A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations

作者：Rhebergen Sander^*; Cockburn Bernardo; van der Vegt Jaap J W

来源：Journal of Computational Physics, 2013, 233: 339-358.

DOI：10.1016/j.jcp.2012.08.052

• Space-time discontinuous Galerkin method
• Incompressible Navier-Stokes equations
• Deforming domains

We introduce a space-time discontinuous Galerkin (DG) finite element method for the incompressible Navier-Stokes equations. Our formulation can be made arbitrarily high-order accurate in both space and time and can be directly applied to deforming domains. Different stabilizing approaches are discussed which ensure stability of the method. A numerical study is performed to compare the effect of the stabilizing approaches, to show the method%26apos;s robustness on deforming domains and to investigate the behavior of the convergence rates of the solution. Recently we introduced a space-time hybridizable DG (HDG) method for incompressible flows [S. Rhebergen, B. Cockburn, A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains, J. Comput. Phys. 231 (2012) 4185-4204]. We will compare numerical results of the space-time DG and space-time HDG methods. This constitutes the first comparison between DG and HDG methods.

• 出版日期2013-1-15