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Maximum principle preserving high or...

Jiang, Yi.

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Maximum principle preserving high order schemes for convection-dominated diffusion equations.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Maximum principle preserving high order schemes for convection-dominated diffusion equations./
作者:	Jiang, Yi.
面頁冊數:	96 p.
附註:	Source: Masters Abstracts International, Volume: 52-02.
Contained By:	Masters Abstracts International52-02(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1545588
ISBN:	9781303408731

Maximum principle preserving high order schemes for convection-dominated diffusion equations.
Jiang, Yi.

Maximum principle preserving high order schemes for convection-dominated diffusion equations. - 96 p.

Source: Masters Abstracts International, Volume: 52-02.

Thesis (M.S.)--Michigan Technological University, 2013.

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving (MPP) high order finite volume (FV) WENO scheme, and then propose a new parametrized MPP high order finite difference (FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

ISBN: 9781303408731Subjects--Topical Terms:

515831
Mathematics.

Maximum principle preserving high order schemes for convection-dominated diffusion equations.
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500 $a Adviser: Zhengfu Xu.
502 $a Thesis (M.S.)--Michigan Technological University, 2013.
520 $a The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving (MPP) high order finite volume (FV) WENO scheme, and then propose a new parametrized MPP high order finite difference (FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.
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650 4 $a Mathematics. $3 515831
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710 2 $a Michigan Technological University. $b Mathematical Sciences. $3 2096669
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