Premium
Several iterative schemes for the stationary natural convection equations at different R ayleigh numbers
Author(s) -
Huang Pengzhan,
Li Wenqiang,
Si Zhiyong
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21915
Subject(s) - discretization , mathematics , scheme (mathematics) , partial differential equation , partial derivative , natural convection , finite element method , triangulation , iterative method , mathematical analysis , convection , mathematical optimization , geometry , physics , mechanics , thermodynamics
Several iterative schemes based on finite element discretization with triangulation for solving two‐dimensional natural convection equations are studied in this article. We establish some reference points for evaluation of the possible impact from three kinds of schemes with respect to Rayleigh numbers. In case of 0 < σ < 1 4 , all schemes are stable and convergent. Moreover, in case of1 4 ≤ σ < 1 3 , Schemes I and II can run well. Finally, in case of1 3 ≤ σ < 1 , only Scheme I is still stable and convergent. Numerical experiment is presented and discussed for testing of the performances of the proposed schemes, which confirms the theoretic analysis. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 761–776, 2015