A blended semi-implicit model for weakly compressible atmospheric dynamics

Tommaso Benacchio
UK Met Office, Exeter UK
Tuesday 27th January 2015
Aula Saleri presso VI Piano Dipartimento di Matematica Ed. 14 -Politecnico di Milano
Physical processes in the atmosphere develop on a wide range of spatial and temporal scales. Meteorologically relevant phenomena move at speeds much lower than that of sound waves. Despite their unimportance in weather and climate studies, the latter enforce the use of very small time steps in explicit discretizations of the fully compressible equations. Traditionally, the problem has been tackled using reduced analytical formulations -- anelastic and pseudo-incompressible models on small scales, hydrostatic models on large scales -- that lack the terms that generate acoustics. Alternatively, fully compressible equations have been solved with split-explicit or semi-implicit numerical methods free of acoustic-dependent stability constraints. However, most existing numerical approaches resort to various forms of numerical filtering to achieve stability at the expense of accuracy. We present a semi-implicit fully compressible numerical model for the simulation of low-speed atmospheric flows. The second-order accurate finite volume scheme extends a projection method for the pseudo-incompressible model and agrees with it by construction in the small-scale limit. Quantities are advanced in time in an explicit advection step limited by a stability threshold independent of sound speed, with compressibility handled implicitly in a correction step. Well-balancing techniques are used to discretize buoyancy without reference to a hydrostatically balanced background state. Equations are then cast in a blended soundproof-compressible multimodel formulation allowing for controlled introduction of compressibility in the scheme in a unified and uniformly accurate framework. Convergence properties are evaluated on the advection of a smooth vortex, while the ability of the scheme to accurately simulate gravity-driven flows with large time steps is assessed on thermal benchmarks in neutrally and stably stratified atmospheres. Then, the blending feature is employed to filter acoustic perturbations in the initial stages of thermal simulations. The technique can find application in an atmospheric data assimilation context, enabling on-the-fly incorporation of unbalanced data in the numerical model. Nota: seminario MOX (che vale anche come seminario del gruppo Fluids) Contact: luca.bonaventura@polimi.it