This dissertation covers four topics relevant for particle-laden flow simulation and modeling. First we perform verification of three techniques for mesoscale simulation of particle-laden flows: the volume filtered Euler-Lagrange method, the two fluid model, and the anisotropic Gaussian method. We verify that statistics from Euler-Lagrange simulations of cluster-induced turbulence (CIT) can be extracted with weak parameter sensitivity. These statistics were also found to match well with CIT simulations using the anisotropic Gaussian method. Next, we use the volume filtered Euler-Lagrange method to perform simulations of homogeneous shear cluster-induced turbulence (HSCIT). We find the evolution of HSCIT to be strongly dependent on the relative orientation of shear and gravity. Third, we provide a 3-D extension to the conditional hyperbolic method of moments (CHyQMOM) for mesoscale particle-laden flows. CHyQMOM is a high order, hyperbolic closure to the kinetic moment equations. Lastly, we introduce a regression technique combining Fourier pseudospectral numerical methods and neural networks for finding nonlinear spatial operators from data.