The potential for laser-produced plasmas to yield fundamental insights into high energy density physics (HEDP) and deliver other useful applications can sometimes be frustrated by uncertainties in modeling the properties and expansion of these plasmas using radiation-hydrodynamics codes. In an effort to overcome this and to corroborate the accuracy of the HEDP capabilities recently added to the publicly available FLASH radiation-hydrodynamics code, we present detailed comparisons of FLASH results to new and previously published results from the HYDRA code used extensively at Lawrence Livermore National Laboratory. We focus on two very different problems of interest: (1) an Aluminum slab irradiated by 15.3 and 76.7 mJ of "pre-pulse" laser energy and (2) a mm-long triangular groove cut in an Aluminum target irradiated by a rectangular laser beam. Because this latter problem bears a resemblance to astrophysical jets, Grava et al., Phys. Rev. E, 78, (2008) performed this experiment and compared detailed x-ray interferometric measurements of electron number densities to HYDRA simulations. Thus, the former problem provides an opportunity for code-to-code comparison, while the latter provides an opportunity for both code-to-code comparison and validation. Despite radically different schemes for determining the computational mesh, and different equation of state and opacity models, the HYDRA and FLASH codes yield results that are in excellent agreement for both problems and with the experimental data for the latter. Having validated the FLASH code in this way, we use the code to further investigate the formation of the jet seen in the Grava et al. (2008) experiment and discuss its relation to the Wan et al. (1997) experiment at the NOVA laser.