Asymptotic Solution for Coupled Heat and Mass Transfer During the Solidification of High Water Content Materials

This paper focuses on obtaining an asymptotic solution for coupled heat and mass transfer problem during the solidification of high water content materials. It is found that a complicated function involved in governing equations can be approached by Taylor polynomials unlimitedly, which leads to the simplification of governing equations. The unknown functions involved in governing equations can then be approximated by Chebyshev polynomials. The coefficients of Chebyshev polynomials are determined and an asymptotic solution is obtained. With the asymptotic solution, the dehydration and freezing fronts of materials are evaluated easily, and are consistent with numerical results obtained by using an explicit finite difference method.

行星际深空探测中双程测速的高精度计算方法

对于行星际深空探测(距地球1亿km以上)任务,由于受到计算机字长的限制,传统双程测速模型的计算精度无法满足高精度定轨的需要,其最大误差源于多普勒频移周计数终点和始点上行几何距离之间和下行几何距离之间差分值的计算过程。对此建立行星际双程测速模型,高精度地计算了两个差分值,推导模型的计算公式并给出详细步骤,同时给出计算过程中需要的切比雪夫差分多项式递推公式的形式。将该模型在深空探测器精密定轨与重力场解算软件系统(Wuhan University deep-space orbit determination and gravity recovery system,WUDOGS)中进行了实现,并以欧空局火星快车号(Mars express,MEX)探测任务为背景,利用该软件进行仿真测试,从计算精度和定轨结果两个方面验证该模型的优越性。结果表明,该模型将双程测速的计算值在计算机中表达的精度提高2个数量级,同时避免了定轨过程中引入额外的数值误差,可以为后续高精度的行星际深空探测任务的定轨提供参考。