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A unified numerical procedure is proposed as a solver both for compressible and incompressible fluids. The method approaches the MAC algorithm at very high sound speed and continuously approaches the algorithm for compressible fluid with decreasing sound speed. The advection term is treated by the CIP algorithm which was previously proposed and gives quite accurate and less-diffusive results. This unified procedure is tested both by one-dimensional shock-tube problem and two-dimensional cavity flow at high-Reynolds number.
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Yabe et al. (1991) studied this question.
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