Semi-Implicit Time Integration of Atmospheric Flows with Characteristic-Based Flux Partitioning

This paper presents a characteristic-based flux partitioning for the semi-implicit time integration of atmospheric flows. Nonhydrostatic models require the solution of the compressible Euler equations. The acoustic time-scale is significantly faster than the advective scale, yet it is typically not relevant to atmospheric and weather phenomena. The acoustic and advective components of the hyperbolic flux are separated in the characteristic space. High-order, conservative additive Runge-Kutta methods are applied to the partitioned equations so that the acoustic component is integrated in time implicitly with an unconditionally stable method, while the advective component is integrated explicitly. The time step of the overall algorithm is thus determined by the advective scale. Benchmark flow problems are used to demonstrate the accuracy, stability, and convergence of the proposed algorithm. The computational cost of the partitioned semi-implicit approach is compared with that of explicit time integration.