Flux-corrected transport II: Generalizations of the method

Book, D. L.; Boris, J. P.; Hain, K.

doi:10.1016/0021-9991(75)90002-9

Cited by 501 publications

(180 citation statements)

References 4 publications

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“…Flux-Corrected-Transport (FCT) it Method first adds a sufficient positive dissipation to the numerical solution so as to suppress instabilities associated with shocks, and then exerts an adequate negative dissipation to compensate for numerical errors introduced by the positive dissipation so as to raise the accuracy and the resolution of shock calculation. The FCT method was first developed by Boris and Book [Boris and Book, 1973;Book et al, 1975;Boris and Book, 1976] Zalesak [1979]. With the FCT method, the shock layer thickness may reduce to 2-3 spatial meshes.…”

Section: Numerical Techniques In the Treatment Of Shocksmentioning

confidence: 99%

Numerical Modelling of Shock Waves in the Solar Wind

1996

International Astronomical Union Colloquium

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Abstract. This review briefly surveys some recent progress in the numerical simulation study of magnetohydrodynamic (MHD) shock waves in the solar wind. STANDING SHOCKS IN STEADY SOLAR W I N DIn order to accelerate the solar wind it is necessary to add energy or momentum to it. The energy or momentum addition creates more than one critical points, resulting in discontinuous solar wind solutions involving standing shocks [Holzer, 1977]. In terms of an isothermal model, Habbal and Tsinganos [1983] showed that multiple transonic solutions may exist for a given set of coronal base parameters owing to the presence of multiple critical points. One of these solutions is continuous while the others are all discontinuous, containing one or more standing shocks. Habbal and Rosner [1984] further examined the temporal evolution of an isothermal solar wind from one steady state to another under the action of momentum addition, and concluded that the pattern of the final steady state depends on the amplitude and the rate of momentum addition. This conclusion also holds for the polytropic solar wind [Habbal 1985]. Using a two-fluid model, Habbal et al. [1994] found a solar wind solution with two standing shocks. These studies indicate that solar winds with standing shocks are not only allowed by the steady state equations, but also physically accessible and stable. The presence of standing shocks bring about a remarkable change of the inner solar wind structure, which could be observationally detected [Esser and Habbal, 1990]. The transversal nonuniformity of the interplanetary magnetic field provides another physical basis for the formation of standing shocks. Whang [1982, 1986] suggested that a slow shock develops at the inner edge of the heliospheric current sheet and extends polewards to form a close surface around the Sun, and showed a typical solar wind solution with the close slow shock. If the prediction of discontinuous solar winds turns out to be confirmed by future observations, it will certainly bring about a revolution in the solar wind theory.A great upsurge in the study of the heliospheric boundary started several years ago and has since maintained since one or more of the deep space

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Section: Numerical Techniques In the Treatment Of Shocksmentioning

confidence: 99%

Numerical Modelling of Shock Waves in the Solar Wind

1996

International Astronomical Union Colloquium

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“…The extension of this technique to non-orthogonal grid cases results in a complex pressure correction equation (Peric, 1990). For calculating the fluxes through the element interface, research has focused on developing and solving the flow equations with high-resolution schemes, which include the total variation diminishing (TVD) schemes of Harten (1983), the flux-corrected transport (FCT) methods of Boris and Book (1973), Book et al (1975), Zalesak (1979) and Scott et al (1999) the switches and cell-averaged piecewise fits utilized in the piecewise parabolic method of Collela and Woodward(1984), and the essentially non-oscillatory (ENO) schemes of Harten and Osher (1987), Osher and Solomone (1982) and Shu and Osher (1988). Applications also show that the scheme of Roe (1981) meets the requirement of high accuracy and computational efficiency (Ye and McCorquodale, 1996).…”

Section: Introductionmentioning

confidence: 99%

Simulating the hydraulic characteristics of the lower Yellow River by the finite‐volume technique

Wan

Zhou

et al. 2002

Hydrological Processes

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Abstract:The finite-volume technique is used to solve the two-dimensional shallow-water equations on unstructured mesh consisting of quadrilateral elements. In this paper the algorithm of the finite-volume method is discussed in detail and particular attention is paid to accurately representing the complex irregular computational domain. The lower Yellow River reach from Huayuankou to Jiahetan is a typical meandering river. The generation of the computational mesh, which is used to simulate the flood, is affected by the distribution of water works in the river channel. The spatial information about the two Yellow River levee, the protecting dykes, and those roads that are obviously higher than the ground, need to be used to generate the computational mesh. As a result these dykes and roads locate the element interfaces of the computational mesh. In the model the finite-volume method is used to solve the shallow-wave equations, and the Osher scheme of the empirical function is used to calculate the flux through the interface between the neighbouring elements. The finite-volume method has the advantage of using computational domain with complex geometry, and the Osher scheme is a method based on characteristic theory and is a monotone upwind numerical scheme with high resolution. The flood event with peak discharge of 15 300 m 3 /s, occurring in the period from 30 July to 10 August 1982, is simulated. The estimated result indicates that the simulation method is good for routing the flood in a region with complex geometry.

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“…In addition to the merits of FCT in handling the steep gradient, it also acts to stabilize the calculation, which is essential in the simulation, especially from sub-Alfv6nic and subsonic regions to super-Alfv6nic and supersonic regions. Thus artificial diffusion appears unavoidably in the numerical procedure, although in the area where there are no steep gradients, the additional artificial diffusion is canceled out by the so-called antidiffusion [Book et al, 1975]. In the area of the neutral current sheet, which does appear in the numerical results, which display large neutral sheet current after the disturbance, this kind of diffusion must be constrained to be as small as possible, while numerically it is unavoidable.…”

Section: Introductionmentioning

confidence: 99%

The simulation of the coronal mass ejection‐shock system in the inner corona

Zhang¹,

Wang²

2000

J. Geophys. Res.

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Abstract. In the concept that coronal mass ejections (CME) are usually originated in large closed magnetic field regions which are found in the coronal streamer belt near the solar surface, we have used a thermal driving force so strong that portions of the closed magnetic fields were carried away by tl•e strong disturbance. A CME-shock system is obtained in the im•er corona. The "legs" of loop-like CMEs are again obtained at the interface between the coronal open and closed magnetic fields. However, there is no counterpart in outer space. The shock is a combined one with an intermediate shock near the equator at its early stage. Ultimately, it becmnes a pure fast shock. A plasmoid with higher density and bubble-like magnetic fields is formed behind the MHD shock wave. It propagates at high speed. The results show that the high-speed plasmoid does not propel the MHD shock in front of it; rather, the plasmoid forms behind the MHD shock.

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Flux-corrected transport II: Generalizations of the method

Cited by 501 publications

References 4 publications

Numerical Modelling of Shock Waves in the Solar Wind

Numerical Modelling of Shock Waves in the Solar Wind

Simulating the hydraulic characteristics of the lower Yellow River by the finite‐volume technique

The simulation of the coronal mass ejection‐shock system in the inner corona

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