Analysis of a projection/characteristic scheme for incompressible flow | Zendy

Guermond JeanLuc | Zendy; Minev Peter D. | Zendy

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Analysis of a projection/characteristic scheme for incompressible flow

Author(s) -

Guermond JeanLuc,

Minev Peter D.

Publication year - 2003

Publication title -

communications in numerical methods in engineering

Language(s) - English

Resource type - Journals

eISSN - 1099-0887

pISSN - 1069-8299

DOI - 10.1002/cnm.611

Subject(s) - projection method , advection , compressibility , mathematics , convergence (economics) , scheme (mathematics) , vector field , projection (relational algebra) , divergence (linguistics) , incompressible flow , inversion (geology) , rate of convergence , grid , numerical analysis , mathematical analysis , flow (mathematics) , geometry , mathematical optimization , computer science , algorithm , mechanics , physics , dykstra's projection algorithm , geology , philosophy , channel (broadcasting) , structural basin , economic growth , computer network , linguistics , paleontology , thermodynamics , economics

The paper presents the convergence analysis of a characteristic/projection scheme for the incompressible Navier–Stokes equations. This scheme is a modification of the scheme analysed in Achdou and Guermond ( SIAM J. Numer. Anal . 2000; 37 (3):799) which does not eliminate the projected velocity field from the system but rather uses it as the advecting field in the explicit characteristic advection. This field has a zero (generalized) divergence and is therefore more suitable for this purpose. It appears that this scheme has the same convergence rate as the one in Achdou and Guermond ( SIAM J. Numer. Anal . 2000; 37 (3):799) but on a given grid seems to produce more accurate results. The computational cost is not significantly higher since it requires only one extra inversion of the mass matrix which can be done relatively efficiently. We present numerical results which illustrate the properties of the scheme. Copyright © 2003 John Wiley & Sons, Ltd.

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