The parachute inflation process involves fluid–structure interaction problems posing several mathematical and engineering challenges, e.g. accurate aerodynamics calculations for bluff-body geometries involving with moving boundary, appropriate structural models in predicting the behavior of canopy, and realization of the coupling between the fluid and structure. These challenges attract the attention of scholars worldwide, and considerable achievements have been obtained in applying numerical methods and simulations to design multifarious parachutes. In this paper, the authors highlight the advances in the following fields: the methods suitable for time-dependent flow around bluff-body geometries, the accurate structural models in consideration of the under-constrained and no-compression nature of the canopy, and the advantages and disadvantages of different coupling algorithms in terms of numerical stability and computational economics. Moreover, in order to simulate the parachute inflation more realistically, we focus on accurate representation of three physical phenomena, as follows: an appropriate model of the flow through porous media, an accurate treatment of the wrinkling phenomenon of the canopy, and a consistent representation of the impact-contact problem associated with the inflation process. Finally, based on a review of existing literature, we offer recommendations for future research on the application of numerical methods for simulating the inflation process.
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