渗透系数的空间变异性是影响地下水运动和溶质迁移过程的主要因素。本文利用改进的连续随机增加方法(Successive random additional method,简称SRA)生成了渗透系数对数(lnK)具有分维Levy运动统计特征的随机场,并对生成样本的统计特征...渗透系数的空间变异性是影响地下水运动和溶质迁移过程的主要因素。本文利用改进的连续随机增加方法(Successive random additional method,简称SRA)生成了渗透系数对数(lnK)具有分维Levy运动统计特征的随机场,并对生成样本的统计特征进行了分析验证,同时应用蒙特卡罗方法研究含水层渗透系数的空间变异性对地下水运动和溶质迁移过程的影响。结果表明:Levy指数α越小,渗透系数空间变异性越强。当研究区域渗透系数的对数lnK增量符合Levy稳定分布时,其纵向流速对数lnv增量同样具有Levy稳定分布,且所对应的Levy指数αlnK与αlnv的大小基本一致。污染羽一阶矩纵向分量Mx随lnK平均值的增大而增大,而与α的大小无关。同一lnK均值条件下,纵向分量Mx随时间增大而增大,横向分量My与时间无关。污染羽二阶矩分量Mxx和Myy随α的减小而增大,表明渗透系数的空间变异性越强,污染物质心的扩散范围越大。渗透系数的空间变异程度对地下水运动和溶质迁移过程的影响十分明显。展开更多
We study the stationary Wigner equation on a bounded, one- dimensional spatial domain with inflow boundary conditions by using the parity decomposition of L. Barletti and P. F. Zweifel [Transport Theory Statist. Phys....We study the stationary Wigner equation on a bounded, one- dimensional spatial domain with inflow boundary conditions by using the parity decomposition of L. Barletti and P. F. Zweifel [Transport Theory Statist. Phys., 2001, 30（4-6）： 507-520]. The decomposition reduces the half-range, two-point boundary value problem into two decoupled initial value problems of the even part and the odd part. Without using a cutoff approximation around zero velocity, we prove that the initial value problem for the even part is well-posed. For the odd part, we prove the uniqueness of the solution in the odd L2-spaee by analyzing the moment system. An example is provided to show that how to use the analysis to obtain the solution of the stationary Wigner equation with inflow boundary conditions.展开更多
文摘渗透系数的空间变异性是影响地下水运动和溶质迁移过程的主要因素。本文利用改进的连续随机增加方法(Successive random additional method,简称SRA)生成了渗透系数对数(lnK)具有分维Levy运动统计特征的随机场,并对生成样本的统计特征进行了分析验证,同时应用蒙特卡罗方法研究含水层渗透系数的空间变异性对地下水运动和溶质迁移过程的影响。结果表明:Levy指数α越小,渗透系数空间变异性越强。当研究区域渗透系数的对数lnK增量符合Levy稳定分布时,其纵向流速对数lnv增量同样具有Levy稳定分布,且所对应的Levy指数αlnK与αlnv的大小基本一致。污染羽一阶矩纵向分量Mx随lnK平均值的增大而增大,而与α的大小无关。同一lnK均值条件下,纵向分量Mx随时间增大而增大,横向分量My与时间无关。污染羽二阶矩分量Mxx和Myy随α的减小而增大,表明渗透系数的空间变异性越强,污染物质心的扩散范围越大。渗透系数的空间变异程度对地下水运动和溶质迁移过程的影响十分明显。
文摘We study the stationary Wigner equation on a bounded, one- dimensional spatial domain with inflow boundary conditions by using the parity decomposition of L. Barletti and P. F. Zweifel [Transport Theory Statist. Phys., 2001, 30（4-6）： 507-520]. The decomposition reduces the half-range, two-point boundary value problem into two decoupled initial value problems of the even part and the odd part. Without using a cutoff approximation around zero velocity, we prove that the initial value problem for the even part is well-posed. For the odd part, we prove the uniqueness of the solution in the odd L2-spaee by analyzing the moment system. An example is provided to show that how to use the analysis to obtain the solution of the stationary Wigner equation with inflow boundary conditions.
