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A continuous surface tension force formulation for diffuse-interface models. (English) Zbl 1329.76103
Summary: We present a new surface tension force formulation for a diffuse-interface model, which is derived for incompressible, immiscible Navier-Stokes equations separated by free interfaces. The classical infinitely thin boundary of separation between the two immiscible fluids is replaced by a transition region of small but finite width, across which the composition of the one of two fluids changes continuously. Various versions of diffuse-interface methods have been used successfully for the numerical simulations of two phase fluid flows. These methods are robust, efficient, and capable of computing interface singularities such as merging and pinching off. But prior studies used modified surface tension force formulations, therefore it is not straightforward to calculate pressure field because pressure includes the gradient terms resulting from the modified surface tension term. The new formulation allows us to calculate the pressure field directly from the governing equations. Computational results showing the accuracy and effectiveness of the method are given for a drop deformation and Rayleigh capillary instability.

MSC:
76D45 Capillarity (surface tension) for incompressible viscous fluids
76T99 Multiphase and multicomponent flows
76E17 Interfacial stability and instability in hydrodynamic stability
76M25 Other numerical methods (fluid mechanics) (MSC2010)
Software:
PROST
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