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On the theory and computation of surface tension: the elimination of parasitic currents through energy conservation in the second-gradient method. (English) Zbl 1058.76597

Summary: Errors in the computation of fluid flows with surface tension are examined. These errors cause large parasitic flows when the capillary number is large, and have often been attributed to truncation error in underresolved interfacial regions. A study using the second-gradient method reveals that when truncation error is eliminated in the computation of energy exchanges between surface and kinetic energies so that the energy is strictly conserved, and the parasitic currents are reduced to round-off. The results are based on general thermodynamic arguments and can be used to guide improvements in other methods, such as the continuum-surface-force method, which is commonly used with the volume-of-fluid method.

MSC:

76M99 Basic methods in fluid mechanics
76A05 Non-Newtonian fluids
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