Evaluating Implementations of the Immersed Boundary Method in the Weather Research and Forecasting Model

Abstract

The terrain-following coordinate system used by many atmospheric models can cause numerical instabilities due to discretization errors as resolved terrain slopes increase and the grid becomes highly skewed. The immersed boundary (IB) method, which does not require the grid to conform to the terrain, has been shown to alleviate these errors, and has been used successfully for high-resolution atmospheric simulations over steep terrain, including vertical building surfaces. Since many previous applications of IB methods to atmospheric models have used very fine grid resolution (5 m or less), the present study seeks to evaluate IB method performance over a range of grid resolutions and aspect ratios. Two classes of IB algorithms, velocity reconstruction and shear stress reconstruction, are tested within the common framework of the Weather Research and Forecasting (WRF) Model. Performance is evaluated in two test cases, one with flat terrain and the other with the topography of Askervein Hill, both under neutrally stratified conditions. WRF-IB results are compared to similarity theory, observations, and native WRF results. Despite sensitivity to the location at which the IB intersects the model grid, the velocity reconstruction IB method shows consistent performance when used with a hybrid RANS/LES surface scheme. The shear stress reconstruction IB method is not sensitive to the grid intersection, but is less consistent and near-surface velocity errors can occur at coarse resolutions. This study represents an initial investigation of IB method variability across grid resolutions in WRF. Future work will focus on improving IB method performance at intermediate to coarse resolutions.

Boundary-Layer Flow Over Complex Topography

“…The advent of grid nesting capabilities has enabled many larger-scale numerical modelling codes to now refine their meshes sufficiently to include an LES-mode in the innermost domain (e.g., Chow et al 2006;Golaz et al, 2009). While the idea of nesting an LES within a larger-scale model might seem straightforward, doing so accurately remains an ongoing challenge (e.g., Wyngaard, 2004;Talbot et al, 2012;Muñoz-Esparza et al, 2014;Shin and Hong, 2015;Honnert, 2016;Rai et al, 2016;Muñoz-Esparza et al, 2017;Bao et al, 2018;Muñoz-Esparza and Kosovic, 2018;Hald et al, 2019;Arthur et al, 2020). Indeed, Cuxart (2015) argues for a more stringent definition rather than simply describing this style of calculation as LES.…”