An efficient and long-time accurate third-order algorithm for the Stokes-Darcy system
An efficient and long-time accurate third-order algorithm for the Stokes-Darcy system
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一种高效、长时间准确的Stokes-Darcy系统三阶算法
DOI：
10.1007/s00211-015-0789-3
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发表时间：
2016
影响因子：
2.1
通讯作者：
Wang XM
中科院分区：
文献类型：
--
作者：
Chen Wenbin;Gunzburger Max;Sun Dong;Wang Xiaoming;Wang XM
本文提出了一种适用于岩溶含水层渗流的Stokes-Darcy方程组的三阶时间数值算法。一种新的三阶Adams-Moulton格式用于耗散项的离散，而三阶显式Adams-Bashforth格式用于耦合Stokes和Darcy分量的界面项的时间离散。该计划是有效的，在这个意义上，一个需要解决，在每个时间步，解耦的斯托克斯和达西问题。因此，传统的斯托克斯和达西求解器可以并行应用。该方案也是无条件稳定的，并在一个温和的时间步长的限制，长时间的意义上的误差是一致有界的时间准确的。数值实验用来说明理论结果。据作者所知，新算法是Stokes-Darcy方程组的第一个三阶精度数值格式，具有良好的效率、稳定性和精度。
A third-order in time numerical IMEX-type algorithm for the Stokes–Darcy system for flows in fluid saturated karst aquifers is proposed and analyzed. A novel third-order Adams–Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams–Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. The scheme is efficient in the sense that one needs to solve, at each time step, decoupled Stokes and Darcy problems. Therefore, legacy Stokes and Darcy solvers can be applied in parallel. The scheme is also unconditionally stable and, with a mild time-step restriction, long-time accurate in the sense that the error is bounded uniformly in time. Numerical experiments are used to illustrate the theoretical results. To the authors’ knowledge, the novel algorithm is the first third-order accurate numerical scheme for the Stokes–Darcy system possessing its favorable efficiency, stability, and accuracy properties.