Artificial boundary conditions for incompressible Navier–Stokes equations: A well-posed result

✍ Scribed by Weizhu Bao

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 364 KB
• Volume: 188
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(99)00285-6

✦ Synopsis

Numerical simulation of two-dimensional incompressible viscous ¯ows around an obstacle is considered. Two horizontal straight line arti®cial boundaries are introduced and the original ¯ow is approximated by a ¯ow in an in®nite channel with slip boundary condition on the wall. Then two vertical segment arti®cial boundaries are introduced and a series of approximate arti®cial boundary conditions on them are derived by imposing the continuity of velocity and the normal stress. Thus the original problem is reduced to a problem de®ned in a bounded computational domain. The well-posedness of the reduced problem is proved. The ®nite element approximation of this problem is given and error estimates are obtained. Furthermore numerical examples show the accuracy and ef-®ciency of our arti®cial boundary conditions.