Extraction immersed finite element method for Stokes flow with singular forces = 특이력을 가지고 있는 스톡스 유체에 대한 적출내재유한요소법

Cited 0 time in webofscience Cited 0 time in scopus
  • Hit : 218
  • Download : 0
We propose a new numerical method to solve an elliptic problem with jumps both in the solution and derivative along an interface. By considering a suitable function which has the same jumps as the solution, we transform the problem into the one without jumps. Then we apply the immersed finite element method in which we allow uniform meshes so that the interface may cut through elements to discretize the problem as introduced in [1,2,3]. Some convenient way of approximating the jumps of the solution by piecewise linear functions is suggested. Our method can also handle the case when the interface passes through grid points. We believe the treatment of such cases was first resolved in our paper. Numerical experiments for various problems show that second order convergence in $\It{L^2}$ and first order in $\It{H^1}$-norms. Moreover, the convergence order is very robust for all problems tested. Next, we consider a stationary, constant viscosity, incompressible Stokes flow with singular forces along one or several interfaces. Assuming only the jumps of the pressure are present along the interface, we develop a new numerical scheme for such a problem. By constructing an approximate singular function and removing it, we can apply a standard finite element method to solve it. A main advantage of our scheme is that one can use a uniform grid. We observe optimal $\It{O(h)}$ order for the pressure and $\It{O(h^2)}$ order for the velocity.
Advisors
Kwak, Do-Youngresearcher곽도영researcher
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2010
Identifier
418840/325007  / 020037943
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2010.2, [ v, 47 p. ]

Keywords

불연속; 유한요소법; 적출; 내재; discontinuous; finite; extraction; immersed; Stokes; 스톡스

URI
http://hdl.handle.net/10203/41939
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=418840&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
Files in This Item
There are no files associated with this item.

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0