A C2-continuous high-resolution upwind convection scheme

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 functi...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2013-08, Vol.72 (12), p.1263-1285
Main Authors: Corrêa, L., Lima, G.A. B., Candezano, M.A. C., Braun, M.P. S., Oishi, C.M., Navarro, H.A., Ferreira, V.G.
Format: Article
Language:English
Subjects:
convection scheme
monotonic interpolation
shock-capturing
TVD/CBC stability criteria
upwind-biased
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Summary: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. Eight‐degree polynomial upwind scheme (EPUS) is an alternative upwind scheme for stable computation of fluid dynamics algorithms. It is a three‐point stencil for numerical flux reconstruction of class C2 and formulated by employing the convection boundedness criterion and total variation diminishing stability criteria. The advantage of the EPUS scheme is that it adopts a free parameter that can be used to control dissipation and dispersion. The EPUS scheme is simple implement in existent codes, transports scalars maintaining nonoscillatory profiles, and provides accurate solutions to complex fluid flows.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.3785