Numerical solution of the incompressible Navier-Stokes equations with Coriolis forces based on the discretization of the total time derivative

JOURNAL OF COMPUTATIONAL PHYSICS

卷:148

Article

Codina, R

关键词: incompressible flows;    Coriolis forces;    method of characteristics;    inertial bases;    stabilized finite element methods;   

DOI  :  10.1006/jcph.1998.6126

来源: Elsevier

【 摘 要 】

In this paper we present a numerical formulation to solve the incompressible Navier-Stokes equations written in a rotating frame of reference. The method is based on a finite difference discretization in time and a finite element discretization in space. When the viscosity is very small, numerical oscillations map appear due both to the high Reynolds number and to the presence of the Coriolis forces. To overcome these oscillations, a special discretization in time is proposed. The idea is to discretize the total time derivative in an inertial basis rather than only the partial time derivative in the rotating reference system. After this is done, a further high-order approximation is introduced, leading to a problem posed in the rotating frame of reference and in spatial coordinates. In contrast with the straightforward discretization of the original equations, some additional terms appear that enhance the stability of the numerical scheme. In the absence of Coriolis forces, the method is a generalization of the characteristic Galerkin technique for convection-dominated hows. (C) 1999 Academic Press.

【 授权许可】

Free