Abstract
In this paper, we propose a spectral method for the n-dimensional Navier–Stokes equations with non-slip boundary conditions by using the divergence-free base functions. The numerical solutions fulfill the incompressibility and the physical boundary conditions automatically. In particular, we only need to evaluate the unknown coefficients of expansions of arbitrary \(n-1\) components of the velocity. These facts simplify actual computation and numerical analysis, and save computational time essentially. As the mathematical foundation of this new approach, we establish some approximation results, with which we prove the spectral accuracy in space of the suggested algorithm. Numerical results demonstrate its high efficiency and coincide the analysis very well.
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Ben-yu Guo: The work of this author is supported in part by NSF of China No. 11171227, Fund for Doctoral Authority of China No. 20123127110001, Fund for E-institute of Shanghai Universities No. E03004, and Leading Academic Discipline Project of Shanghai Municipal Education Commission No. J50101.
Yu-jian Jiao: The work of this author is supported in part by NSF of China Nos. 11171227 and 11371123, Fund for Doctoral Authority of China No. 20123127110001, and NSF of Shanghai No. 13ZR1429800.
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Guo, By., Jiao, Yj. Spectral Method For Navier–Stokes Equations With Non-slip Boundary Conditions By Using Divergence-Free Base Functions. J Sci Comput 66, 1077–1101 (2016). https://doi.org/10.1007/s10915-015-0054-z
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DOI: https://doi.org/10.1007/s10915-015-0054-z
Keywords
- Spectral method using divergence-free base functions
- Navier–Stokes equations
- Non-slip boundary conditions