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Volume 4, Issue 1
A Direction Splitting Approach for Incompressible Brinkman Flow.

T. GORNAK, J.L. GUERMOND, O. ILIEV, AND P.D. MINEV

Int. J. Numer. Anal. Mod. B,4 (2013), pp. 1-13

Published online: 2013-04

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  • Abstract
The direction splitting approach proposed earlier in [7], aiming at the efficient solution of Navier-Stokes equations, is extended and adopted here to solve the Navier-Stokes-Brinkman equations describing incompressible flows in pure fluid and in porous media. The resulting pressure equation is a perturbation of the incompressibility constraint using a direction-wise factorized operator as proposed in [7]. We prove that this approach is unconditionally stable for the unsteady Navier-Stokes-Brinkman problem. We also provide numerical illustrations of the method's accuracy and effciency.
  • Keywords

Direction splitting Navier-Stokes-Brinkman equations

  • AMS Subject Headings

65N30 65N35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-4-1, author = {T. GORNAK, J.L. GUERMOND, O. ILIEV, AND P.D. MINEV}, title = {A Direction Splitting Approach for Incompressible Brinkman Flow.}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2013}, volume = {4}, number = {1}, pages = {1--13}, abstract = {The direction splitting approach proposed earlier in [7], aiming at the efficient solution of Navier-Stokes equations, is extended and adopted here to solve the Navier-Stokes-Brinkman equations describing incompressible flows in pure fluid and in porous media. The resulting pressure equation is a perturbation of the incompressibility constraint using a direction-wise factorized operator as proposed in [7]. We prove that this approach is unconditionally stable for the unsteady Navier-Stokes-Brinkman problem. We also provide numerical illustrations of the method's accuracy and effciency.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/243.html} }
TY - JOUR T1 - A Direction Splitting Approach for Incompressible Brinkman Flow. AU - T. GORNAK, J.L. GUERMOND, O. ILIEV, AND P.D. MINEV JO - International Journal of Numerical Analysis Modeling Series B VL - 1 SP - 1 EP - 13 PY - 2013 DA - 2013/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/243.html KW - Direction splitting KW - Navier-Stokes-Brinkman equations AB - The direction splitting approach proposed earlier in [7], aiming at the efficient solution of Navier-Stokes equations, is extended and adopted here to solve the Navier-Stokes-Brinkman equations describing incompressible flows in pure fluid and in porous media. The resulting pressure equation is a perturbation of the incompressibility constraint using a direction-wise factorized operator as proposed in [7]. We prove that this approach is unconditionally stable for the unsteady Navier-Stokes-Brinkman problem. We also provide numerical illustrations of the method's accuracy and effciency.
T. GORNAK, J.L. GUERMOND, O. ILIEV, AND P.D. MINEV. (2013). A Direction Splitting Approach for Incompressible Brinkman Flow.. International Journal of Numerical Analysis Modeling Series B. 4 (1). 1-13. doi:
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