# Large-Eddy Simulations of Atmospheric Flows Over Complex Terrain Using the Immersed-Boundary Method in the Weather Research and Forecasting Model

## Abstract

Atmospheric flow over complex terrain, particularly recirculation flows, greatly influences wind-turbine siting, forest-fire behaviour, and trace-gas and pollutant dispersion. However, there is a large uncertainty in the simulation of flow over complex topography, which is attributable to the type of turbulence model, the subgrid-scale (SGS) turbulence parametrization, terrain-following coordinates, and numerical errors in finite-difference methods. Here, we upgrade the large-eddy simulation module within the Weather Research and Forecasting model by incorporating the immersed-boundary method into the module to improve simulations of the flow and recirculation over complex terrain. Simulations over the Bolund Hill indicate improved mean absolute speed-up errors with respect to previous studies, as well an improved simulation of the recirculation zone behind the escarpment of the hill. With regard to the SGS parametrization, the Lagrangian-averaged scale-dependent Smagorinsky model performs better than the classic Smagorinsky model in reproducing both velocity and turbulent kinetic energy. A finer grid resolution also improves the strength of the recirculation in flow simulations, with a higher horizontal grid resolution improving simulations just behind the escarpment, and a higher vertical grid resolution improving results on the lee side of the hill. Our modelling approach has broad applications for the simulation of atmospheric flows over complex topography.

### Keywords

Bolund Hill experiment Complex terrain Immersed-boundary method Large-eddy simulation Weather Research and Forecasting model## Notes

### Acknowledgements

We thank Brian Lamb, Eric Russell, Justine Missik, Zhongming Gao, and Raleigh Grysko for their comments, which greatly improved this work. We are grateful to three anonymous reviewers for their constructive suggestions, which also greatly improved the manuscript. We acknowledge support by National Science Foundation AGS under Grants #1419614. We acknowledge high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation.

