Recent Developments in the Pure Streamfunction Formulation of the Navier-Stokes System

被引：17

作者：

Fishelov, D. ^{[1
]}

Ben-Artzi, M. ^{[2
]}

Croisille, J-P. ^{[3
]}

机构：

[1] Afeka Tel Aviv Acad Coll Engn, IL-69107 Tel Aviv, Israel

[2] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel

[3] Univ Paul Verlaine Metz, Dept Math, LMAM, UMR 7122, F-57045 Metz, France

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2010年 / 45卷 / 1-3期

关键词：

Navier-Stokes equations; Streamfunction formulation; Vorticity; Numerical algorithm; Compact schemes; BIHARMONIC PROBLEMS; COMPACT SCHEME; EQUATIONS;

D O I：

10.1007/s10915-010-9374-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we review fourth-order approximations of the biharmonic operator in one, two and three dimensions. In addition, we describe recent developments on second and fourth order finite difference approximations of the two dimensional Navier-Stokes equations. The schemes are compact both for the biharmonic and the Laplacian operators. For the convective term the fourth order scheme invokes also a sixth order Pade approximation for the first order derivatives, using an approximation suggested by Carpenter-Gottlieb-Abarbanel (J. Comput. Phys. 108:272-295, 1993). We also introduce the derivation of a pure streamfunction formulation for the Navier-Stokes equations in three dimensions.

引用

页码：238 / 258

页数：21

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