The capturing of free surfaces in incompressible multi-fluid flows. (English) Zbl 0972.76067
Summary: By treating it as a contact discontinuity in the density field, a free surface between two immiscible fluids can be automatically ‘captured’ by the enforcement of conservation laws. A surface-capturing method of this kind requires no special tracking or fitting treatment for the free surface, thereby offering the advantage of algorithm simplicity over the surface-tracking or the sufface-fitting method. Here we develop a surface-capturing method based on a new multi-fluid incompressible Navier-Stokes formulation. To demonstrate the validity of the present method, it is applied to a variety of free-surface flows, including the Rayleigh-Taylor instability problem, the ship waves around a Wigley hull, and a model bubble-rising problem.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76T30 | Three or more component flows |
| 76D27 | Other free boundary flows; Hele-Shaw flows |
| 76E17 | Interfacial stability and instability in hydrodynamic stability |
Keywords:
contact discontinuity; density field; free surface; two immiscible fluids; surface-capturing method; multi-fluid incompressible Navier-Stokes formulation; Rayleigh-Taylor instability; ship waves; Wigley hull; bubble-rising problemReferences:
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