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Third‐order‐accurate semi‐implicit Runge–Kutta scheme for incompressible Navier–Stokes equations
Author(s) -
Nikitin Nikolay
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1122
Subject(s) - tridiagonal matrix , runge–kutta methods , mathematics , navier–stokes equations , compressibility , inversion (geology) , pressure correction method , poisson's equation , scheme (mathematics) , computational fluid dynamics , operator (biology) , mathematical analysis , numerical analysis , eigenvalues and eigenvectors , physics , paleontology , biochemistry , chemistry , repressor , quantum mechanics , structural basin , biology , gene , transcription factor , thermodynamics , mechanics
A semi‐implicit three‐step Runge–Kutta scheme for the unsteady incompressible Navier–Stokes equations with third‐order accuracy in time is presented. The higher order of accuracy as compared to the existing semi‐implicit Runge–Kutta schemes is achieved due to one additional inversion of the implicit operator I ‐τγ L , which requires inversion of tridiagonal matrices when using approximate factorization method. No additional solution of the pressure‐Poisson equation or evaluation of Navier–Stokes operator is needed. The scheme is supplied with a local error estimation and time‐step control algorithm. The temporal third‐order accuracy of the scheme is proved analytically and ascertained by analysing both local and global errors in a numerical example. Copyright © 2005 John Wiley & Sons, Ltd.