Abstract. The scalability of computational applications on current and next-generation supercomputers is increasingly limited by the cost of inter-process communication. We implement non-blocking asynchronous communication in the High-Order Methods Modeling Environment for the time integration of the hydrostatic fluid equations using both the spectral-element and discontinuous Galerkin methods. This allows the overlap of computation with communication, effectively hiding some of the costs of communication. A novel detail about our approach is that it provides some data movement to be performed during the asynchronous communication even in the absence of other computations. This method produces significant performance and scalability gains in large-scale simulations.