Author(s):

Fischer, Julian

Article Title: 
A posteriori modeling error estimates for the assumption of perfect incompressibility in the NavierStokes equation

Affiliation 

Abstract: 
We derive a posteriori estimates for the modeling error caused by the assumption of perfect incompressibility in the incompressible NavierStokes equation: Real fluids are never perfectly incompressible but always feature at least some low amount of compressibility. Thus, their behavior is described by the compressible NavierStokes equation, the pressure being a steep function of the density. We rigorously estimate the difference between an approximate solution to the incompressible NavierStokes equation and any weak solution to the compressible NavierStokes equation in the sense of Lions (without assuming any additional regularity of solutions). Heuristics and numerical results suggest that our error estimates are of optimal order in the case of "wellbehaved" flows and divergencefree approximations of the velocity field. Thus, we expect our estimates to justify the idealization of fluids as perfectly incompressible also in practical situations.

Keywords: 
A posteriori estimate; Compressible fluid; Incompressible limit; Modeling error; NavierStokes equation

Journal Title:

SIAM Journal on Numerical Analysis

Volume: 
53

Issue 
5

ISSN:

10957170

Publisher:

Society for Industrial and Applied Mathematics

Date Published:

20150101

Start Page: 
2178

End Page:

2205

Sponsor: 
The research of the author was supported by the LithuanianSwiss cooperation program under the project agreement CHSMM01/0.

DOI: 
10.1137/140966654

Open access: 
no 