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AN ALGEBRAIC MULTIGRID SOLVER FOR NAVIER–STOKES PROBLEMS IN DISCRETE SECOND–ORDER APPROXIMATION
Author(s) -
WEBSTER R.
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(19960615)22:11<1103::aid-fld406>3.0.co;2-k
Subject(s) - multigrid method , polygon mesh , solver , mathematics , truncation error , convergence (economics) , navier–stokes equations , algebraic number , rate of convergence , mathematical optimization , computer science , partial differential equation , mathematical analysis , geometry , economics , channel (broadcasting) , computer network , aerospace engineering , compressibility , engineering , economic growth
An algebraic multigrid scheme is presented for solving the discrete Navier–Stokes equations to second‐order accuracy using the defect correction method. Solutions for the driven cavity and asymmetric, sudden expansion test problems have been obtained for both structured and unstructured meshes, the resolution and resolution grading being controlled by global and local mesh refinements. The solver is efficient and robust to the extent that, for problems attempted so far, no underrelaxation of variables has been required to ensure convergence. Provided that the computational mesh can resolve the flow field, convergence characteristics are almost mesh‐independent. Rates of convergence actually improve with refinement, asymptotically approaching mesh‐independent values. For extremely coarse meshes, where dispersive truncation errors would be expected to prevent convergence (or even induce divergence), solutions can still be obtained by using explicit underrelaxation in the iterative cycle.