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A time discontinuous Galerkin isogeometric analysis method for non-Fourier thermal wave propagation problem

Yang Xia (School of Automotive Engineering, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China)
Pan Guo (National Center for International Joint Research of Micro-nano Moulding Technology, School of Mechanics and Engineering Science, Zhengzhou University, Zhengzhou, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 9 September 2019

Issue publication date: 12 September 2019




Numerical instability such as spurious oscillation is an important problem in the simulation of heat wave propagation. The purpose of this study is to propose a time discontinuous Galerkin isogeometric analysis method to reduce numerical instability of heat wave propagation in the medium subjected to heat sources, particularly heat impulse.


The essential vectors of temperature and the temporal gradients are assumed to be discontinuous and interpolated individually in the discretized time domain. The isogeometric analysis method is applied to use its property of smooth description of the geometry and to eliminate the mesh-dependency. An artificial damping scheme with proportional stiffness matrix is brought into the final discretized form to reduce the numerical spurious oscillations.


The numerical spurious oscillations in the simulation of heat wave propagation are effectively eliminated. The smooth description of geometry with spline functions solves the mesh-dependency problem and improves the numerical precision.


The time discontinuous Galerkin method is applied within the isogeometric analysis framework. The proposed method is effective in the simulation of the wave propagation problems subjecting to impulse load with numerical stability and accuracy.



This work was funded by the Project of the National Natural Science Foundation of China (Nos 11702056, 61572021), Fundamental Research Funds for the Central Universities (No. DUT17JC32), the Startup Research Fund of Zhengzhou University (1511327001), the National Key Basic Research and Development Program through contract grant number (2011CB013705) and (2011ZX05026–002–02). These supports are gratefully acknowledged.


Xia, Y. and Guo, P. (2019), "A time discontinuous Galerkin isogeometric analysis method for non-Fourier thermal wave propagation problem", Engineering Computations, Vol. 36 No. 7, pp. 2240-2259.



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