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Volume 16, Issue 3
A Partitioned Method with Different Time Steps for Coupled Stokes and Darcy Flows with Transport

Jingyuan Zhang, Hongxing Rui & Yanzhao Cao

Int. J. Numer. Anal. Mod., 16 (2019), pp. 463-498.

Published online: 2018-11

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  • Abstract

A decoupled finite element algorithm with different time steps on different physical variables for a Stokes-Darcy interface system coupled with the solution transport is studied. The viscosity of the Stokes equation is assumed to depend on the concentration of the transported solution. The numerical algorithm consists of two steps. In the first step, the system is decoupled on the interface. In the second step, the time derivatives are discretized with different step sizes for different partial differential equations in the system. A careful error analysis provides a guidance on the ratio of the step sizes with respect to the ratio of the physical parameters. Numerical examples are presented to verify the theoretical results and illustrate the effectiveness of the decoupled algorithm of using different time steps.

  • Keywords

Coupled Stokes and Darcy flows, solute transport, decoupled algorithm, different time steps, error estimates.

  • AMS Subject Headings

65M12, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

iamzjy00@126.com (Jingyuan Zhang)

hxrui@sdu.edu.cn (Hongxing Rui)

yzc0009@auburn.edu (Yanzhao Cao)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-463, author = {Zhang , JingyuanRui , Hongxing and Cao , Yanzhao}, title = {A Partitioned Method with Different Time Steps for Coupled Stokes and Darcy Flows with Transport}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {3}, pages = {463--498}, abstract = {

A decoupled finite element algorithm with different time steps on different physical variables for a Stokes-Darcy interface system coupled with the solution transport is studied. The viscosity of the Stokes equation is assumed to depend on the concentration of the transported solution. The numerical algorithm consists of two steps. In the first step, the system is decoupled on the interface. In the second step, the time derivatives are discretized with different step sizes for different partial differential equations in the system. A careful error analysis provides a guidance on the ratio of the step sizes with respect to the ratio of the physical parameters. Numerical examples are presented to verify the theoretical results and illustrate the effectiveness of the decoupled algorithm of using different time steps.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12878.html} }
TY - JOUR T1 - A Partitioned Method with Different Time Steps for Coupled Stokes and Darcy Flows with Transport AU - Zhang , Jingyuan AU - Rui , Hongxing AU - Cao , Yanzhao JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 463 EP - 498 PY - 2018 DA - 2018/11 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12878.html KW - Coupled Stokes and Darcy flows, solute transport, decoupled algorithm, different time steps, error estimates. AB -

A decoupled finite element algorithm with different time steps on different physical variables for a Stokes-Darcy interface system coupled with the solution transport is studied. The viscosity of the Stokes equation is assumed to depend on the concentration of the transported solution. The numerical algorithm consists of two steps. In the first step, the system is decoupled on the interface. In the second step, the time derivatives are discretized with different step sizes for different partial differential equations in the system. A careful error analysis provides a guidance on the ratio of the step sizes with respect to the ratio of the physical parameters. Numerical examples are presented to verify the theoretical results and illustrate the effectiveness of the decoupled algorithm of using different time steps.

Zhang , JingyuanRui , Hongxing and Cao , Yanzhao. (2018). A Partitioned Method with Different Time Steps for Coupled Stokes and Darcy Flows with Transport. International Journal of Numerical Analysis and Modeling. 16 (3). 463-498. doi:
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