摘要
对三维非线性对流扩散问题提出一类适合并行计算的二阶迎风分数步差分格式,采用分数步技术,将三维问题化为连续解3个一维问题计算.利用变分形式、能量方法、差分算子乘积交换性、高阶差分算子的分解、微分方程先验估计的理论和技巧,得到收敛性的最佳阶的误差估计.该方法已成功的应用油资源运移聚集渗流力学数值模拟计算、海水入侵预测和防治的工程实践中.
For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic were put forward. Fractional steps techniques were needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates were adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicthag the consequences of seawater intrusion and protection projects.
出处
《应用数学和力学》
CSCD
北大核心
2006年第5期605-614,共10页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(1037025210271066)
国家重点基础研究专项经费资助项目(G19990328)
国家攻关基金资助项目(20050200069)
国家教育部博士点基金资助项目(20030422047)
关键词
非线性对流扩散
渗流力学
迎风分数步
差分方法
收敛性
油资源数值模拟
nonlinear convection-dominated
dynamics of fluids
upwind fractional steps
finite difference method
convergence
numerical simulation
