Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 412, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cam.2022.114326
Keywords
Second-order/third-order temporal scheme; Rotational pressure-correction schemes; Stokes/Darcy system; Stability; Numerical experiments
Categories
Funding
- NSF of China [11771259, 11171359, 11371031]
- NSF of Shanghai, China [19ZR1414300]
- Science and Technology Commission of Shanghai Municipality, China [18dz2271000]
- innovation team on computationally efficient numerical methods based on new energy problems in Shaanxi province
- innovative team project of Shaanxi Provincial Department of Education, China [21JP013]
- special support program to develop innovative talents in the region of Shaanxi province
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In this paper, the authors develop local and parallel rotational pressure-correction schemes for a coupled Stokes/Darcy system. These schemes solve the Stokes problem and Darcy problems in their respective domains, leading to efficient parallel computation. The unconditional stability and long-time stability of the schemes are theoretically proved, and numerical experiments demonstrate their accuracy and efficiency.
In this paper, the local and parallel two- and three-step backward differentiation formula (BDF2/BDF3) rotational pressure-correction schemes are developed for a coupled Stokes/Darcy system. The central advantage of these schemes is a time-dependent version of domain decomposition by solving the Stokes problem and Darcy problems in their respective domain. By following a similar idea in Guermond et al. (2005), the Stokes problem is solved by a vector-valued elliptic equation and a scalar Poisson equation per time step. The whole system can be composed of three simple linear equations that consume almost the same computational time. Thus, the presented methods can be efficiently applied with less communication requirements and has good parallelism. In theorey, we prove the unconditional stability and long-time stability of the BDF2/BDF3 rotational pressure-correction schemes for the coupled Stokes/Darcy system. Furthermore, some numerical experiments are presented to show the accuracy and efficiency of these schemes in terms of numerical convergence rates and reservoir engineering. (c) 2022 Elsevier B.V. All rights reserved.
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