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It is aim of this work to develop, implement, and apply a new numerical scheme for modeling turbulent, multiphase astrophysical flows such as galaxy cluster cores and star forming regions. The method combines the capabilities of adaptive mesh refinement (AMR) and large-eddy simulations (LES) to capture localized features and to represent unresolved turbulence, respectively; it will be referred to as Fluid mEchanics with Adaptively Refined Large-Eddy SimulationS or FEARLESS.