NDLI: Spectral Method for Navier–Stokes Equations with Slip Boundary Conditions

Content Provider	Springer Nature Link
Author	Guo, Ben yu Jiao, Yu jian
Copyright Year	2013
Abstract	In this paper, we propose a spectral method for the $$n$$ -dimensional Navier–Stokes equations with slip boundary conditions by using divergence-free base functions. The numerical solutions fulfill the incompressibility and the physical boundary conditions automatically. Therefore, we need neither the artificial compressibility method nor the projection method. Moreover, we only have to evaluate the unknown coefficients of expansions of $$n-1$$ components of the velocity. These facts simplify actual computation and numerical analysis essentially, and also save computational time. As the mathematical foundation of this new approach, we establish some approximation results, with which we prove the spectral accuracy in space of the proposed algorithm. Numerical results demonstrate its high efficiency and coincide the analysis very well. The main idea, the approximation results and the techniques developed in this paper are also applicable to numerical simulations of other problems with divergence-free solutions, such as certain partial differential equations describing electro-magnetic fields.
Starting Page	249
Ending Page	274
Page Count	26
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	58
Issue Number	1
e-ISSN	15737691
Language	English
Publisher	Springer US
Publisher Date	2013-05-25
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Spectral method Navier–Stokes equations Slip boundary conditions Spectral, collocation and related methods Approximation by polynomials Navier-Stokes equations Algorithms Computational Mathematics and Numerical Analysis ApplicationMathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis Software

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