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Interior penalty variational multiscale method for the incompressible Navier-Stokes equation: monitoring artificial dissipation

journal contribution
posted on 2023-06-07, 22:14 authored by Erik Burman
In this paper, we apply the interior penalty method analyzed in [E. Burman and M.--A. Fernndez, Numer. Math. 107 (2007), no. 1, 39--77; MR2317827 (2008c:65317)] to flows at high Reynolds number. As a possible measure of solution quality we propose to monitor the ratio between the artificial dissipation induced by the numerical method and the computed physical dissipation. For smooth flows we prove that for our method the artificial dissipation serves as an a posteriori error estimator and also that it vanishes at an optimal rate. In the case of flows with multiscale features, we discuss a heuristic approach relating the decay of the artificial dissipation to the decay rate of the power spectrum. Some numerical results in two space dimensions are presented examining the relation between the numerical dissipation and solution quality.

History

Publication status

  • Published

Journal

Computer Methods in Applied Mechanics and Engineering

ISSN

0045-7825

Publisher

Elsevier

Issue

41-44

Volume

196

Page range

4045-4058

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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