Volume 7, Issue 6
A Simplified Parallel Two-Level Iterative Method for Simulation of Incompressible Navier-Stokes Equations

Yueqiang Shang & Jin Qin

Adv. Appl. Math. Mech., 7 (2015), pp. 715-735.

Published online: 2018-05

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  • Abstract

Based on two-grid discretization, a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed. The method is based on a fixed point iteration for the equations on a coarse grid, where a Stokes problem is solved at each iteration. Then, on overlapped local fine grids, corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution. Error bounds of the approximate solution are derived. Numerical results on examples of known analytical solutions, lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.

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@Article{AAMM-7-715, author = {Yueqiang Shang and Jin Qin}, title = {A Simplified Parallel Two-Level Iterative Method for Simulation of Incompressible Navier-Stokes Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {6}, pages = {715--735}, abstract = {

Based on two-grid discretization, a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed. The method is based on a fixed point iteration for the equations on a coarse grid, where a Stokes problem is solved at each iteration. Then, on overlapped local fine grids, corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution. Error bounds of the approximate solution are derived. Numerical results on examples of known analytical solutions, lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m464}, url = {http://global-sci.org/intro/article_detail/aamm/12072.html} }
TY - JOUR T1 - A Simplified Parallel Two-Level Iterative Method for Simulation of Incompressible Navier-Stokes Equations AU - Yueqiang Shang & Jin Qin JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 715 EP - 735 PY - 2018 DA - 2018/05 SN - 7 DO - http://dor.org/10.4208/aamm.2014.m464 UR - https://global-sci.org/intro/aamm/12072.html KW - AB -

Based on two-grid discretization, a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed. The method is based on a fixed point iteration for the equations on a coarse grid, where a Stokes problem is solved at each iteration. Then, on overlapped local fine grids, corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution. Error bounds of the approximate solution are derived. Numerical results on examples of known analytical solutions, lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.

Yueqiang Shang & Jin Qin. (1970). A Simplified Parallel Two-Level Iterative Method for Simulation of Incompressible Navier-Stokes Equations. Advances in Applied Mathematics and Mechanics. 7 (6). 715-735. doi:10.4208/aamm.2014.m464
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