Modeling Snr shock waves expanding through the magnetized inhomogeneous interstellar medium

We review our recent results on the MHD modeling of supernova shock waves propagating through the magnetized and inhomogeneous ISM. We explore the role of different physical processes simultaneously at work, namely magnetic-field-oriented thermal conduction, radiative cooling and MHD effects, in determining: 1) the mass and energy exchanges between different phases of the ISM and 2) the morphology of supernova remnants as observed in different bands. Our projects required an advanced 3 D MHD code for parallel computers, Flash, and high-performance computing. We discuss the results derived from the analysis of the local interaction of strong shocks with inhomogeneities of the ISM, and those derived from the analysis of the overall expansion of supernova blast waves through inhomogeneous and magnetized ISM.