In this paper we propose and examine numerical algorithms for coupling time-dependent multi-physics modules relevant to computer-aided engineering (CAE) of wind turbines. In particular, we examine algorithms for coupling modules where spatial grids are non- matching at interfaces and module solutions are time advanced with different time increments and different time integrators. Sharing of data between modules is accomplished with a predictor-corrector approach, which allows for either implicit or explicit time integration within each module. Algorithms are presented in a general framework, but are applied to simple problems that are representative of the systems found in a whole-turbine analysis. Numerical experiments are used to explore the stability, accuracy, and efficiency of the proposed algorithms. This work is motivated by an in-progress major revision of FAST, the National Renewable Energy Laboratory's (NREL's) premier aero-elastic CAE simulation tool. The algorithms described here will greatly increase the flexibility and efficiency of FAST.