A two-level variational multiscale method for convection-dominated convection-diffusion equations


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Volker J., KAYA MERDAN S. , Layton W.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, vol.195, pp.4594-4603, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 195
  • Publication Date: 2006
  • Doi Number: 10.1016/j.cma.2005.10.006
  • Title of Journal : COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
  • Page Numbers: pp.4594-4603
  • Keywords: convection-dominated convection-diffusion equation, variational multiscale method, two-level method, efficient implementation, NAVIER-STOKES EQUATIONS, LARGE-EDDY SIMULATION, FINITE-ELEMENT-METHOD, CONSERVATION-LAWS, VISCOSITY METHOD, FORMULATION

Abstract

This paper studies the error in, the efficient implementation of and time stepping methods for a variational multiscale method (VMS) for solving convection-dominated problems. The VMS studied uses a fine mesh C-O finite element space X-h to approximate the concentration and a coarse mesh discontinuous vector finite element space L-H for the large scales of the flux in the two scale discretization. Our tests show that these choices lead to an efficient VMS whose complexity is further reduced if a (locally) L-2-orthogonal basis for L-H is used. A fully implicit and a semi-implicit treatment of the terms which link effects across scales are tested and compared. The semi-implicit VMS was much more efficient. The observed global accuracy of the most straightforward VMS implementation was much better than the artificial diffusion stabilization and comparable to a streamline-diffusion finite element method in our tests. (c) 2005 Elsevier B.V. All rights reserved.