Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method

LIU Wensheng; LIXuan; MA Yunzhu; YANG Su

doi:10.21656/1000-0887.380166

Volume 39 Issue 4

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LIU Wensheng, LIXuan, MA Yunzhu, YANG Su. Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method[J]. Applied Mathematics and Mechanics, 2018, 39(4): 403-414. doi: 10.21656/1000-0887.380166

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Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method

doi: 10.21656/1000-0887.380166

Central South University (State Key Laboratory of Powder Metallurgy), Changsha 410083, P.R.China

Funds: The National High-tech R&D Program of China (863 Program) (2009AA034300)

Received Date: 2017-06-13
Rev Recd Date: 2017-09-25
Publish Date: 2018-04-15

Abstract

Abstract

To overcome the numerical oscillation in solving transient temperature fields with the finite element method, the heat conduction matrix and the heat capacity matrix were analyzed, and the cause for the oscillation of numerical solution as well as the method of eliminating oscillation were studied. According to the results, the cause for the numerical oscillation is that the thermal conduction matrix violates the second law of thermodynamics, and at the beginning of the iteration, the continuity hypothesis of the temperature change rate of the elements in the heat capacity matrix is far from the actual situation. Regularization of element shapes and application of appropriate lumped mass heat capacity matrices can effectively eliminate the numerical oscillation. With an infinite plate in the heat transfer process as an example, the conclusion was verified through comparison between different calculation methods.
- transient temperature field,
- finite element,
- oscillation,
- second law of thermodynamics,
- lumped mass heat capacity matrix

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References(15)

References

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