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Implementation of some higher‐order convection schemes on non‐uniform grids
Author(s) -
Li Yuguo,
Baldacchino Lisa
Publication year - 1995
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.1650211206
Subject(s) - mathematics , grid , convection–diffusion equation , upwind scheme , scalar (mathematics) , compressibility , flow (mathematics) , interpolation (computer graphics) , quadratic equation , vector field , numerical diffusion , mathematical optimization , mathematical analysis , geometry , mechanics , classical mechanics , physics , discretization , motion (physics)
A generalized formulation is applied to implement the quadratic upstream interpolation (QUICK) scheme, the second‐order upwind (SOU) scheme and the second‐order hybrid scheme (SHYBRID) on non‐uniform grids. The implementation method is simple. The accuracy and efficiency of these higher‐order schemes on non‐uniform grids are assessed. Three well‐known bench mark convection‐diffusion problems and a fluid flow problem are revisited using non‐uniform grids. These are: (1) transport of a scalar tracer by a uniform velocity field; (2) heat transport in a recirculating flow; (3) two‐dimensional non‐linear Burgers equations; and (4) a two‐dimensional incompressible Navier‐Stokes flow which is similar to the classical lid‐driven cavity flow. The known exact solutions of the last three problems make it possible to thoroughly evaluate accuracies of various uniform and non‐uniform grids. Higher accuracy is obtained for fewer grid points on non‐uniform grids. The order of accuracy of the examined schemes is maintained for some tested problems if the distribution of non‐uniform grid points is properly chosen.