论文标题
非组织双孔隙率 - 尼维尔 - stokes模型的不同子域时间步骤的脱钩修改的特征有限元方法
Decoupled Modified Characteristic Finite Element Method with Different Subdomain Time Steps for Nonstationary Dual-Porosity-Navier-Stokes Model
论文作者
论文摘要
在本文中，我们开发了脱钩的修改特征有限元法的数值理论，具有不同的子域时间步骤，用于非组织双孔隙率 - 尼维尔 - 孔 - 斯托克斯模型的混合稳定公式。基于分区的时间稳定方法，将系统解耦，这意味着在子域的每个时间步骤中，独立求解Navier-Stokes方程和两个不同的Darcy方程。特别是，Navier-Stokes方程是通过修改的特征有限元方法求解的，该方法克服了由非线性项造成的计算困难。为了提高效率，不同的时间步骤用于不同的子域。证明了这种方法的稳定性。此外，我们通过数学诱导验证解决方案的最佳$ l^2 $ norm误差收敛顺序，其证明意味着完全离散的速度解决方案的均匀$ l^{\ infty} $ - 界面。最后，提出了一些数值测试以显示所提出的方法的效率。
In this paper, we develop the numerical theory of decoupled modified characteristic finite element method with different subdomain time steps for the mixed stabilized formulation of nonstationary dual-porosity-Navier-Stokes model. Based on partitioned time-stepping methods, the system is decoupled, which means that the Navier-Stokes equations and two different Darcy equations are solved independently at each time step of subdomain. In particular, the Navier-Stokes equations are solved by the modified characteristic finite element method, which overcome the computational difficulties caused by the nonlinear term. In order to increase the efficiency, different time steps are used to different subdomains. The stability of this method is proved. In addition, we verify the optimal $L^2$-norm error convergence order of the solutions by mathematical induction, whose proof implies the uniform $L^{\infty}$-boundedness of the fully discrete velocity solution. Finally, some numerical tests are presented to show efficiency of the proposed method.
