| Summary: | 博士 === 國立臺北科技大學 === 機電科技研究所 === 100 === The difficulty encountered in the numerical solutions of hyperbolic heat conduction problems (HHC) is the numerical oscillation in vicinity of sharp discontinuities. In the present study, we have proposed collection method, hybrid Green function and hybrid integral transform method to overcome the numerical oscillation on HHC.
Using the collection method investigates the effect of the surface curvature of a solid body on HHC. The present method combined the Laplace transform and the hyperbolic shape function to solve time dependent HHC equation; four different examples have been analyzed by the current method.
The hybrid Green function is developed to solve HHC problems in Cartesian, cylindrical and spherical coordinates system. The present method combines with the Laplace transform for the time domain, Green function for the space domain. For one- two-, and three- dimensional problems, four to six different examples have been analyzed.
A hybrid Integral transform method is applied in Cartesian, cylindrical and spherical coordinates of HHC problems. The present method combines with the Laplace transform for the time domain, integral transform scheme for the space domain. For one- two-, and three- dimensional problems, five to six different examples have been analyzed.
It is found from these examples that the three methods are in good agreement with the analytical solutions [19] and do not exhibit numerical oscillations at the wave front.
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