Numerical models of surface tension play an increasingly important role in our capacity to understand and predict a wide range of multiphase flow problems. The accuracy and robustness of these models have improved markedly in the past 20 years, so that they are now applicable to complex, three-dimensional configurations of great theoretical and practical interest. In this review, I attempt to summarize the most significant recent developments in Eulerian surface tension models, with an emphasis on well-balanced estimation, curvature estimation, stability, and implicit time stepping, as well as test cases and applications. The advantages and limitations of various models are discussed, with a focus on common features rather than differences. Several avenues for further progress are suggested.


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