We present two- and three-dimensional simulations involving Richtmyer–Meshkov and Rayleigh-Taylor instabilities run with the adaptive mesh refinement code, flash. Variations in the rate of mixing layer growth due to dimensionality, perturbation modes, and simulation resolution are explored. These simulations are designed for detailed comparisons with experiments run on the Omega laser to gain understanding of the mixing processes and to prepare for validation of the Flash code.