scholarly journals Some Applications of Parabolic Dirac Operators to the Instationary Navier-Stokes Problem on Conformally Flat Cylinders and Tori in $$\mathbb {R}^3$$

2018 ◽  
pp. 19-37 ◽  
Author(s):  
P. Cerejeiras ◽  
U. Kähler ◽  
R. S. Kraußhar
Keyword(s):  
Stokes Problem ◽  
Dirac Operators ◽  
Navier Stokes ◽  
Conformally Flat

A Simplified Parallel Two-Level Iterative Method for Simulation of Incompressible Navier-Stokes Equations

2015 ◽  
Vol 7 (6) ◽  
pp. 715-735
Author(s):  
Yueqiang Shang ◽  
Jin Qin
Keyword(s):  
Stokes Equations ◽  
Stokes Problem ◽  
Coarse Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Step Flow ◽  
Grid Solution ◽  
Oseen Problem ◽  
Parallel Iterative

AbstractBased 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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