We have performed simulations of the evolution of the turbulent Rayleigh–Taylor instability with an arbitrary Lagrange–Eulerian code. The problem specification was defined by Dimonte et al. (2003) for the “alpha group” code intercomparison project. Perfect γ = 5/3 gases of densities 1 and 3 g/cm3 are accelerated by constant gravity. The nominal problem uses a 2562 × 512 mesh with initial random multiwavelength interface perturbations. We have also run three-dimensional problems with smaller meshes and two-dimensional (2D) problems of several mesh sizes. Under-resolution lowered linear growth rates of the seed modes to 5-60% of the analytic values, depending on wavelength and orientation to the mesh. However, the mix extent in the 2D simulations changed little with grid refinement. Simulations without interface reconstruction gave penetration only slightly reduced from the case with interface reconstruction. Energy dissipation differs little between the two cases. The slope of the penetration distance versus time squared, corresponding to the α parameter in h = αAgt2, decreases with increasing time in these simulations. The slope, α, is consistent with the linear electric motor data of Dimonte and Schneider (2000), but the growth is delayed in time.