求解非均质多孔介质中随机水流问题的多尺度有限元降基方法

Reduced multiscale finite element basis method for solving the stochastic water flow problems in heterogeneous porous media

为高效求解地下非均质多孔介质中的随机水流问题,通过构造一组独立于随机参数取样的多尺度有限元降基函数和生成一个降阶多尺度模型,发展了一种多尺度有限元降基方法(RMsBM)。并应用矩阵离散的经验插值方法(MDEIM)仿射分解非仿射的随机参数问题的离散系统以加速降阶模型的在线计算。为评估所提出方法的性能与效率,对随机非均质多孔介质中的饱和水流问题执行了若干数值试验。数值结果表明:所提出的RMsBM通过选择合适的粗网格和最优数目的局部多尺度降基函数,可在维持良好计算精度的同时,显著提高在线计算效率。

For effectively solving the stochastic groundwater flow problems in heterogeneous porous media,a reduced multiscale finite element basis method(RMsBM)was developed by constructing a set of reduced multiscale finite element basis functions independent of the parameter sampling and generating a reduced-order multiscale model.Moreover,in order to improve the online computation of reduced-order model,a matrix discrete empirical interpolation method(MDEIM)was used to affinely decompose the discrete system of the nonaffine parametrized problem.Finally,several numerical experiments were carried out for saturated flow problems in heterogeneous random porous media to evaluate the performance and efficiency of the proposed method.The numerical results showed that the proposed RMsBM can significantly enhance online computation efficiency and maintain comparative accuracy for the flow problems by choosing a suitable coarse mesh and an optimal number of local reduced multiscale basis functions.