冻土活动层相变温度场Chebyshev拟谱分析

Chebyshev pseudo-spectral method for the calculation of temperature in active layer of permafrost with phase-change

在冻土相变温度热传导机理基础上,应用冻土计算中水热输运过程成熟的通用物理模型,提出冻土活动层温度的一种全新的数值分析方法-谱方法。应用Chebyshev多项式作为基函数将温度解展开,在研究域(或单元)内采用伪谱Chebyshev逼近的谱方法。为了与谱方法的高精度相配合及提高时程积分解的稳定性,本文应用四阶Runger-Kutta法进行时程积分,变物性温度泛函-热导系数、热容量等考虑效应滞后的处理方法。本文提出冻土非线性问题数值计算拟谱分析的理论构架,其计算方法在冻土工程应用中具有一定的理论导向作用和较大的实用价值。

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.