A blended semi-implicit numerical model for weakly compressible atmospheric dynamics

摘要: 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 sound waves. The latter, despite their unimportance weather climate studies, enforce use very small time steps explicit discretizations fully compressible equations. Traditionally, problem has been analytically tackled using reduced formulations – anelastic pseudo-incompressible models scales, hydrostatic large scales lack terms generate acoustics. Alternatively, equations have solved with split-explicit or semi-implicit numerical methods free acoustic-dependent stability constraints. However, most existing approaches this context resort to various forms filtering achieve expense accuracy. The present study discusses model for simulation low-speed flows atmosphere. second-order accurate finite volume scheme extends projection method agrees it by construction small-scale limit. Unlike meteorology, are non-perturbational form thermodynamic pressure variable. Quantities advanced an advection step limited threshold independent speed. Compressibility is handled implicitly correction solves two elliptic problems increments. Well-balancing techniques used discretize buoyancy without reference hydrostatically balanced background state. Convergence properties evaluated smooth vortex compressibility effects assessed case simple acoustic wave. Then, we test ability accurately simulate gravity-driven thermal benchmarks neutrally stably stratified atmospheres. Obtained solutions found be line published work. Equations then cast blended soundproof-compressible multimodel formulation allowing controlled introduction scheme. In unified uniformly framework, blending feature employed filter perturbations initial stages simulations. technique can find application data assimilation context, enabling on-the-fly incorporation unbalanced model. The proposed extension implicit treatment envisages as flexible tool multiscale atmospheric flows.