Siu Wun Cheung

Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations

In this paper, we present a staggered discontinuous Galerkin method for the approximation of the incompressible Navier-Stokes equations. Our new method combines the advantages of discontinuous Galerkin methods and staggered meshes, and results in many good properties, namely local and global conservations, optimal convergence and superconvergence through the use of a local postprocessing technique. Another key feature is that our method provides a skew-symmetric discretization of the convection term, with the aim of giving a better conservation property compared with existing discretizations. We will present extensive numerical results, including Kovasznay flow, Taylor vortex flow, lid-driven cavity flow, parallel plate flow and channel expansion flow, to show the performance of the method.

A Mass Conservative Scheme for Fluid–Structure Interaction Problems by the Staggered Discontinuous Galerkin Method

In this paper, we develop a new mass conservative numerical scheme for the simulations of a class of fluid–structure interaction problems. We will use the immersed boundary method to model the fluid–structure interaction, while the fluid flow is governed by the incompressible Navier–Stokes equations. The immersed boundary method is proven to be a successful scheme to model fluid–structure interactions. To ensure mass conservation, we will use the staggered discontinuous Galerkin method to discretize the incompressible Navier–Stokes equations. The staggered discontinuous Galerkin method is able to preserve the skew-symmetry of the convection term. In addition, by using a local postprocessing technique, the weakly divergence free velocity can be used to compute a new postprocessed velocity, which is exactly divergence free and has a superconvergence property. This strongly divergence free velocity field is the key to the mass conservation. Furthermore, energy stability is improved by the skew-symmetric discretization of the convection term. We will present several numerical results to show the performance of the method.