2000 character limit reached
A conservative discontinuous Galerkin scheme for the 2D incompressible Navier--Stokes equations (1311.7477v1)
Published 29 Nov 2013 in physics.comp-ph, cs.NA, math.NA, physics.flu-dyn, and physics.plasm-ph
Abstract: In this paper we consider a conservative discretization of the two-dimensional incompressible Navier--Stokes equations. We propose an extension of Arakawa's classical finite difference scheme for fluid flow in the vorticity-stream function formulation to a high order discontinuous Galerkin approximation. In addition, we show numerical simulations that demonstrate the accuracy of the scheme and verify the conservation properties, which are essential for long time integration. Furthermore, we discuss the massively parallel implementation on graphic processing units.