부산대학교 도서관

Integration of the fully compressible non-hydrostatic equations with horizontally implicit schemes creates scalability problems for massively parallel computing architectures. An alternative is to use horizontally explicit and vertically implicit (HEVI) approaches, where the implicit problems are only along the vertical direction. Besides this, various multi-stage implicit-explicit (IMEX) methods, based on Runge-Kutta (RK) schemes, have been developed over recent years in order to achieve time discretizations free of any computational modes and possessing specified properties (accuracy-order, number of implicit iterations, amount of storage, etc.). This article compares the analytical responses of three RK-IMEX HEVI schemes (identified as attractive for atmospheric modelling), for a linear fully compressible system supporting gravity and acoustic waves as well as advection. Each scheme is analyzed in two variants, 'UFPreF' and 'UFPreB', recently proposed in the literature. The propagation of gravity waves is found to be generally well represented, but advection makes all UFPreB variants unstable; in contrast, they were more stable without advection. The instability is analyzed in a one-dimensional framework and a new class of schemes is proposed to circumvent the problem (using four Butcher tableaux, at no extra cost). A particular member of this class is examined in detail: it is shown to be accurate and stable even with advection. Some numerical testing is provided to support the analyses in a more realistic context. [ABSTRACT FROM AUTHOR]