Development and analysis of new numerical methods for two-fluid problems

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A new numerical scheme has been developed for two-fluid problems such as gas-liquid two-phase flows, where multiple fluids coexist. This scheme is based on the mathematical theory established in the single-fluid problem, is applicable to problems in the domain of any shape and subject to the force at the interface of fluids, and has the advantage of low computation cost since the resultant linear system is symmetric. Simulating the movement of two fluids with different densities in a container of hourglass shape by this scheme, we have realized numerically the phenomena of splitting and merging of fluids.