Application of a bounded upwinding scheme to complex fluid dynamics problems

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Ferreira, V.G. and Kaibara, M.K. and Lima, G.A.B. and Silva, J.M. and Sabatini, M.H. and Mancera, P.F.A. and McKee, Sean (2013) Application of a bounded upwinding scheme to complex fluid dynamics problems. Mathematical and Computer Modelling, 57 (3-4). pp. 435-459. ISSN 0895-7177 (https://doi.org/10.1016/j.mcm.2012.06.021)

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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. 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.

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