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Abstract
An Eulerian method to numerically solve incompressible bifluid problems with high density ratio is presented. This method can be considered as an improvement of the Ghost Fluid method, with the specificity of a sharp second-order numerical scheme for the spatial resolution of the discontinuous elliptic problem for the pressure. The Navier–Stokes equations are integrated in time with a fractional step method based on the Chorin scheme and discretized in space on a Cartesian mesh. The bifluid interface is implicitly represented using a level-set function. The advantage of this method is its simplicity to implement in a standard monofluid Navier–Stokes solver while being more accurate and conservative than other simple classical bifluid methods. The numerical tests highlight the improvements obtained with this sharp method compared to the reference standard first-order methods.
Highlights
We have developed a new method on Cartesian grids for the simulation of incompressible flows with large density ratios
This method relies on a sharp resolution of the pressure term across the interface defined by a level-set function
The advantage of the proposed approach is its simplicity to implement in an existing Cartesian monofluid Navier–Stokes solver as for instance the Ghost Fluid or CSF methods
Summary
Bifluid problems are ubiquitous in nature and in many industrial applications such as combustion in engines, water waves energy converters, and jet printers to cite only a few. In such applications, the density ratio between the two fluids can be large, for instance the ratio is equal to 1000 between water and air. In this paper we are concerned with the numerical modeling of incompressible bifluid flows with large density ratios, like air and water, and by the accurate description of the phenomena occurring at their interface. This method is an extension of the second-order Cartesian method for elliptic problems with immersed interfaces developed in [1]
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