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Interface modeling involves surface tension effects and topological transitions such as breakup and coalescence. In order to simulate the dynamics of interfaces as well as phase transitions, we introduce diffuse-interface modeling. This model describes the interface evolution with a high-order diffusion equation based on the van der Waals–Cahn–Hilliard theory of interfaces. Thus, unlike other methods...
High order interpolation methods improve the accuracy of semi-Lagrangian advection, however, mostly due to oscillations, only up to third order methods have been used. B-splines are known to have good qualities in terms of accuracy, resolution, and conservation and these properties improve as the order increases. However, high orders suffer from oscillations. In this paper, we propose the use of high...
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