On the stability analysis of approximate factorization methods for 3-D Euler and Navier-Stokes equations
Journal Article
·
· Numerical Heat Transfer. Part B, Fundamentals; (United States)
OSTI ID:7045322
- Old Dominion Univ., Norfolk, VA (United States). Dept. of Mechanical Engineering and Mechanics
The convergence characteristics of various approximate factorization for the 3-D Euler and Navier-Stokes equations are examined using the von Neuman stability analysis method. Three upwind difference-based factorizations and several central difference-based factorizations are considered for the Euler equations. In the upwind factorizations, both the flux-vector splitting methods of Steger and Warming and van Leer are considered. Analysis of the Navier-Stokes equations is performed only on the Beam and Warming central difference scheme. The range of CFL numbers over which each factorization is stable is presented for one-, two-, and three-dimensional flow. Also presented for each factorization is the CFL number at which the maximum eigenvalue is minimized, for all Fourier components, as well as for the high-frequency range only. The latter is useful for predicting the effectiveness of multigrid procedures with these schemes as smoothers. Further, local mode analysis is performed to test the suitability of using a uniform flow field in the stability analysis. Some inconsistencies in the results from previous analyses are resolved.
- OSTI ID:
- 7045322
- Journal Information:
- Numerical Heat Transfer. Part B, Fundamentals; (United States), Journal Name: Numerical Heat Transfer. Part B, Fundamentals; (United States) Vol. 25:1; ISSN 1040-7790; ISSN NHBFEE
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FLUID FLOW
FUNCTIONS
JACOBIAN FUNCTION
MATHEMATICAL MODELS
NAVIER-STOKES EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SENSITIVITY ANALYSIS
420400* -- Engineering-- Heat Transfer & Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FLUID FLOW
FUNCTIONS
JACOBIAN FUNCTION
MATHEMATICAL MODELS
NAVIER-STOKES EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SENSITIVITY ANALYSIS