IJPAM: Volume 42, No. 2 (2008)
Departamento de Bioestatística, IBB-UNESP
Campus de Botucatu
Universidade Estadual Paulista ``Júlio De Mesquita Filho"
Botucatu, 18618-000, BRAZIL
Departamento de Matemática Aplicada e Estatística, ICMC-USP
São Carlos, 13560-970, BRAZIL
Departamento de Matemática, FC-UNESP
Bauru, 17033-360, BRAZIL
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