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Error analysis and iterative solvers for Navier–Stokes projection methods with standard and sparse grad-div stabilization
Publikationstyp
Journal Article
Date Issued
2014-06-15
Sprache
English
Institut
TORE-URI
Volume
275
Start Page
1
End Page
19
Citation
Computer Methods in Applied Mechanics and Engineering (275): 1-19 (2014)
Publisher DOI
Scopus ID
Publisher
Elsevier
This paper shows that use of a recently introduced sparse grad-div stabilization can increase the accuracy of projection methods for solving the Navier–Stokes equations. Sparse grad-div stabilization has recently been introduced as an alternative to standard grad-div stabilization which has a sparser matrix representation. For both sparse and standard grad-div stabilized projection methods, we prove error estimates and provide numerical experiments which reveal that both stabilizations can cause a significant decrease in the error. We then compare iterative solvers for the linear systems of equations arising from the use of both of the stabilizations. A theoretical analysis of a simplified model problem as well as numerical tests show that iterative solvers perform better for systems arising from sparse grad-div compared to standard grad-div stabilized systems.
Subjects
Navier–Stokes equations
Projection methods
Sparse grad-div stabilization
Mass conservation
Iterative solvers
DDC Class
510: Mathematik