A regularization approach for a vertical‐slice model and semi‐Lagrangian Störmer–Verlet time stepping

Abstract

ABSTRACT:In this paper, we provide a systematic derivation of regularized equations for a non-hydrostatic and compressible vertical-slice model of the dry atmosphere. The derivation is based on an analysis of a semi-implicit discretization of the equations of motion and a recent regularized formulation is obtained as a special case. An implementation of the regularized equations, using a recent second-order, centred-in-time, two-time-level semi-Lagrangian Störmer-Verlet method, is discussed and a series of numerical experiments is conducted.

An inherently mass‐conserving iterative semi‐implicit semi‐Lagrangian discretization of the non‐hydrostatic vertical‐slice equations

“…Figures 1(c) and 2(c)) models both give visually indistinguishable results for both hydrostatic and non-hydrostatic flow regimes. These results are in good agreement with other published results (see, for example, Hundertmark and Reich (2007) and the standard test set documentation). Figure 1(d) shows the result of applying the hydrostatic switch (δ V = 0) in the mass-conserving model to the case of the hydrostatic flow regime.…”

“…Skamarock and Klemp (1994) present solutions of a Boussinesq model, for both hydrostatic and nonhydrostatic flow regimes, and find good agreement between numerical and linear analytic solutions. Simulations of the full compressible equation set are presented in Hundertmark and Reich (2007), and also in the standard test documentation (available on the website given above) for the WRF and ARPS models. Whilst there are some differences in the solutions of the compressible equation set, most noticeably in the ARPS results, the overall agreement between models is good.…”

A framework for testing global non‐hydrostatic models

“…With the emergence of nonhydrostatic dynamical cores, this testing framework has been extended to reference simulations with vertical slice models of the proposed three-dimensional model, e.g. Hundertmark and Reich (2007). Thus initial tests proposed for global non-hydrostatic models are typically set for two-dimensional or limited-area domains.…”