### References

- Abdi DS, Bitsuamlak GT (2014) Wind flow simulations on idealized and real complex terrain using various turbulence models. Adv Eng Softw 75:30–41CrossRefGoogle Scholar
- Allen T, Brown AR (2002) Large-eddy simulation of turbulent separated flow over rough hills. Boundary-Layer Meteorol 102:177–198CrossRefGoogle Scholar
- Bechmann A, Sørensen NN (2010) Hybrid RANS/LES method for wind flow over complex terrain. Wind Energy 13:36–50CrossRefGoogle Scholar
- Bechmann A, Sørensen NN, Berg J, Mann J, Rethore PE (2011) The Bolund experiment, part II: blind comparison of microscale flow models. Boundary-Layer Meteorol 141:245–271CrossRefGoogle Scholar
- Berg J, Mann J, Bechmann A, Courtney MS, Jorgensen HE (2011) The Bolund experiment, part I: flow over a steep, three-dimensional hill. Boundary-Layer Meteorol 141:219–243CrossRefGoogle Scholar
- Bou-Zeid E, Meneveau C, Parlange M (2005) A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys Fluids 17:025105CrossRefGoogle Scholar
- Bou-Zeid E, Overney J, Rogers BD (2009) The effects of building representation and clustering in large-eddy simulations of flows in urban canopies. Boundary-Layer Meteorol 132:415–436CrossRefGoogle Scholar
- Castro FA, Palma JMLM, Lopes AS (2003) Simulation of the Askervein flow. Part 1: Reynolds averaged Navier–Stokes equations (k - \(\varepsilon \) turbulence model). Boundary-Layer Meteorol 107:501–530CrossRefGoogle Scholar
- Cavar D, Réthoré P-E, Bechmann A, Sørensen NN, Martinez B, Zahle F, Berg J, Kelly MC (2016) Comparison of OpenFOAM and EllipSys3D for neutral atmospheric flow over complex terrain. Wind Energy Sci 1:55–70CrossRefGoogle Scholar
- Chester S, Meneveau C, Parlange MB (2007) Modeling turbulent flow over fractal trees with renormalized numerical simulation. J Comput Phys 225:427–448CrossRefGoogle Scholar
- Chow FK, Moin P (2003) A further study of numerical errors in large-eddy simulations. J Comput Phys 184:366–380CrossRefGoogle Scholar
- Chow FK, Street RL (2009) Evaluation of turbulence closure models for large-eddy simulation over complex terrain: flow over Askervein hill. J Appl Meteor Climatol 48:1050–1065CrossRefGoogle Scholar
- Conan B, Chaudhari A, Aubrun S, van Beeck J, Hämäläinen J, Hellsten A (2016) Experimental and numerical modelling of flow over complex terrain: the Bolund hill. Boundary-Layer Meteorol 158:183–208CrossRefGoogle Scholar
- Deardorff JW (1980) Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorol 18:495–527CrossRefGoogle Scholar
- Diebold M, Higgins C, Fang J, Bechmann A, Parlange MB (2013) Flow over hills: a large-eddy simulation of the Bolund case. Boundary-Layer Meteorol 148:177–194CrossRefGoogle Scholar
- Ding L, Street RL (2003) Numerical study of the wake structure behind a three-dimensional hill. J Atmos Sci 60:1678–1690CrossRefGoogle Scholar
- Grinstein FF, Margolin LG, Rider WJ (eds) (2007) Implicit large eddy simulation: computing turbulent fluid dynamics. Cambridge University Press, CambridgeGoogle Scholar
- Ishihara T, Hibi K, Oikawa S (1999) A wind tunnel study of turbulent flow over a three-dimensional steep hill. J Wind Eng Ind Aerodyn 83:95–107CrossRefGoogle Scholar
- Jafari S, Chokani N, Abhari RS (2012) An immersed boundary method for simulation of wind flow over complex terrain. J Sol Energy Eng 134:011006CrossRefGoogle Scholar
- Kim HG, Patel VC (2000) Test of turbulence models for wind flow over terrain with separation and recirculation. Boundary-Layer Meteorol 94:5–21CrossRefGoogle Scholar
- Kirkil G, Mirocha J, Bou-Zeid E, Chow FK, Kosović B (2012) Implementation and evaluation of dynamic subfilter-scale stress models for large-eddy simulation using WRF. Mon Weather Rev 140:266–284CrossRefGoogle Scholar
- Klemp JB, Skamarock WC, Fuhrer O (2003) Numerical consistency of metric terms in terrain-following coordinates. Mon Weather Rev 131:1229–1239CrossRefGoogle Scholar
- Knievel JC, Bryan GH, Hacker JP (2007) Explicit numerical diffusion in the WRF model. Mon Weather Rev 135:3808–3824CrossRefGoogle Scholar
- Lange J, Mann J, Angelou N, Berg J, Sjöholm M, Mikkelsen T (2016) Variations of the wake height over the Bolund escarpment measured by a scanning lidar. Boundary-Layer Meteorol 159:147–159CrossRefGoogle Scholar
- Lateb M, Meroney RN, Yataghene M, Fellouah H, Saleh F, Boufadel MC (2016) On the use of numerical modelling for near-field pollutant dispersion in urban environments—a review. Environ Pollut 208:271–283CrossRefGoogle Scholar
- Lopes AS, Palma JMLM, Castro FA (2007) Simulation of the Askervein flow. Part 2: large-eddy simulations. Boundary-Layer Meteorol 125:85–108CrossRefGoogle Scholar
- Lund TS, Wu X, Squires KD (1998) Generation of turbulent Inflow data for spatially-developing boundary layer simulations. J Comput Phys 140:233–258CrossRefGoogle Scholar
- Lundquist KA, Chow FK, Lundquist JK (2010) An immersed boundary method for the weather research and forecasting model. Mon Weather Rev 138:796–817CrossRefGoogle Scholar
- Lundquist KA, Chow FK, Lundquist JK (2012) An immersed boundary method enabling large-eddy simulations of flow over complex terrain in the WRF model. Mon Weather Rev 140:3936–3955CrossRefGoogle Scholar
