Application of a bounded upwinding scheme to complex fluid dynamics problems

Author(s)

Ferreira, V. G. ^[1] ; Kaibara, M. K. ^[2] ; Lima, G. A. B. ^[1] ; Silva, J. M. ^[3] ; Sabatini, M. H. ^[4] ; Mancera, P. F. A. ^[5] ; McKee, S. ^[6]

Affiliation

^[1] Univ Sao Paulo, Dept Matemat Aplicada & Estat, Inst Ciencias Matemat & Comp, Sao Carlos, SP - Brazil

^[2] Univ Fed Fluminense, Dept Matemat Aplicada, Niteroi, RJ - Brazil

^[3] Univ Fed Alfenas UNIFAL, Inst Ciencia & Tecnol, Pocos De Caldas, MG - Brazil

^[4] Univ Estadual Ctr Oeste Parana UNICTR, Dept Matemat, Guarapuava, PR - Brazil

^[5] UNESP, Inst Biociencias, Dept Bioestat, Botucatu, SP - Brazil

^[6] Univ Strathclyde, Dept Math & Stat, Glasgow, Lanark - Scotland

• Document type: Journal article
• Source: Mathematical and Computer Modelling; v. 57, n. 3-4, p. 435-459, FEB 2013.
• Web of Science Citations: 1

Abstract

This paper is concerned with an overview of upwinding schemes, and further nonlinear applications of a recently introduced high resolution upwind differencing scheme, namely the ADBQUICKEST {[}V.G. Ferreira, F.A. Kurokawa, R.A.B. Queiroz, M.K. Kaibara, C.M. Oishi, J.A. Cuminato, A.F. Castelo, M.F. Tome, S. McKee, assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems, International Journal for Numerical Methods in Fluids 60 (2009) 1-26]. The ADBQUICKEST scheme is a new TVD version of the QUICKEST {[}B.P. Leonard, A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Computer Methods in Applied Mechanics and Engineering 19 (1979) 59-98] for solving nonlinear balance laws. The scheme is based on the concept of NV and TVD formalisms and satisfies a convective boundedness criterion. The accuracy of the scheme is compared with other popularly used convective upwinding schemes (see, for example, Roe (1985) {[}19], Van Leer (1974) {[}18] and Arora \& Roe (1997) {[}17]) for solving nonlinear conservation laws (for example, Buckley-Leverett, shallow water and Euler equations). The ADBQUICKEST scheme is then used to solve six types of fluid flow problems of increasing complexity: namely, 2D aerosol filtration by fibrous filters; axisymmetric flow in a tubular membrane; 2D two-phase flow in a fluidized bed; 2D compressible Orszag-Tang MHD vortex; axisymmetric jet onto a flat surface at low Reynolds number and full 3D incompressible flows involving moving free surfaces. The numerical simulations indicate that this convective upwinding scheme is a good generic alternative for solving complex fluid dynamics problems. Crown Copyright (C) 2012 Published by Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 09/16954-8 - Computational simulation of turbulent non Newtonian fluids with free surfaces
• Grantee: Giseli Aparecida Braz de Lima
• Support Opportunities: Scholarships in Brazil - Doctorate