mostly) based on the moving least squares (MLS) scheme to approximate the trial space. In this paper the MLS is used for approximation in both time and space domains, and we avoid using the time difference discretization or Laplace transform method to overcome the time variable. The technique is applied for continuously nonhomogeneous functionally graded materials (FGM) in a finite More >