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Computer modeling is an indispensable research tool in advancing our understanding of astrophysical phenomena. With the rapid increase in both quality and quantity of astronomical data from ground-based and space-based facilities, a major challenge facing computational astrophysicists is to construct models with increasing degree of realism (in terms of physical and chemical processes, as well as source geometry) to interpret these data. The continuing advance in computer hardware and the associated increase in computing power allow the inclusion of more realistic microphysics and physico- chemical processes in the models. While many astrophysical phenomena are dominated by the collective effects of gas dynamics, there are many situations in which radiation transport, heterogeneous chemical kinetics, and gas dynamics all play an important role, making the modeling of radiative and reactive flow problems difficult. In particular, the modeling of astrophysical phenomena involving radiative, reactive, and multiphase flows not only increases the number of simultaneous processes occurring but also expands the range of both time and space scales in the problem. Counterintuitive behavior arises from the interactions of the various local, diffusive, convective, and oscillatory phenomena in the flow. Some examples are chemical and dynamical evolution of interstellar clouds involving both gas-phase and grain-surface chemistry, dust formation in radiation-driven stellar winds, and grain alignment in magnetohydrodynamic shocks. In this talk I will first review the basic concepts and computational techniques in modeling astrophysical systems involving radiation hydrodynamics, chemical kinetics, and heterogeneous components. I will describe a few selected results to demonstrate some recent progress made and identify the technical challenges that we still need to overcome.
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