FAlCon-DNS (Framework of time schemes for direct numerical simulation of annular convection) solves for 2-D convection in an annulus and analyzes different time integration schemes. The framework contains a suite of IMEX, IMEXRK and RK time integration schemes. The code uses a pseudospectral method for spatial discretization. The governing equations contain both numerically stiff (diffusive) and non-stiff (advective) components for time discretization. The software offers OpenMP for parallelization.