A high-order discontinuous Galerkin method for 2D incompressible flows

In this paper we introduce a high-order discontinuous Galerkin method for t wo-dimensional incompressible flow in the vorticity stream-function formula tion. The momentum equation is treated explicitly, utilizing the efficiency of the discontinuous Galerkin method. The stream function is obtained by a standard Poisson solver using continuous finite elements. There is a natur al matching between these two finite element spaces, since the normal compo nent of the velocity field is continuous across element boundaries. This al lows for a correct upwinding gluing in the discontinuous Galerkin framework , while still maintaining total energy conservation with no numerical dissi pation and total enstrophy stability. The method is efficient for inviscid or high Reynolds number flows. Optimal error estimates are proved and verif ied by numerical experiments. (C) 2000 Academic Press.