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Volume 12, Issue 4
Analysis of a Second-Order, Unconditionally Stable, Partitioned Method for the Evolutionary Stokes-Darcy Model

Michaela Kubacki & Marina Moraiti

Int. J. Numer. Anal. Mod., 12 (2015), pp. 704-730.

Published online: 2015-12

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  • Abstract

We propose and analyze a partitioned numerical method for the fully evolutionary Stokes-Darcy equations that model the coupling between surface and groundwater flows. The proposed method uncouples the surface from the groundwater flow by using the implicit-explicit combination of the Crank-Nicolson and Leapfrog methods for the discretization in time with added stabilization terms. We prove that the method is asymptotically, unconditionally stable — requiring no time step condition — and second-order accurate in time with optimal rates in space. We verify the method's unconditional stability and second-order accuracy numerically.

  • Keywords

Stokes, Darcy, groundwater, surface water, partitioned, decoupled, second-order accuracy, unconditional stability, asymptotic stability.

  • AMS Subject Headings

65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-12-704, author = {Michaela Kubacki and Marina Moraiti}, title = {Analysis of a Second-Order, Unconditionally Stable, Partitioned Method for the Evolutionary Stokes-Darcy Model}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {4}, pages = {704--730}, abstract = {

We propose and analyze a partitioned numerical method for the fully evolutionary Stokes-Darcy equations that model the coupling between surface and groundwater flows. The proposed method uncouples the surface from the groundwater flow by using the implicit-explicit combination of the Crank-Nicolson and Leapfrog methods for the discretization in time with added stabilization terms. We prove that the method is asymptotically, unconditionally stable — requiring no time step condition — and second-order accurate in time with optimal rates in space. We verify the method's unconditional stability and second-order accuracy numerically.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/508.html} }
TY - JOUR T1 - Analysis of a Second-Order, Unconditionally Stable, Partitioned Method for the Evolutionary Stokes-Darcy Model AU - Michaela Kubacki & Marina Moraiti JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 704 EP - 730 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/508.html KW - Stokes, Darcy, groundwater, surface water, partitioned, decoupled, second-order accuracy, unconditional stability, asymptotic stability. AB -

We propose and analyze a partitioned numerical method for the fully evolutionary Stokes-Darcy equations that model the coupling between surface and groundwater flows. The proposed method uncouples the surface from the groundwater flow by using the implicit-explicit combination of the Crank-Nicolson and Leapfrog methods for the discretization in time with added stabilization terms. We prove that the method is asymptotically, unconditionally stable — requiring no time step condition — and second-order accurate in time with optimal rates in space. We verify the method's unconditional stability and second-order accuracy numerically.

Michaela Kubacki and Marina Moraiti. (2015). Analysis of a Second-Order, Unconditionally Stable, Partitioned Method for the Evolutionary Stokes-Darcy Model. International Journal of Numerical Analysis and Modeling. 12 (4). 704-730. doi:
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