Application of residual correction method to laser heating process

Peng, Huan; Chen, Chieh Li; Li, Guo Sin

doi:10.1016/j.ijheatmasstransfer.2011.09.021

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…Wang et al [12] used residual correction method which applys the maximum principle to the finite difference method to analyze the error bounds of non-linear Burger's equation. This method was also employed by Peng, Chen and Li [13] to the laser heating process. Both works presented the efficiency and accuracy of this numerical method.…”

Section: Introductionmentioning

confidence: 99%

Application of Double Side Approach Method to the Solution of Fully Developed Laminar Flow in Duct Problems

Tang

Chen

2013

J. mech.

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The double side approach method combines the method of weighted residuals (MWR) with mathematical programming to solve the differential equations. Once the differential equation is proved to satisfy the maximum principle, collocation method and mathematical programming are used to transfer the problem into a bilateral inequality. By utilizing Genetic Algorithms optimization method, the maximum and minimum solutions which satisfy the inequality can be found. Adopting this method, quite less computer memory and time are needed than those required for finite element method.In this paper, the incompressible-Newtonian, fully-developed, steady-state laminar flow in equilateral triangular, rectangular, elliptical and super-elliptical ducts is studied. Based on the maximum principle of differential equations, the monotonicity of the Laplace operator can be proved and the double side approach method can be applied. Different kinds of trial functions are constructed to meet the no-slip boundary condition, and it was demonstrated that the results are in great agreement with the analytical solutions or the formerly presented works. The efficiency, accuracy, and simplicity of the double side approach method are fully illustrated in the present study to indicate that the method is powerful for solving boundary value problems.

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Section: Introductionmentioning

confidence: 99%

Application of Double Side Approach Method to the Solution of Fully Developed Laminar Flow in Duct Problems

Tang

Chen

2013

J. mech.

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“…Therefore, the numerical solution of spline function has been widely applied. In recent years, many numerical methods are developed from the spline theory, such as quartic spline method with higher accuracy [8], residual correction method [9] and parametric spline method ( [10] and [11]).…”

Section: Introductionmentioning

confidence: 99%

Analysis of Convective-Radiative Fins by Using Hybrid Spline Difference Method

Wang

Liao

Chao

2013

AMM

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This study used rectangular fins with constant heat transfer coefficient as material to discuss convective and radiative heat transfer, so as to prove that the hybrid spline difference method proposed in this study is an easy to operate method with high accuracy. According to the computational process described in this paper, the hybrid spline difference method is as simple as finite difference method and is easy to use. The complex computational process of traditional spline method can be simplified by using this method, but the numerical accuracy can be increased to second order. Therefore, the high accuracy numerical method of hybrid spline difference method replacing traditional spline method for future heat transfer analyses is expectable.

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