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A C 2 ‐continuous high‐resolution upwind convection scheme
Author(s) -
Corrêa L.,
Lima G.A. B.,
Candezano M.A. C.,
Braun M.P. S.,
Oishi C.M.,
Navarro H.A.,
Ferreira V.G.
Publication year - 2013
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.3785
Subject(s) - upwind scheme , mathematics , total variation diminishing , conservation law , nonlinear system , benchmark (surveying) , flux limiter , convergence (economics) , mathematical analysis , physics , geology , geodesy , quantum mechanics , economic growth , discretization , economics
SUMMARY A bounded upwinding scheme for numerical solution of hyperbolic conservation laws and Navier–Stokes equations is presented. The scheme is based on convection boundedness criterion and total variation diminishing stability criteria and developed by employing continuously differentiable functions. The accuracy of the scheme is verified by assessing the error and observed convergence rate on 1‐D benchmark test cases. A comparative study between the new scheme and conventional total variation diminishing/convection boundedness criterion‐based upwind schemes to solve standard nonlinear hyperbolic conservation laws is also accomplished. The scheme is then examined in the simulation of Newtonian and non‐Newtonian fluid flows of increasing complexity; a satisfactory agreement has been observed in terms of the overall behavior. Finally, the scheme is used to study the hydrodynamics of a gas‐solid flow in a bubbling fluidized bed. Copyright © 2013 John Wiley & Sons, Ltd.