论文标题
多孔介质中非盲目流动的高级紧凑型有限差异方法
High Order Compact Finite Difference Methods for Non-Fickian Flows in Porous Media
论文作者
论文摘要
在这项工作中，构建并分析了与曲柄 - 尼科尔森离散化结合的四阶紧凑型有限差（CBCFD）方案，用于在一维和二维病例中求解抛物线抛物线透明型非叉型非叉型流动。构造方案的稳定性分析是严格得出的。我们还以时间增量获得了最佳的二阶收敛，并在空间方向上获得了速度和压力的四阶收敛。为了验证CBCFD方案的有效性，我们提出了一些实验，以表明数值结果与我们的理论分析一致。
In this work, fourth-order compact block-centered finite difference (CBCFD) schemes combined with the Crank-Nicolson discretization are constructed and analyzed for solving parabolic integro-differential type non-Fickian flows in one-dimensional and two-dimensional cases. Stability analyses of the constructed schemes are derived rigorously. We also obtain the optimal second-order convergence in temporal increment and the fourth-order convergence in spatial direction for both velocity and pressure. To verify the validity of the CBCFD schemes, we present some experiments to show that the numerical results are in agreement with our theoretical analysis.
