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The solar wind is a turbulent medium with physical properties fluctuating on multiple scales. We model the three-dimensional, time-dependent solar wind plasma flow using our own software Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS), which, in addition to the thermal solar wind plasma, takes into account charge exchange of solar wind protons with interstellar neutral atoms and treats nonthermal ions (i.e., pickup ions) born during this process as a separate fluid. Additionally, MS-FLUKSS allows us to model turbulence generated by pickup ions. Using adaptive mesh refinement, we can efficiently model propagation of sophisticated structures such as coronal mass ejections at high resolution. As part of our long-term goal to build realistic time-dependent solar wind models capable of reproducing the plasma flow, magnetic field, and turbulence throughout the heliosphere, we have been experimenting with time-dependent boundary conditions derived from remote-sensing observations (e.g., interplanetary scintillation) of the solar wind and also from empirically-driven coronal model outputs. We report on the progress of these modeling efforts. In a more focused study, we used MS-FLUKSS to investigate the evolution of plasma and turbulent fluctuations along the trajectory of the New Horizons spacecraft using plasma and turbulence parameters from OMNI data as time-dependent boundary conditions at 1 AU for the Reynolds-averaged MHD equations. We compare this model with in situ plasma observations by New Horizons.