不可压热对流方程的参数识别方法研究及其在冰盖模拟中的应用

Parameter identification for impressible fluid thermal convection problem has many important applications, e.g. heat transfer coefficient identification of magneto heat-conducting fluid, and basal friction coefficient identification of ice sheet. In this project, parameter identification of impressible fluid thermal convection problem is studied, the well-posedness of the optimal problem will be established, and the optimaility system will be derived, and the multilevel model correction method for the optimal problem will be presented and analyzed...The dispute of CO2 emission between developed and developing countries is in fact the dispute of the privilege of prosperity of China and other developing countries. The result of global climate simulation, especially the ice sheet simulation, is an important source to determine whether the catastrophic climate change will happen including melting of ice sheet and rising of sea level. In this project, the basal friction parameter, which affects the flow of ice sheet directly, is identified from the thermal coupled ice sheet model. Numerical method for computing the stationary solution of the ice sheet model will be derived, and the multilevel model correction method will be employed to solve the the optimal problem of the inverse problem.

不可压热对流方程的参数识别在磁流体的传热系数识别以及冰盖模型底部摩擦系数识别等问题中具有重要应用。本项目将对不可压热对流方程参数识别的理论分析和算法设计方面进行研究，包括研究该反问题的最小二乘最优化问题的适定性和最优性条件等，并研究求解该最优化问题的多水平模型修正方法。.　　.　　温室气体排放权之争是我国等发展中国家的发展权之争。评价温室气体排放是否会产生冰盖融化和海平面上升等全球气候灾难性影响，全球气候模拟尤其冰盖模拟是气候变化预测的重要判断依据。本项目拟对直接影响冰盖运动的底部摩擦系数这个重要参数的参数识别问题进行研究，通过考虑温度耦合的冰盖模型从而使参数识别问题更加可靠。本项目将研究该参数识别问题中正问题稳态解的高效求解方法，以及求解相应反问题的最小二乘最优化问题的多水平模型修正方法。

格陵兰和南极的冰盖融化会导致海平面上升，对于近海岸地区的人类社会经济生活造成直接威胁，冰盖模型的数值模拟能够估计冰盖的融化对海平面上升的贡献，在目前的冰盖研究中越来越受到关注。本项目研究提出了冰盖模拟的正问题的高效预调件算法，研究了伴随问题的非精确 Newton 迭代求解算法，提出了针对粘性有奇性的局部区域的自适应算法，通过伴随方法对冰盖模型的参数进行了反演，完成了与冰盖模拟相关的几项基础算法的研究，开发了具有自主知识产权的三维大规模并行冰盖模型数值模拟软件。