Stable and Spectrally Accurate Schemes for the Navier-Stokes Equations

Journal Article · Sat Jan 01 04:00:00 EST 2011 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/090754340· OSTI ID:1029211

Jia, Jun ^[1]; Liu, Jie ^[2]

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1. ORNL
2. University of California, Irvine

In this paper, we present an accurate, efficient and stable numerical method for the incompressible Navier-Stokes equations (NSEs). The method is based on (1) an equivalent pressure Poisson equation formulation of the NSE with proper pressure boundary conditions, which facilitates the design of high-order and stable numerical methods, and (2) the Krylov deferred correction (KDC) accelerated method of lines transpose (mbox MoL{sup T}), which is very stable, efficient, and of arbitrary order in time. Numerical tests with known exact solutions in three dimensions show that the new method is spectrally accurate in time, and a numerical order of convergence 9 was observed. Two-dimensional computational results of flow past a cylinder and flow in a bifurcated tube are also reported.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: SC USDOE - Office of Science (SC)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1029211
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 5 Vol. 33; ISSN 1064-8275; ISSN SJOCE3
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
BOUNDARY CONDITIONS
CONVERGENCE
DESIGN
DIMENSIONS
EXACT SOLUTIONS
NAVIER-STOKES EQUATIONS
POISSON EQUATION