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A CELL VERTEX ALGORITHM FOR THE INCOMPRESSIBLE NAVIER–STOKES EQUATIONS ON NON‐ORTHOGONAL GRIDS
Author(s) -
JESSEE J. P.,
FIVELAND W. A.
Publication year - 1996
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/(sici)1097-0363(19960815)23:3<271::aid-fld423>3.0.co;2-c
Subject(s) - mathematics , multigrid method , navier–stokes equations , discretization , stencil , finite volume method , solver , cartesian coordinate system , laminar flow , incompressible flow , polygon mesh , bounded function , hexahedron , mathematical analysis , compressibility , geometry , finite element method , flow (mathematics) , mathematical optimization , partial differential equation , mechanics , physics , computational science , thermodynamics
The steady, incompressible Navier–Stokes (N–S) equations are discretized using a cell vertex, finite volume method. Quadrilateral and hexahedral meshes are used to represent two‐ and three‐dimensional geometries respectively. The dependent variables include the Cartesian components of velocity and pressure. Advective fluxes are calculated using bounded, high‐resolution schemes with a deferred correction procedure to maintain a compact stencil. This treatment insures bounded, non‐oscillatory solutions while maintaining low numerical diffusion. The mass and momentum equations are solved with the projection method on a non‐staggered grid. The coupling of the pressure and velocity fields is achieved using the Rhie and Chow interpolation scheme modified to provide solutions independent of time steps or relaxation factors. An algebraic multigrid solver is used for the solution of the implicit, linearized equations. A number of test cases are anlaysed and presented. The standard benchmark cases include a lid‐driven cavity, flow through a gradual expansion and laminar flow in a three‐dimensional curved duct. Predictions are compared with data, results of other workers and with predictions from a structured, cell‐centred, control volume algorithm whenever applicable. Sensitivity of results to the advection differencing scheme is investigated by applying a number of higher‐order flux limiters: the MINMOD, MUSCL, OSHER, CLAM and SMART schemes. As expected, studies indicate that higher‐order schemes largely mitigate the diffusion effects of first‐order schemes but also shown no clear preference among the higher‐order schemes themselves with respect to accuracy. The effect of the deferred correction procedure on global convergence is discussed.