An IMEX-DG solver for atmospheric dynamics simulations with adaptive mesh refinement

A novel Large Eddy Simulation model for the Quasi-Geostrophic equations in a Finite Volume setting

“…We use the setting from [6,20] for the thermal bubble benchmark and the setting provided in [14,47] for the density current benchmark. The setting for the inertia-gravity waves test case is taken from [23,37].…”

“…where h m is the height of the mountain, a c is the half-width, and x c is the center. We use the setting from [12,33,21] for the equilibrium test and the setting provided in [37,23] for the linear hydrostatic and non-hydrostatic mountain tests.…”

“…On the the bottom boundary, we impose an impenetrable, free-slip boundary condition, while nonreflecting boundary conditions need to be enforced on the top boundary and the lateral boundaries [37,23]. To this aim, we introduce the following forcing terms in the momentum equation ( 16) and in the potential temperature equation (19):…”

“…We set z T = 30000 m, x R = 120000 m and x S = −120000 m, which are related to the dimensions of the computational domain. Following [37], we set z B = 15000 m, x B1 = 40000 m and x B2 = −40000 m. This means that we apply the damping layer in the topmost 15 km of the domain and in the first and last 40 km along the horizontal direction. Finally, we set α v = α h1 = α h2 = 0.1.…”

“…where θ 0 = 300 K and θ c = 0.01 K. The initial velocity field is u 0 = (20, 0) m/s, while the initial density ρ 0 is computed by solving the hydrostatic balance. We consider a uniform mesh with size h = ∆x = ∆z = 250 m [23,37] and set the time step to ∆t = 1 s. For this test, we set µ a = 0, i.e, no stabilization is introduced. The CE1 solution becomes unstable and thus it is not reported, while the spatial distribution of the vertical velocity w at t = 3000 s given by CE2 and CE3 models is shown in Fig.…”