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Multiscale modeling and simulation has been a growing interest for researchers as computational power and speed has increased. Multiscale models allow for the study of different size scales, which may be governed by different sets of physical laws. Typically, the homogenization between the different scales is done at a zero temperature. The main goal of this thesis is to develop and conduct multiscale modeling and simulation of shock wave propagation with the removal of numerical errors and inclusion of temperature effects.