IJPAM: Volume 42, No. 2 (2008)

HIGH ORDER COMPACT AND UPWIND METHODS

P.F.A. Mancera$^1$, V.G. Ferreira$^2$, M.K. Kaibara$^3$
$^1$Departamento de Bioestatística, IBB-UNESP
Campus de Botucatu
Universidade Estadual Paulista ``Júlio De Mesquita Filho"
Botucatu, 18618-000, BRAZIL
e-mail: pmancera@ibb.unesp.br
$^2$Departamento de Matemática Aplicada e Estatística, ICMC-USP
São Carlos, 13560-970, BRAZIL
e-mail: pvgf@icmc.usp.br
$^3$Departamento de Matemática, FC-UNESP
Bauru, 17033-360, BRAZIL
e-mail: kaibara@fc.unesp.br


Abstract.We consider two types of high order numerical methods for solving the Navier-Stokes equations: compact and upwind methods. Firstly, we analyze procedures for obtaining compact fourth order method to the steady 2D Navier-Stokes equations in the context of stream function-vorticity formulations. Results are compared with those obtained using second order central differences to moderate Reynolds numbers. Secondly, we show a new high order upwind method (called adaptative QUICKEST ) for simulating free surface flows at high Reynolds numbers. A crucial point is the discretization of the advective terms in the transport equations, which is of primordial importance for the prediction of the flow problem. Several numerical tests are presented.

Received: August 17, 2007

AMS Subject Classification: 74S20

Key Words and Phrases: compact methods, upwind methods, Navier-Stokes equations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 2