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Computer simulations play a pivotal role in studying active colloids, offering detailed microscopic insights to elucidate experimental findings and validate theoretical predictions without significant approximations. Investigating the structural and dynamic properties of active colloids in solvent environments is complex due to their out-of-equilibrium nature and the interplay of various interactions, including hydrodynamic effects. This chapter focuses on three prevalent hydrodynamic simulation techniques: Stokesian dynamics, the lattice Boltzmann method, and multiparticle collision dynamics. Each method is presented with a brief introduction, followed by examples of their applications.

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