The shifted boundary method for embedded domain computations. Part II: Linear advection–diffusion and incompressible Navier–Stokes equations


Journal Article

© 2018 Elsevier Inc. We propose a new embedded finite element method for the linear advection–diffusion equation and the laminar and turbulent incompressible Navier–Stokes equations. The proposed method belongs to the class of surrogate/approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary. Accordingly, boundary conditions, enforced weakly, are appropriately modified to preserve optimal error convergence rates. We include the full analysis of stability and convergence of the method in the linear advection–diffusion equation, and a battery of tests for the case of laminar and turbulent incompressible Navier–Stokes equations. We also discuss the conservation properties of the proposed method in all cases.

Full Text

Duke Authors

Cited Authors

  • Main, A; Scovazzi, G

Published Date

  • November 1, 2018

Published In

Volume / Issue

  • 372 /

Start / End Page

  • 996 - 1026

Electronic International Standard Serial Number (EISSN)

  • 1090-2716

International Standard Serial Number (ISSN)

  • 0021-9991

Digital Object Identifier (DOI)

  • 10.1016/

Citation Source

  • Scopus