Intercomparison of terrain-following coordinate transformation and immersed boundary methods in large-eddy simulation of wind fields over complex terrain

Abstract

Abstract. Accurate modeling of complex terrain, especially steep terrain, in the simulation of wind fields remains a challenge. It is well known that the terrain-following coordinate transformation method (TFCT) generally used in atmospheric flow simulations is restricted to non-steep terrain with slope angles less than 45 degrees. Due to the advantage of keeping the basic computational grids and numerical schemes unchanged, the immersed boundary method (IBM) has been widely implemented in various numerical codes to handle arbitrary domain geometry including steep terrain. However, IBM could introduce considerable implementation errors in wall modeling through various interpolations because an immersed boundary is generally not co-located with a grid line. In this paper, we perform an intercomparison of TFCT and IBM in large-eddy simulation of a turbulent wind field over a three-dimensional (3D) hill for the purpose of evaluating the implementation errors in IBM. The slopes of the three-dimensional hill are not steep and, therefore, TFCT can be applied. Since TFCT is free from interpolation-induced implementation errors in wall modeling, its results can serve as a reference for the evaluation so that the influence of errors from wall models themselves can be excluded. For TFCT, a new algorithm for solving the pressure Poisson equation in the transformed coordinate system is proposed and first validated for a laminar flow over periodic two-dimensional hills by comparing with a benchmark solution. For the turbulent flow over the 3D hill, the wind-tunnel measurements used for validation contain both vertical and horizontal profiles of mean velocities and variances, thus allowing an in-depth comparison of the numerical models. In this case, TFCT is expected to be preferable to IBM. This is confirmed by the presented results of comparison. It is shown that the implementation errors in IBM lead to large discrepancies between the results obtained by TFCT and IBM near the surface. The effects of different schemes used to implement wall boundary conditions in IBM are studied. The source of errors and possible ways to improve the IBM implementation are discussed.

Wall modeled immersed boundary method for high Reynolds number flow over complex terrain

“…The centre of the hill is located at x/L x = 1/4 and y/L y = 1/2. The roughness height of the hill surface is z 0,IB = 2z 0 , see also Fang and Porté-Agel [32]. Figures 9 and 10 show that the vertical profiles of (…”

“…The figure shows that the agreement at z/h = 1 is also very good and that the maximum difference of the velocity and turbulence intensity obtained from the high resolution simulation and the experiments is only about 5% and 15%, respectively. We note that the simulations somewhat underestimate the velocity close to the ground (z/h = 0.125) [19,32]. The reason is that the large-eddy simulation in which the wall effect is modeled is less accurate close to the wall.…”

“…Figure 9: Time averaged (a) streamwise and (b) vertical velocity profiles over a threedimensional hill. Open circles: experimental data by Ishihara et al [40]; green dotted lines: simulation results using the smearing method by Diebold et al [19]; cyan dashed lines: simulation results using the smearing method with normal derivative correction by Fang and Porté-Agel [32]; blue dashed-dotted lines: simulation results using the present method on a 384 × 192 × 192 grid; black solid lines: simulation results using the present method on a 768 × 384 × 385 grid. The vertical dashed lines indicate the measurement locations.…”

“…9-11. Aiming to improve the simulation accuracy of the smearing method, Fang and Porté-Agel [32] proposed a normal derivation correction for the velocity gradient near the solid surface and simulated the [40]; green dotted lines: simulation results using the smearing method by Diebold et al [19]; cyan dashed lines: simulation results using the smearing method with normal derivative correction by Fang and Porté-Agel [32]; blue dashed-dotted lines: simulation results using the present method on a 384 × 192 × 192 grid; black solid lines: simulation results using the present method on a 768 × 384 × 385 grid.…”

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“…The melting of snow cover occurs faster with increasing slope inclination, but also with increasing wind speed (Grünewald et al 2010), which is indirectly influenced by the topography. This is because topography modifies the wind field, creating various types of effects increasing or decreasing the speed and direction of air flow (Kondo et al 2002;Hertenstein and Kuettner 2005;Lewis et al 2008;Fang and Porté-Agel 2016), thus changing the conditions of snow cover deposition and ablation.…”