Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems

Autor(es)

Ferreira, V. G. ^[1] ; Kurokawa, F. A. ^[1] ; Queiroz, R. A. B. ^[1] ; Kaibara, M. K. ^[2] ; Oishi, C. M. ^[1] ; Cuminato, J. A. ^[1] ; Castelo, A. ^[1] ; Tome, M. F. ^[1] ; McKee, S. ^[3]

Afiliação do(s) autor(es)

^[1] USP, Inst Ciencias Matemat & Computacao, Dept Matemat Aplicada & Estatist, BR-13560970 Sao Carlos, SP - Brazil

^[2] UNESP, Fac Ciencias, Dept Matemat, Bauru, SP - Brazil

^[3] Univ Strathclyde, Dept Math, Glasgow, Lanark - Scotland

• Tipo de documento: Artigo Científico
• Fonte: International Journal for Numerical Methods in Fluids; v. 60, n. 1, p. 1-26, MAY 10 2009.
• Citações Web of Science: 19

Resumo

This article deals with the Study of the development and application of the high-order upwind ADBQUICKEST scheme, an adaptative bounded version of the QUICKEST for unsteady problems (Commun. Numer Meth. Engng 2007; 23:419-445), employing both linear and nonlinear convection term discretization. This scheme is applicable to a wide range of computational fluid dynamics problems, where transport phenomena are of special importance. In particular, the performance of the scheme is assessed through an extensive numerical simulation study of advection-diffusion problems. The scheme, implemented in the context of finite difference methodology, combines a good approximation of shocks (or discontinuities) with a good approximation of the smooth parts of the solutions. In order to assess the performance of the scheme, seven problems are solved, namely (a) advection of scalars; (b) non-linear viscous Burgers equation; (c) Euler equations of gas dynamics; (d) Newtonian flow in a channel; (e) axisymmetric Newtonian jet flow; (f) axisymnietric non-Newtonian (generalized Newtonian) flow in a pipe; and (g) collapse of a fluid column. The numerical experiments clearly show that the scheme provides more consistent solutions than those found in the literature. From the study, the flexibility and robustness of the ADBQUICKEST scheme is confirmed by demonstrating its capability to solve a variety of linear and nonlinear problems with and without discontinuous solutions. Copyright (C) 2008 John Wiley \& Sons, Ltd. (AU)

• Processo FAPESP: 06/05910-1 - Simulacao computacional das equacoes de navier stokes incompressiveis em qualquer regime do numero de reynolds.
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