- Mason PJ, Callen NS (1986) On the magnitude of the subgrid-scale eddy coefficient in large-eddy simulations of turbulent channel flow. J Fluid Mech 162:439–462CrossRefGoogle Scholar
- Mirocha J, Kirkil G, Bou-Zeid E, Chow FK, Kosović B (2013) Transition and equilibration of neutral atmospheric boundary layer flow in one-way nested large-eddy simulations using the weather research and forecasting model. Mon Weather Rev 141:918–940CrossRefGoogle Scholar
- Mirocha J, Kosović B, Kirkil G (2014) Resolved turbulence characteristics in large-eddy simulations nested within mesoscale simulations using the weather research and forecasting model. Mon Weather Rev 142:806–831CrossRefGoogle Scholar
- Mirocha JD, Lundquist JK, Kosović B (2010) Implementation of a nonlinear subfilter turbulence stress model for large-eddy simulation in the advanced research WRF model. Mon Weather Rev 138:4212–4228CrossRefGoogle Scholar
- Mittal R, Dong H, Bozkurttas M, Najjar FM, Vargas A, von Loebbecke A (2008) A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries. J Comput Phys 227:4825–4852CrossRefGoogle Scholar
- Mittal R, Iaccarino G (2005) Immersed boundary methods. Annu Rev Fluid Mech 37:239–261CrossRefGoogle Scholar
- Moeng C-H, Dudhia J, Klemp J, Sullivan P (2007) Examining two-way grid nesting for large eddy simulation of the PBL using the WRF model. Mon Weather Rev 135:2295–2311CrossRefGoogle Scholar
- Mohd-Yusof J (1997) Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries. Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford Univ 317–327Google Scholar
- Peskin CS (1972) Flow patterns around heart valves: a numerical method. J Comput Phys 10:252–271CrossRefGoogle Scholar
- Porté-Agel F, Meneveau C, Parlange MB (2000) A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J Fluid Mech 415:261–284CrossRefGoogle Scholar
- Prospathopoulos JM, Politis ES, Chaviaropoulos PK (2012) Application of a 3D RANS solver on the complex hill of Bolund and assessment of the wind flow predictions. J Wind Eng Ind Aerodyn 107–108:149–159CrossRefGoogle Scholar
- Sadique J, Yang XIA, Meneveau C, Mittal R (2017) Aerodynamic properties of rough surfaces with high aspect-ratio roughness elements: effect of aspect ratio and arrangements. Boundary-Layer Meteorol 163:203–224Google Scholar
- Senocak I, Ackerman AS, Stevens DE, Mansour NN (2004) Topography modeling in atmospheric flows using the immersed boundary method. Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford Univ 331–341Google Scholar
- Simpson CC, Sharples JJ, Evans JP, McCabe MF (2013) Large eddy simulation of atypical wildland fire spread on leeward slopes. Int J Wild Fire 22:599–614CrossRefGoogle Scholar
- Skamarock W, Klemp J, Dudhia J, Gill D, Barker D, Duda M, Huang X, Wang W, Powers J (2008) A description of the advanced research WRF version 3. NCAR, BoulderGoogle Scholar
- Smagorinsky J (1963) General circulation experiments with the primitive equations. I. The basic experiment. Mon Weather Rev 91:99–164CrossRefGoogle Scholar
- Talbot C, Bou-Zeid E, Smith J (2012) Nested mesoscale large-eddy simulations with WRF: performance in real test cases. J Hydrometeorol 13:1421–1441CrossRefGoogle Scholar
- Tseng Y-H, Meneveau C, Parlange MB (2006) Modeling flow around bluff bodies and predicting urban dispersion using large eddy simulation. Environ Sci Technol 40:2653–2662CrossRefGoogle Scholar
- Udina M, Sun J, Kosović B, Soler MR (2016) Exploring vertical turbulence structure in neutrally and stably stratified flows using the weather research and forecasting-large-eddy simulation (WRF-LES) model. Boundary-Layer Meteorol 161:355–374CrossRefGoogle Scholar
- Vuorinen V, Chaudhari A, Keskinen JP (2015) Large-eddy simulation in a complex hill terrain enabled by a compact fractional step OpenFOAM® solver. Adv Eng Softw 79:70–80CrossRefGoogle Scholar
- Wan F, Porté-Agel F (2011) Large-eddy simulation of stably-stratified flow over a steep hill. Boundary-Layer Meteorol 138:367–384CrossRefGoogle Scholar
- Xie S, Archer C (2015) Self-similarity and turbulence characteristics of wind turbine wakes via large-eddy simulation. Wind Energy 18:1815–1838CrossRefGoogle Scholar
- Xie S, Ghaisas N, Archer CL (2015) Sensitivity issues in finite-difference large-eddy simulations of the atmospheric boundary layer with dynamic subgrid-scale models. Boundary-Layer Meteorol 157:421–445CrossRefGoogle Scholar
- Yang X, Howard KB, Guala M (2015a) Effects of a three-dimensional hill on the wake characteristics of a model wind turbine. Phys Fluids 27:025103CrossRefGoogle Scholar
- Yang XIA, Sadique J, Mittal R, Meneveau C (2015b) Integral wall model for large eddy simulations of wall-bounded turbulent flows. Phys Fluids 27:025112–33Google Scholar
- Yeow TS, Cuerva-Tejero A, Perez-Alvarez J (2015) Reproducing the Bolund experiment in wind tunnel. Wind Energy 18:153–169Google Scholar
- Zhang N, Wang X, Peng Z (2013) Large-eddy simulation of mesoscale circulations forced by inhomogeneous urban heat island. Boundary-Layer Meteorol 151:179–194CrossRefGoogle Scholar