A front tracking method applied to Burgers' equation and two-phase porous flow

Lötstedt, Per

doi:10.1016/0021-9991(82)90075-4

Cited by 21 publications

(5 citation statements)

References 14 publications

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“…One of the first methods is known as the SLIC method (Simple Line Interface Calculation) [6], with several extensions and improvements [11][12][13][14], and can be interpreted as relying on an explicit Lagrangian advection of reconstructed interface segments. The basic idea of these schemes is that a predefined set of rules based on volume fraction values of the neighbouring cells is used to reconstruct the fluid distribution for a cell.…”

Section: Introductionmentioning

confidence: 99%

A Method for Capturing Sharp Fluid Interfaces on Arbitrary Meshes

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1999

Journal of Computational Physics

671

438

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Section: Introductionmentioning

confidence: 99%

A Method for Capturing Sharp Fluid Interfaces on Arbitrary Meshes

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Issa

1999

Journal of Computational Physics

671

438

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“…Compared to single-phase numerical solutions, interface tracking and the treatment of surface tension are the two main additional problems to address when modelling and computing gas/liquid flows with evolving interfaces (Scardovelli & Zaleski 1999). Localizing the interfaces, applying correctly the stress balances at them and computing their evolution can be achieved using either moving grids (Hirt, Amsdem & Cook 1974;Fritts & Boris 1979;Harten & Hyman 1983;Hyman 1983Hyman , 1984Ryskin & Leal 1984;Cristini, Blawzdziewics & Lowenberg 1998) or fixed ones (Hirt & Nichols 1981;Lötstedt 1982;Ashgriz & Poo 1991;Lafaurie et al 1994;Mashayek & Ashgriz 1995;Zaleski 1996;Chen et al 1999). Additionally, scalar markers (Hirt & Nichols 1981;Zaleski 1996) as well as particle tracers (Welch et al 1966;Nichols & Hirt 1975;Glimm, Marchesin & McBryan 1981) can be employed; while Welch et al (1966) distribute the particles within the whole volume to be traced, Nichols & Hirt (1975) and Glimm et al (1981) place the particles on the surface to be tracked.…”

Section: Introductionmentioning

confidence: 99%

Very-near-field dynamics in the injection of two-dimensional gas jets and thin liquid sheets between two parallel high-speed gas streams

2004

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A numerical investigation of the velocity, pressure and vorticity fields very near the injection of flat and thin two-dimensional gas jets or liquid sheets between two parallel high-speed gas coflows is performed. The motivation of this research is to uncover some basic physical mechanisms underlying twin-fluid atomization. Conservation equations and boundary and initial conditions are presented for both single-phase jets and two-phase liquid sheet/gas-stream systems. Both infinitely thin and thick solid walls are considered. Apart from the gas Strouhal and Reynolds numbers appearing in the dimensionless single-phase flow equations, the liquid Reynolds number, the momentum flux ratio, the gas/liquid velocity ratio and the Weber number enter the two-phase flow dimensionless formulation. The classical numerical techniques for single-phase jets are supplemented with the volume-of-fluid (VOF) method for interface tracking and the continuum surface force (CSF) method to include surface tension in two-phase flow systems. Ad hoc convection algorithms in combination with a developed version of the fractional-step scheme allows a significant reduction of the numerical diffusion, maintaining localized and sharp interfaces. The action of the surface tension is correctly found via the CSF with a smoothed scalar-field approximation.Results for single-phase jets with thin-wall injectors indicate qualitatively correct features and trends when varying the Reynolds number and the coflow/jet ratios: thick-wall injectors significantly modify the vorticity and pressure near fields; increasing the Reynolds number leads to larger flow disturbances; larger coflow/jet velocity ratios yield more perturbed near flow fields. For single-phase jets the Strouhal number as a function of the Reynolds number follows the usual trends of flows behind a circular cylinder.For two-phase flows, increasing the gas Reynolds number leads to larger liquid-sheet deformations and to a reduction of the breakup length; a plot of the gas Strouhal number, in the presence of a liquid sheet, as a function of the gas Reynolds number displays a monotonically decreasing curve, contrary to that for a gas jet. This observation strongly suggests that the gas vortex shedding mechanism is modified by the liquid-sheet motion. The gas vortex shedding frequency as a function of the liquid-sheet oscillation frequency follows a straight line with a slope of approximately $45^{\circ}$ for momentum flux ratios greater than roughly 0.45; for values below 0.45 the gas vortex shedding frequency remains constant while the liquid sheet varies its oscillation frequency. Increasing the surface tension leads to a larger breakup length. Thin trailing edges almost double the sheet oscillation frequency and more than halve the perturbation wavelength compared to thick trailing edges.

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“…The two-wave Roe matrix approximation, is constructed using the least expensive possibilities, namely the diagonal where A is the unique Roe matrix given in (12). We call this method 2G.…”

Section: -mentioning

confidence: 99%