STOKES COUPLING METHOD FOR THE EXTERIOR FLOW PART Ⅱ:WELL-POSEDNESS ANALYSIS

ＳＴＯＫＥＳＣＯＵＰＬＩＮＧ　ＭＥＴＨＯＤＦＯＲＴＨＥＥＸＴＥＲＩＯＲＦＬＯＷ　ＰＡＲＴＩＩ：ＷＥＬＬ－ＰＯＳＥＤＮＥＳＳ　ＡＮＡＬＹＳＩＳ￥ＬｉＫａｉｔａｉ（李开泰）ＢｅＹｉｎｎｉａｎ（何银年）（Ｒｏｓｅ４ｒｃｈＣｅｎｔｅｒｆｏｒＡｐｐｌｉｅｄＭａ...     

GLOBAL SOLUTIONS TO THE NAVIER-STOKES EQUATIONS FOR COMPRESSIBLE HEAT-CONDUCTING FLOW WITH SYMMETRY AND FREE BOUNDARY

ABSTRACT

Global solutions of the multidimensional Navier-Stokes equations for compressible heat-conducting flow are constructed, with spherically symmetric initial data of large oscillation between a static solid core and a free boundary connected to a surrounding vacuum state. The free boundary connects the compressible heat-conducting fluids to the vacuum state with free normal stress and zero normal heat flux. The fluids are initially assumed to fill with a finite volume and zero density at the free boundary, and with bounded positive density and temperature between the solid core and the initial position of the free boundary. One of the main features of this problem is the singularity of solutions near the free boundary. Our approach is to combine an effective difference scheme to construct approximate solutions with the energy methods and the pointwise estimate techniques to deal with the singularity of solutions near the free boundary and to obtain the bounded estimates of the solutions and the free boundary as time evolves. The convergence of the difference scheme is established. It is also proved that no vacuum develops between the solid core and the free boundary, and the free boundary expands with finite speed.     

三维含弥散可压核废料污染问题的交替方向有限元方法

考虑到数值求解三维可压缩核废料污染问题计算量大,利用块有限元逼近技术提出了交替方向有限元格式,将三维问题化为一系列一维问题逐次求解,大大降低了计算量.由于考虑的模型问题为可压缩且同时包含分子扩散和弥散的一般情形,这为误差分析带来困难,本文采用对误差方程进行差商(dt)处理的技巧,证明了格式的最优H1-模误差估计.     

GALERKIN METHOD FOR COMPRESSIBLE FLOW OF CONTAMINATION FROM NUCLEAR WASTE WITH MOLECULAR DIFFUSION AND DISPERSION*

Abstract A system of quasilinear coupled equations which arise from simulation of contamination of geologic nulear waste in porous media is studied. We'll discuss Galerkin method for the model of compressible flow with molecular diffusion and dispersion. Some new techniques are introcued to error analysis. Only one dimensional case is considered. The optimal error estimate in both L~2 and H~1 is proved. A contribution of this paper is how the dispersion term can be handled,     

含弥散可压核废料污染问题的交替方向特征有限元格式及分析

对可压缩并含弥散的核废料污染问题,利用有限元块逼近技术提出了交替方向特征有限元格式,格式兼具特征线逼近技术及交替方向技术的优点,证明了格式的最佳H^1-收敛阶。