Well-balanced compressible cut-cell simulation of atmospheric flow

Abstract

Cut-cell meshes present an attractive alternative to terrain-following coordinates for the representation of topography within atmospheric flow simulations, particularly in regions of steep topographic gradients. In this paper, we present an explicit twodimensional method for the numerical solution on such meshes of atmospheric flow equations including gravitational sources. This method is fully conservative and allows for time steps determined by the regular grid spacing, avoiding potential stability issues due to arbitrarily small boundary cells. We believe that the scheme is unique in that it is developed within a dimensionally split framework, in which each coordinate direction in the flow is solved independently at each time step. Other notable features of the scheme are: (i) its conceptual and practical simplicity, (ii) its flexibility with regard to the one-dimensional flux approximation scheme employed, and (iii) the well-balancing of the gravitational sources allowing for stable simulation of near-hydrostatic flows. The presented method is applied to a selection of test problems including buoyant bubble rise interacting with geometry and lee-wave generation due to topography.

Partially implicit peer methods for the compressible Euler equations

“…parts of the bubble will be computed with the full Jacobian while other parts are updated with the partial Jacobian. A detailed description of the initial conditions can be found in [11] but our setup differs a little bit from that one. There is the same warm bubble as in the first test with the same grid but the bubble is located 1 km in the left and there is no background wind.…”

ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach

“…A 1 km tall hill is added at the left side of the domain so that the resulting current overflows over the mountain. Considering moisture effects and phase changes, the moist bubble case by Bryan and Fritsch (2002) with the addition of a mid-air zeppelin (Klein et al, 2009;Jebens et al, 2011) is performed. Besides analyzing the flow field in the vicinity of the obstacles, conservation studies regarding total energy are performed for both cases.…”

“…9, but for the zeppelin and the lateral transported moist bubble test cases. duced in Klein et al (2009) andJebens et al (2011). However, their tests were carried out with the dry bubble, which was also shifted 1 km to the left.…”

Performance of the cut‐cell method of representing orography in idealized simulations

“…Subsequent analysis of a 5-day hindcast over the Himalaya region exhibited improvements in the temperature field and precipitation field (Steppeler et al, 2011(Steppeler et al, , 2013. Klein et al (2009) developed a 2D cut-cell model using directional operator splitting and the wellbalancing strategy described in Botta et al (2004) to reduce the stability constraints from small cells, showing simulations of flow over hills and bubbles interacting with a zeppelin.…”