Communications in Mathematical Sciences

Gauge Method for Viscous Incompressible Flows

Weinan E and Jian-Guo Liu

Abstract

We present a new formulaiton of the incompressible Navier-Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation. The gauge freedom allows us to assign simple and specific boundary conditions for both the auxiliary field and the gauge field, thus eliminating the issue of pressure boundary condition in the usual primitive variable formulation. The resulting dynamic and kinematic equations can then be solved by standard methods for heat and Poisson equations. A normal mode analysis suggests that in contrast to the classical projection method, the gauge method does not suffer from the problem of numerical boundary layers. Thus the subtleties on the spatial discretization for the projection methods are removed. Consequently, the projection step in the gauge method can be accomplished by standard Poissin solves. We demonstrate the efficiency and accuracy of the gauge method by several numerical examples, including the flow past cylinder.

Article information

Source
Commun. Math. Sci. Volume 1, Number 2 (2003), 317-332.

Dates
First available in Project Euclid: 7 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.cms/1118152073

Mathematical Reviews number (MathSciNet)
MR1980478

Zentralblatt MATH identifier
1160.76329

Citation

E, Weinan; Liu, Jian-Guo. Gauge Method for Viscous Incompressible Flows. Commun. Math. Sci. 1 (2003), no. 2, 317--332. https://projecteuclid.org/euclid.cms/1118152073.


Export citation