Decoupled Crank-Nicolson/Adams-Bashforth scheme for the Boussinesq equations with smooth initial data
Decoupled Crank-Nicolson/Adams-Bashforth scheme for the Boussinesq equations with smooth initial data
复制标题
具有平滑初始数据的 Boussinesq 方程的解耦 Crank-Nicolson/Adams-Bashforth 格式
DOI：
10.1080/00207160.2018.1455092
复制
发表时间：
2019
影响因子：
1.8
通讯作者：
靳娇娇
中科院分区：
文献类型：
--
作者：
张通;靳娇娇
本文基于混合有限元方法，研究了具有光滑初值的Boussinesq方程的解耦Crank-Nicolson/Adams-Bashforth格式。空间离散Boussinesq方程的时间处理是基于隐式Crank-Nicolson计划的线性项和显式Adams-Bashforth计划的非线性项。由于解耦的方法，所考虑的问题被分成两个子问题，这些子问题可以并行求解。在一定的时间步长限制条件下，给出了数值解的稳定性和收敛性结果。最后，通过数值实验验证了数值格式的性能和理论分析结果。
Based on the mixed finite element method, we consider the decoupled Crank–Nicolson/Adams–Bashforth scheme for the Boussinesq equations with smooth initial data in this paper. The temporal treatment of the spatial discrete Boussinesq equations is based on the implicit Crank–Nicolson scheme for the linear terms and the explicit Adams–Bashforth scheme for the nonlinear terms. Thanks to the decoupled method, the considered problem is split into two subproblems and these subproblems can be solved in parallel. Under some restriction on the time step, we present the stability and convergence results of numerical solutions, Finally, some numerical experiments are provided to test the performance of the developed numerical scheme and verify the established theoretical findings.