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| Chebyshev pseudo-spectral method for the calculation of temperature in active layer of permafrost with phase-change |
| Received:June 28, 2007 |
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| DOI：10.7511/jslx20095015 |
| KeyWord:active-layer permafrost temperature phase-change Chebyshev’ pseudo-spectral non-constant coefficients |
| Author | Institution |
| 李南生 |
同济大学 土木工程学院 水利工程系,上海 |
| 吴青柏 |
中国科学院 寒区旱区环境与工程研究所,兰州 |
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| Abstract: |
| On the basis of the modern mechanism of heat conduction with phase-change for frozen-soil and the well-grounded physical model of heat-transfer coupled with moisture using in the numerical calculation of frozen-soil, an unique numerical formulation, spectral method, is applied in the calculation of temperature field of frozen-soil active layer for the first time. Unknown active layer temperature solution is asymptotically expanded by using Chebyshev polynomials as its base functions and the Chebyshev expansion is interpolated at collocation points, so called "pseudo-spectral" is applied to solve nonlinear differential heat-transfer equations for an unknown temperature function. In consistent with the high precision of spectral method, it is appropriate to introduce the fourth order Runger-Kutta time-integration method in the evolution equation after spatial discretized. A special method, coefficients hysteresis, is used to treat with non-constant conductivity and specific heat coefficients in the evolution equation. The proposed numerical formulation keeps the common predominance, excellent numerical precision, of spectral method, which results are showed in examples. |
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