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A C2‐continuous high‐resolution upwind convection scheme |
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| Authors: | L Corrêa GA B Lima MA C Candezano MP S Braun CM Oishi HA Navarro VG Ferreira |
| Institution: | 1. Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computa??o – USP, , S?o Carlos, SP, Brazil;2. Universidad del Atlántico, , Barranquilla, Colombia;3. Departamento de Engenharia Mecanica, Escola de Engenharia de S?o Carlos – USP, , S?o Carlos, SP, Brazil;4. Departamento de Matemática e de Computa??o, Universidade Estadual Paulista Júlio de Mesquita Filho – UNESP, , Presidente Prudente, SP, Brazil |
| Abstract: | 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. |
| Keywords: | upwind‐biased convection scheme TVD/CBC stability criteria monotonic interpolation shock‐capturing |