scholarly journals Entropy-stable p-nonconforming discretizations with the summation-by-parts property for the compressible Navier–Stokes equations

2020 ◽  
Vol 210 ◽  
pp. 104631 ◽  
Author(s):  
David C. Del Rey Fernández ◽  
Mark H. Carpenter ◽  
Lisandro Dalcin ◽  
Lucas Fredrich ◽  
Andrew R. Winters ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Summation By Parts ◽  
Entropy Stable

scholarly journals Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces

2014 ◽  
Vol 36 (5) ◽  
pp. B835-B867 ◽  
Author(s):  
Mark H. Carpenter ◽  
Travis C. Fisher ◽  
Eric J. Nielsen ◽  
Steven H. Frankel
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Spectral Collocation ◽  
Navier Stokes Equations ◽  
Entropy Stable

scholarly journals Entropy stable spectral collocation schemes for the 3-D Navier-Stokes equations on dynamic unstructured grids

2019 ◽  
Vol 399 ◽  
pp. 108897 ◽  
Author(s):  
Nail K. Yamaleev ◽  
David C. Del Rey Fernández ◽  
Jialin Lou ◽  
Mark H. Carpenter
Keyword(s):  
Stokes Equations ◽  
Unstructured Grids ◽  
Navier Stokes ◽  
Spectral Collocation ◽  
Navier Stokes Equations ◽  
Entropy Stable

ENTROPY STABLE APPROXIMATIONS OF NAVIER–STOKES EQUATIONS WITH NO ARTIFICIAL NUMERICAL VISCOSITY

2006 ◽  
Vol 03 (03) ◽  
pp. 529-559 ◽  
Author(s):  
EITAN TADMOR ◽  
WEIGANG ZHONG
Keyword(s):  
Heat Conduction ◽  
Stokes Equations ◽  
Heat Fluxes ◽  
Difference Schemes ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
New Family ◽  
Entropy Dissipation ◽  
Numerical Viscosity ◽  
Entropy Stable

We construct a new family of entropy stable difference schemes which retain the precise entropy decay of the Navier–Stokes equations, [Formula: see text] To this end we employ the entropy conservative differences of [24] to discretize Euler convective fluxes, and centered differences to discretize the dissipative fluxes of viscosity and heat conduction. The resulting difference schemes contain no artificial numerical viscosity in the sense that their entropy dissipation is dictated solely by viscous and heat fluxes. Numerical experiments provide a remarkable evidence for the different roles of viscosity and heat conduction in forming sharp monotone profiles in the immediate neighborhoods of shocks and contacts.

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