Conservative integrals of adiabatic Durran's equations

Abstract

SUMMARYPotential advances are investigated in the area of generalized anelastic approximations. Consistent controlvolume integrals are designed and compared for the established Lipps-Hemler form (of anelastic approximation) and Durran's pseudo-incompressible form. The Durran system provides a unique theoretical tool-useful for research of geophysical and stellar flows-within the existing set of reduced, Boussinesqtype fluid models. It represents thermal aspects of compressibility free of sound waves, yet the momentum equation is unapproximated. The latter admits unabbreviated baroclinic production of vorticity, thus facilitating separation of compressibility and baroclinicity effects per se. Compared with other reduced fluid models, there is little cumulative experience with integrating the Durran system. Perhaps the first conservative integrations of Durran's equations are presented, using flux-form transport methods and exact projection for the associated elliptic problem. Because the resulting code is built from a preexisting anelastic model, the consistency of the numerics is assured thus minimizing uncertainties associated with ad hoc code comparisons. While broader physical implications are addressed, theoretical considerations are illustrated with examples of atmospheric flows.

Iterated upwind schemes for gas dynamics

“…Our first implementation is an extension to compressible flows of the EUlerianLAGrangian (EULAG) model for fluids [29], established in simulation of multiscale geophysical flows [45][46][47]11,48]. Because EULAG uses continuous mappings for Cartesian grid adaptation to either curvilinear boundaries or flow features, the governing PDE (8) evinces additional complexity due to its tensorial formulation [45,49,46].…”

“…For discussions of benefits of differentiating between the reference " o "and ambient " e " states, and for examples, see [47,48,29]. The reference state assumes constant stratification S o = H −1 ln[θ e (H)/(θ e (0)], with H denoting the depth of the domain; θ o (0) = θ e (0) and ρ o (0) = ρ e (0) .…”

“…First, it facilitates designing of alternative fluid models for multiscale, multiphysics flows. Second, it minimizes uncertainties associated with ad hoc code comparisons, thus enabling unerring analysis of alternate theoretical formulations of complex fluid systems; see [38,48] for examples. cell step, but using the newly updated ψ and the antidiffusive velocity…”

On the Interpretation of Gravity Wave Measurements by Ground-Based Lidars

“…In general, EULAG owes its versatility to a unique design that combines a rigorous theoretical formulation in generalized curvilinear coordinates ( [40]) with non-oscillatory forward-in-time (NFT) differencing for fluids built on MPDATA, which is based on the convexity of upwind advection ( [34,38]) and a robust, exact-projection-type elliptic Krylov solver [34]. The flow solver has been applied to a wider range of scales simulating various problems, like boundary layer flow through complex geometries [41,42], baroclinic instability [43], gravity waves [44][45][46] or even solar convection [47]. Recently, the solver has been advanced to unstructured meshes; see [48].…”

CAM-EULAG: A non-hydrostatic atmospheric climate model with grid stretching

“…In the formulation used here and in previous global applications, nonhydrostatic behavior is obtained through the anelastic approximation. Experimental versions of EULAG are under development that use the fully compressible equations as well as other sound-proof approximations permitting nonhydrostatic flow, such as the Durran equations (Durran 2008, Smolarkiewicz andDörnbrack 2008). Future development will consider implementation of these formulations in CEU.…”