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Study of the mixed finite volume method for Stokes and Navier‐Stokes equations
Author(s) -
Droniou Jérôme,
Eymard Robert
Publication year - 2009
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.20333
Subject(s) - finite volume method , navier–stokes equations , orthogonality , mathematics , stokes problem , mathematical analysis , dimension (graph theory) , partial differential equation , grid , convergence (economics) , unstructured grid , finite volume method for one dimensional steady state diffusion , non dimensionalization and scaling of the navier–stokes equations , space (punctuation) , stokes flow , numerical partial differential equations , finite element method , physics , compressibility , geometry , computer science , mechanics , pure mathematics , flow (mathematics) , economics , thermodynamics , economic growth , operating system
We present finite volume schemes for Stokes and Navier‐Stokes equations. These schemes are based on the mixed finite volume introduced in (Droniou and Eymard, Numer Math 105 (2006), 35‐71), and can be applied to any type of grid (without “orthogonality” assumptions as for classical finite volume methods) and in any space dimension. We present numerical results on some irregular grids, and we prove, for both Stokes and Navier‐Stokes equations, the convergence of the scheme toward a solution of the continuous problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009