带间断扩散系数热传导方程的新型自适应数值解法  

A New Adaptive Numerical Solver for Heat Conduction Equation with Discontinuous Diffusion Coefficient

作　　者：宋淑红[1] 王双虎[2,1,3] 

机构地区：[1]北京应用物理与计算数学研究所,北京100094 [2]北京应用物理与计算数学研究所计算物理实验室,北京100088 [3]北京大学应用物理与技术研究中心,北京100871

出　　处：《应用数学学报》2010年第5期942-960,共19页Acta Mathematicae Applicatae Sinica

基　　金：国家973(2005CB321700);国家自然科学基金重点(10931004);青年科学基金(11001024)资助项目

摘　　要：本文研究带间断扩散系数热传导方程在大变形网格上的高精度数值模拟方法.该方法在算每条边上的能流时采用了本文提出的"孪生逼近"方法,提高了扩散系数间断处能流的计算精度,给出了"孪生逼近"的误差分析.应用该方法于二维大变形网格上热传导问题计算,构造了网格边上能流的一种自适应高精度计算方法,其中自适应指的是自适应选取模板和自适应选取权重大小.数值试验表明该方法能适应网格大变形和扩散系数间断的困难情况.In this paper,a high accuracy numerical simulative method is studied for heat conduction equations with discontinuous diffusion coefficient on large fluid distortion grids. This method applies a so-called ＂twin-fitting＂ approximate method proposed in this paper to the calculation of fluxes on edges,then improves calculational accuracy of fluxes on edges with discontinuous diffusion coefficient,at last is given some related error analysis.In two dimension case,an adaptive and high accuracy method is constructed to calculate fluxes on edges,here the ＂adaptive＂ means to determine the stencils and the weights adaptively. Numerical experiments show that this method can be accommodated to large fluid distortion grids and the difficult case of discontinuous diffusion coefficient.

关 键 词：最小二乘法 热传导方程 差分离散 自适应数值模拟 

分 类 号：O551.3[理学—热学与物质分子运动论]