Abstract: Athree-dimensional finite element model has been constructed for tbe variable viscosity,compressible Netwonian flow in the mantle.In development of the formulations,the motion equation starts from the momentum equation which is described in terms of stress components.The physical properties of the mantle,such as rheology,equation of state,the thermal conductivity and others are of three-dimensional heterogeneities,they can be evaluated either using theempiric formula or the laboratory experiments depending on the problem to be studied.As an example,a medel with variable viscosity and no slip at bottom is shown for the typical three-dimensional flow pattemrn.

Key words: Mantle couvection, Anelastic compressible fluid, Variable viscosity, Three－dimensional fiuite element model

摘要： 建立了描述具有无限大Prandlt数,变粘度的滞弹性流体运动的稳态和动态三维有限元公式,其中运动方程的有限元公式是由用应力分量表示的平衡方程,再利用牛顿流体的本构关系导出的。这种处理方式,不仅能够分析流体粘度变化所起的动力学作用,而且还能够直接计算温度分布和由流体运动所引起的扰动压力。最后,论证了导出的有限元公式和程序的正确性和可靠性,并给出了具有三维流动特征的算例。

关键词: 地幔对流, 滞弹性可压流体, 空粘度, 三维有限元模型