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The magnetorheological fluids are classified as smart materials with controllable rheological properties. The fast growing application of magnetorheological fluids in recent years has increased the demand for simulation and modeling of these fluids. From the invention of magnetorheological fluids up to now, many experimental and also theoretical investigations have been carried out to study these types of smart materials; also many attempts have been made to formulate and simulate their behavior. The aim of this investigation is to present a review on the different models and simulation methods that were applied in the studying of magnetorheological fluids. In this study, the different simulation methods of magnetorheological fluid have been categorized into two general approaches: continuum and discrete phase approaches. The different rheological and structural models of magnetorheological fluids in continuum approach have been summarized in this study. The computational framework of discrete approach and the basic models for magnetorheological fluid in this approach are also discussed.

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