scholarly journals On the stability of projection methods for the incompressible Navier–Stokes equations based on high-order discontinuous Galerkin discretizations

2017 ◽  
Vol 351 ◽  
pp. 392-421 ◽  
Author(s):  
Niklas Fehn ◽  
Wolfgang A. Wall ◽  
Martin Kronbichler
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Projection Methods ◽  
High Order ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Stability

INFLUENCE OF PENALIZATION AND BOUNDARY TREATMENT ON THE STABILITY AND ACCURACY OF HIGH-ORDER DISCONTINUOUS GALERKIN SCHEMES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

2013 ◽  
Vol 21 (01) ◽  
pp. 1250019
Author(s):  
ANDREAS RICHTER ◽  
EVA BRUSSIES ◽  
JÖRG STILLER
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Critical Time ◽  
High Order ◽  
Condition Numbers ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Time Step Size ◽  
Boundary Treatment

A high-order interior penalty discontinuous Galerkin method for the compressible Navier–Stokes equations is introduced, which is a modification of the scheme given by Hartmann and Houston. In this paper we investigate the influence of penalization and boundary treatment on accuracy. By observing eigenvalues and condition numbers, a lower bound for the penalization term μ was found, whereas convergence studies depict reasonable upper bounds and a linear dependence on the critical time step size. By investigating conservation properties we demonstrate that different boundary treatments influence the accuracy by several orders of magnitude, and propose reasonable strategies to improve conservation properties.

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