Towards Adaptive Grids for Atmospheric Boundary-Layer Simulations

Abstract

We present a proof-of-concept for the adaptive mesh refinement method applied to atmospheric boundary-layer simulations. Such a method may form an attractive alternative to static grids for studies on atmospheric flows that have a high degree of scale separation in space and/or time. Examples include the diurnal cycle and a convective boundary layer capped by a strong inversion. For such cases, large-eddy simulations using regular grids often have to rely on a subgrid-scale closure for the most challenging regions in the spatial and/or temporal domain. Here we analyze a flow configuration that describes the growth and subsequent decay of a convective boundary layer using direct numerical simulation (DNS). We validate the obtained results and benchmark the performance of the adaptive solver against two runs using fixed regular grids. It appears that the adaptive-mesh algorithm is able to coarsen and refine the grid dynamically whilst maintaining an accurate solution. In particular, during the initial growth of the convective boundary layer a high resolution is required compared to the subsequent stage of decaying turbulence. More specifically, the number of grid cells varies by two orders of magnitude over the course of the simulation. For this specific DNS case, the adaptive solver was not yet more efficient than the more traditional solver that is dedicated to these types of flows. However, the overall analysis shows that the method has a clear potential for numerical investigations of the most challenging atmospheric cases.

Breakup of thin liquid sheets through hole–hole and hole–rim merging

“…The incompressibility condition is satisfied using a multigrid solver described in detail in Popinet (2003Popinet ( , 2009. The calculation of the surface tension is based on the balanced-force technique (Francois et al 2006) and the mesh is refined/coarsed based on a criterion of wavelet-estimated discretization error (van Hooft et al 2018). Preliminary simulations of the hole expansion in a thin liquid sheet and the end rim retraction of a bounded liquid sheet are performed using liquid and gas properties described in table 1, which correspond to the air/water configuration.…”

A vertically-Lagrangian, non-hydrostatic, multilayer model for multiscale free-surface flows

“…The numerical schemes are implemented within the Basilisk framework [1] which provides transparent quadtree adaptivity and OpenMP/MPI parallelism for Cartesian numerical schemes. A detailed description is beyond the scope of this paper but we refer the interested reader to the web site as well as [46,47].…”

Weak formulation and scaling properties of energy fluxes in three-dimensional numerical turbulent Rayleigh–Bénard convection

“…Furthermore, in a recent work, the numerical approach has been assessed in a one-to-one comparison against a standard code also in the case of an atmospheric boundary layer. The results are satisfying in all respects and numerical dissipation appears to be ineffective, provided the resolution is sufficient to well resolve the boundary layer (van Hooft et al 2017).…”