Xu Liu¹, Guojian Shao¹, Xingxing Yue^2,*, Qingbin Yang³, Jingbo Su⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.117, No.2, pp. 189-211, 2018, DOI:10.31614/cmes.2018.03947

Abstract This paper aims to apply a virtual boundary element method (VBEM) to solve the inverse problems of three-dimensional heat conduction in orthotropic media. This method avoids the singular integrations in the conventional boundary element method, and can be treated as a potential approach for solving the inverse problems of the heat conduction owing to the boundary-only discretization and semi-analytical algorithm. When the VBEM is applied to the inverse problems, the numerical instability may occur if a virtual boundary is not properly chosen. The method encounters a highly ill-conditioned matrix for the larger distance between the physical boundary and the virtual… More >

Akpofure E. Taigbenu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 271-289, 2014, DOI:10.3970/cmes.2014.102.271

Abstract The solutions to inverse heat conduction problems (IHCPs) are provided in this paper by the Green element method (GEM), incorporating the logarithmic fundamental solution of the Laplace operator (Formulation 1) and the timedependent fundamental solution of the diffusion differential operator (Formulation 2). The IHCPs addressed relate to transient problems of the recovery of the temperature, heat flux and heat source in 2-D homogeneous domains. For each formulation, the global coefficient matrix is over-determined and ill-conditioned, requiring a solution strategy that involves the least square method with matrix decomposition by the singular value decomposition (SVD) method, and regularization by the Tikhonov… More >

Hui Zheng¹, Wen Chen^1,2,3, Chuanzeng Zhang⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.3, pp. 179-195, 2013, DOI:10.3970/cmes.2013.090.179

Abstract This paper develops a multi-domain boundary knot method (BKM) formulation to solve the heat conduction problems of ultra-thin coatings. This approach overcomes the troublesome singular integration difficulty in the boundary element method in the simulation of such ultra-thin coating problems. Our numerical results show that the present BKM is very promising with sufficient accuracy in predicting the temperature distributions and the other physical quantities in thin coated layers even when the thickness ranges from 10-1m to 10-9m. The present method can also easily be extended to the three-dimensional problems. More >

S. Brischetto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.5, pp. 367-418, 2012, DOI:10.3970/cmes.2012.088.367

Abstract The paper analyzes the hygrothermal loading effects in the bending of multilayered composite plates. Refined two-dimensional models are used to evaluate these effects, they are implemented in the framework of the Carrera's Unified Formulation (CUF) which also allows classical models to be obtained. Hygroscopic and thermal effects are evaluated by means of hygroscopic and thermal load applications, respectively. Such loads can be determined via a priori linear or constant moisture content and temperature profiles through the thickness of the plate, or by calculating them via the solution of the Fick moisture diffusion law and the Fourier heat conduction equation, respectively.… More >

Chih-Wen Chang^1,2, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 269-292, 2012, DOI:10.3970/cmes.2012.088.269

Abstract In this article, we utilize an optimal vector driven algorithm (OVDA) to cope with the nonlinear heat conduction problems (HCPs). From this set of nonlinear ordinary differential equations, we propose a purely iterative scheme and the spatial-discretization of finite difference method for revealing the solution vector x, without having to invert the Jacobian matrix D. Furthermore, we introduce three new ideas of bifurcation, attracting set and optimal combination, which are restrained by two parameters g and a. Several numerical instances of nonlinear systems under noise are examined, finding that the OVDA has a fast convergence rate, great computation accuracy and… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.2, pp. 77-90, 2006, DOI:10.3970/cmes.2006.014.077

Abstract In this paper we derive the first-order and second-order one-step GPS applied to the estimation of thermophysical properties. Solving the resultant algebraic equations, which usually converges within ten iterations, it is not difficult to estimate the unknown temperature-dependent thermal conductivity and heat capacity simultaneously, if some supplemented data of measured temperature at a time T is provided. When the measured temperature in the conducting slab is contaminated by noise, our estimated results are also good. The new method does not require any prior information on the functional forms of thermal conductivity and heat capacity. Numerical examples are examined to show… More >

Xianwu Ling¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.3, pp. 219-228, 2006, DOI:10.3970/cmes.2006.013.219

Abstract In this paper, two matrix algebraic tools are provided for studying the solution-stabilities of inverse heat conduction problems. The propagations of the computed temperature errors, as caused by a noise in temperature measurement, are presented. The spectral norm analysis reflects the effect of the computational time steps, the sensor locations and the number of future temperatures on the computed error levels. The Frobenius norm analysis manifests the dynamic propagations of the computed errors. As an application of the norm analysis, we propose a method for the best positioning of the thermocouples. More >

C.-S. Liu¹, C.-W. Chang², J.-R. Chang²

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 67-82, 2006, DOI:10.3970/cmes.2006.012.067

Abstract In this paper we are concerned with the backward problems governed by differential equations. It is a first time that we can construct a backward time dynamics on the past cone, such that an augmented dynamical system of the Lie type X^˙ = B(X,t)X with t ∈ R⁻, X ∈ Mⁿ⁺¹ lying on the past cone and B ∈ so(n,1), was derived for the backward differential equations system x^· =f(x,t), t ∈ R⁻, x ∈ Rⁿ. These two differential equations systems are mathematically equivalent. Then we apply the backward group preserving scheme (BGPS), which is an explicit single-step… More >

Yoshihiro Ochiai¹, Vladimir Sladek², Jan Sladek²

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.1, pp. 41-54, 2012, DOI:10.3970/cmes.2012.087.041

Abstract The conventional boundary element method (BEM) requires a domain integral in unsteady thermal stress analysis with heat generation or an initial temperature distribution. In this paper it is shown that the three-dimensional unsteady thermal stress problem can be solved effectively using the triple-reciprocity boundary element method without internal cells. In this method, the distributions of heat generation and initial temperature are interpolated using integral equations and time-dependent fundamental solutions are used. A new computer program was developed and applied to solving several problems. 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 strip and a hallow cylinder.… More >