Staggered Taylor–Hood and Fortin elements for Stokes equations of pressure boundary conditions in Lipschitz domain

2019 ◽  
Vol 36 (1) ◽  
pp. 185-208
Author(s):  
Zhijie Du ◽  
Huoyuan Duan ◽  
Wei Liu
Keyword(s):  
Boundary Conditions ◽  
Lipschitz Domain ◽  
Stokes Equations ◽  
Pressure Boundary Conditions

New Treatment of Pressure Boundary Conditions for DSMC Method in Micro-Channel Flow Simulations

2007 ◽  
Author(s):  
J. J. Ye ◽  
J. Yang ◽  
J. Y. Zheng ◽  
W. Z. Li ◽  
S. Z. He ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Pressure Distribution ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
New Method ◽  
Micro Channel ◽  
Micro Channels ◽  
Micro Flows ◽  
New Treatment ◽  
Pressure Boundary Conditions

Using DSMC to simulate micro flows in micro-channels, the numerical treatment of boundary conditions is very important. In this paper, several previous numerical treatments of boundary conditions are discussed with their merits and demerits, and a new treatment method based on the assumption of certain pressure distribution in the cells for boundary conditions is proposed. As comparable validity tests, it is applied in the DSMC simulations for the Poiseuille micro flows in micro-channels with four types of classical pressure boundary conditions. The dimensionless velocity profiles are shown and compared with analytical solutions derived from the Navier-Stokes equations with slip boundary conditions. The pressure distributions along the centerline of the micro-channel with the different boundary conditions are presented, and the simulation solutions agree well with the slip analytical solutions. As the Knudsen number increased, a strong linearity of the pressure distribution can be evidently predicted by the new method. Compared with the inlet and outlet velocity distribution, it is shown that the new method has better efficiency than the previous methods in the convergence.

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