月幔温度演化的二维有限元模拟

摘要

为研究月球自吸积结束后温度的变化,利用有限元方法构建极坐标系二维温度演化模型.对控制方程进行无量纲化处理,并对动量方程采用Boussinesq近似.结果表明,早期高温月幔产生了多个大尺度的对流环,随后由于内部热量的急剧释放,温度下降,压强减小,早期形成的对流环变得不稳定,月幔的平均温度由1 735 K最终下降至1 278 K左右.数值模拟结果精度较好,表明本文模型及程序代码具有可行性,结合其他地球物理数据,如月表热流值,将模型扩展至三维,可用于研究月球吸积完成后的热演化.%To study the thermal evolution of the moon,the lunar mantle temperature was simulated with two-dimensional finite element method in the polar coordinate system.The governing equations for the dynamics are dimensionless, and Boussinesq approximation is adopted as well.The results indicate that several large-scale hot plumes, resulted from the hot lunar mantle, appear in the initial stage.These unstable plumes release lots of energy, subsequently their temperature drops hugely.The average temperature of the lunar mantle eventually drops from 1 735 K to 1 278 K.Numerical results implies the feasibility of our model and code, which can be extended in three-dimensions to predict the temperature evolution of the Moon with the combination of other geophysical data such as lunar surface heat flux.