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Application of a bounded upwinding scheme to complex fluid dynamics problems
  • Universidade de São Paulo (USP)
  • Universidade Federal Fluminense (UFF)
  • Universidade Federal de Alfenas (UNIFAL)
  • Universidade Estadual do Centro Oeste (UNICENTRO)
  • Universidade Estadual Paulista (UNESP)
  • University of Strathclyde
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. Tomé, 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. © 2012.
Issue Date: 
Mathematical and Computer Modelling, v. 57, n. 3-4, p. 435-459, 2013.
Time Duration: 
  • Advective transport
  • Boundedness
  • CBC/TVD stability
  • Convection modeling
  • Flux limiter
  • Free surface flows
  • High resolution
  • Monotonic interpolation
  • Normalized variables
  • Upwinding
  • Flux limiters
  • Free-surface flow
  • Computational fluid dynamics
  • Crystallography
  • Euler equations
  • Fluidized beds
  • Incompressible flow
  • Interpolation
  • Liquids
  • Microfiltration
  • Reynolds number
  • Two dimensional
  • Magnetohydrodynamics
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Appears in Collections:Artigos, TCCs, Teses e Dissertações da Unesp

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