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.