Analysis of Upwind and High‐resolution Schemes for Solving Convection Dominated Problems in Porous Media

Starikovičius, Vadimas; Čiegis, Remigijus

doi:10.3846/13926292.2006.9637330

Cited by 5 publications

(2 citation statements)

References 11 publications

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“…This model equation describes the 1D flow of two incompressible fluids (usually water and oil) in a porous medium (the reader is referred to [44] for more details of this hyperbolic equation).…”

Section: Buckley-leverett Equationmentioning

confidence: 99%

Application of a bounded upwinding scheme to complex fluid dynamics problems

Ferreira

Kaibara

Lima

et al. 2013

Mathematical and Computer Modelling

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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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Section: Buckley-leverett Equationmentioning

confidence: 99%

Application of a bounded upwinding scheme to complex fluid dynamics problems

Ferreira

Kaibara

Lima

et al. 2013

Mathematical and Computer Modelling

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“…the regularization of the implicit Euler scheme and up-wind approximation is achieved due to numerical diffusion of non-symmetrical (only first-order accurate) discretization (see the analysis of modified differential equations in [9,17]). Thus the implicit Euler scheme automatically defines the "vanishing viscosity" solution, which is a correct physical solution.…”

Section: Computational Experiments: Implicit Euler Schemementioning

confidence: 99%

Numerical Solution of Hyperbolic Heat Conduction Equation

Čiegis

2009

Mathematical Modelling and Analysis

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Hyperbolic heat conduction problem is solved numerically. The explicit and implicit Euler schemes are constructed and investigated. It is shown that the implicit Euler scheme can be used to solve efficiently parabolic and hyperbolic heat conduction problems. This scheme is unconditionally stable for both problems. For many integration methods strong numerical oscillations are present, when the initial and boundary conditions are discontinuous for the hyperbolic problem. In order to regularize the implicit Euler scheme, a simple linear relation between time and space steps is proposed, which automatically introduces sufficient amount of numerical viscosity. Results of numerical experiments are presented.

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High-Accuracy Difference Schemes for the Nonlinear Transfer Equation

Paradzińska

Матус

2007

Mathematical Modelling and Analysis

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In the present paper, for the initial boundary value problem for the non‐homogeneous nonlinear transport equationthe basic principles for constructing difference schemes of any order of accuracy O(#GTM), M ≥ 1, on characteristic grids with the minimal stencil were introduced. To construct a difference scheme the Steklov averaging idea for the right‐hand sidewas used. The case of f(u) = λu2 was investigated in detail. A strict analysis of the order of approximation, stability, and convergence in nonlinear case was made. The performed numerical experiments justify theoretical results.

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Analysis of Upwind and High‐resolution Schemes for Solving Convection Dominated Problems in Porous Media

Cited by 5 publications

References 11 publications

Application of a bounded upwinding scheme to complex fluid dynamics problems

Application of a bounded upwinding scheme to complex fluid dynamics problems

Numerical Solution of Hyperbolic Heat Conduction Equation

High-Accuracy Difference Schemes for the Nonlinear Transfer Equation

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