Numerical Evaluation of Wind Flow over Complex Terrain - CiteSeerX

Numerical Evaluation of Wind Flow over Complex Terrain: Review G. T. Bitsuamlak1; T. Stathopoulos, F.ASCE2; and C. Bédard3 Abstract: This paper reviews the current state of the art in the numerical evaluation of wind flow over different types of topographies. Numerical simulations differing from one another by the type of numerical formulation followed, the turbulence model used, the type of boundary conditions applied, the type of grids adopted, and the type of terrain considered are summarized. A comparative study among numerical and experimental (both wind tunnel and field) existing works establishing the modifications of wind flow over hills, escarpments, valleys, and other complex terrain configurations demonstrates generally good predictions on the upstream but problematic predictions on the downstream areas of the complex terrain. Comparisons are also made with provisions of the current wind standards as well as with speed-up values calculated using guidelines derived from theoretical models. DOI: 10.1061/(ASCE)0893-1321(2004)17:4(135) CE Database subject headings: Wind loads; Computational fluid dynamics technique; Turbulence; Terrain; Topography.

Introduction Wind pressures on buildings and other structures, pedestrain level winds, wind-induced dispersion of pollutants in urban locations depend, among other factors, on the velocity profile and turbulence characteristics of the upcoming wind. These, in turn, depend on the roughness and general configuration of the upstream terrain. Consequently, wind standards and codes of practice typically assume upstream terrain of homogeneous roughness or provide explicit corrections for specific topographies such as hills or escarpments; for more complex situations they refer the practitioner to physical simulation in a boundary layer wind tunnel (BLWT). The evolution of computational wind engineering makes the evaluation of wind velocities over complex terrain very attractive. In fact, significant progress has been made in the application of computational fluid dynamics (CFD) for specific cases of the evaluation of wind flow over escarpments, single and multiple hills, as well as valleys. Numerical modeling of wind flow consists of utilizing a set of differential equations (Navier-Stokes) describing the flow in a particular domain, say near an obstruction. The Reynolds-averaged Navier-Stokes (RANS) equations 1

Graduate Student, Centre for Building Studies, Dept. of Building, Civil and Environmental Engineering, Concordia Univ., 1257 Guy St., 341 Montreal PQ, Canada, H3H 1H5. E-mail:gtsegaye@ cbs-engr.concordia.ca 2 Professor and Associate Dean Graduate Studies, Centre for Building Studies, Dept. of Building, Civil and Environmental Engineering, Concordia Univ., 1257 Guy St., 341 Montreal PQ, Canada, H3H 1H5. E-mail:[email protected] 3 Professor and Dean of Research and Technology Transfer, École de technologie supérieure, 1100 Notre-Dame W. Montreal PQ, Canada, H3C 1K3. E-mail: [email protected] Note. Discussion open until March 1, 2005. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on April 18, 2003; approved on December 23, 2003. This paper is part of the Journal of Aerospace Engineering, Vol. 17, No. 4, October 1, 2004. ©ASCE, ISSN 0893-1321/2004/4-135–145/$18.00.

have been used in most of the studies dealing with wind flow over complex terrain. Turbulence of the flow is represented by a particular model, such as the well-known k - ␧ model, which is appropriate only for the case of homogeneous isotropic turbulence. Discretization of the flow equations leads to a set of solvable algebraic equations. The simplification inherent in the use of algebraic equations together with the fast growth in computer technology is what makes the numerical approach capable of solving more complex, realistic problems than before at reasonable cost. This paper presents and discusses the progress made in the numerical evaluation of wind flow over complex topographies and compares computational results with experimental data. The emphasis is placed on the evaluation of velocity ratios since windinduced pressures are proportional to the square of the wind speeds. Consequently, a small variation of wind speed due to the upstream topography may have a large influence on the loading of the structures. Hills, escarpments, valleys, and more complex terrain conditions have been considered.

Single Two-Dimensional Hills and Escarpments Field measurement results and experimental data from BLWT physical simulations have been compared with CFD predictions and provisions of the National Building Code of Canada [NBCC (1995)] for a number of geometries and roughnesses. It should be noted that the code provisions have also been used by the American wind load standard ASCE 7 in all its recent editions, as well. Figs. 1 and 2 compare typical results for the variation of velocity profiles above several geometries of escarpments and on hilltops respectively. Data has been gathered from literature but they are recalculated and reformatted in order to fit in the same graph for comparison purposes. For different geometries of escarpments (H / L = 0.2 to 1.2) and hills (H / L = 0.2 to 0.6), as well as different values of upstream roughness expressed by Jensen’s number 共H / zo兲 ranging from 400 to 40,000, normalized speed-up ratio values given by 关⌬u共z兲L兴 / 关uo共2L兲H兴 for escarpments and 关⌬u共z兲L兴 / 关uo共L兲H兴 for hills are quite similar. In these expressions H represents the height of the hill/escarpment, L represents the

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Fig. 1. Escarpment: (a) Definitions of parameters; and (b) dimensionless velocity speed-up factors (Bowen 1979; Bowen and Lindely 1977; Jackson 1979)

horizontal distance from the crest to where the ground elevation is half the height of the hill/escarpment, zo represents roughness of the ground, ⌬u共z兲 represent increase in velocity, i.e., u共z兲 − uo共z兲 at height z above the local escarpment/hill surface, uo共2L兲 and uo共L兲 represent upstream reference velocity at the height 2L and L above the ground respectively, similarly uo共z兲 and u共z兲 represent upstream reference velocity and mean velocity at the local hill surface at height z above the ground respectively. Normalized speed-up ratio values based on NBCC (NBCC 1995) were calculated and shown in Figs. 1 and 2 for the steepest and the shallowest hill/escarpment in the group of isolated hills/escarpments considered. Most researchers whose work is considered in this group have used one of the variants of k-␧ turbulence model. Bergeles (1985), Paterson and Holmes (1993), Kim et al. (1997), and Carpenter and Locke (1999) used the standard k-␧ model. Quinn et al. (1998) used three different variants of k-␧ models, and results based on the renormalization group (RNG) k-␧ have been used for the present comparison due to

Fig. 2. Hill: (a) Definitions of parameters; and (b) dimensionless velocity speed-up ratios on top of hill. (Bradley 1980; Pearse et al. 1981)

slightly better agreement with field data when compared with other k-␧ models. Regarding the type of grid, most of the researchers used body-fitted coordinates. The body-fitted coordinates used by Bergeles (1985) and Kim et al. (1997) were orthogonal and were generated by solving elliptical type of differential equations. The use of body-fitted coordinates is advantageous for accurate ground boundary applications. Fig. 3 shows the size of the recirculating region obtained using numerical simulation and experimental visualization for various geometries of hills and ground roughness conditions (Kobayashi et al. 1994; Ferreira et al. 1995). The agreement between the size of the recirculation obtained using numerical simulations and experimental observations is satisfactory. Both Kobayashi and Ferreira’s numerical simulation was based on control volume formulation that uses collocated arrangement of independent variables and body-fitted grids. The body-fitted grids used by Ferreira were or-

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Fig. 3. Flow visualizations of circulation region behind two-dimensional hills: (a) Experimental measurements; and (b) numerical simulations [i Kobayashi et al. (1994); ii–v Ferreira et al. (1995)]

thogonal whereas Kobayashi used nonorthogonal body-fitted grids. The numerical solutions of RANS equations were obtained following the semiimplicit method for pressure linked equations and consistent (SIMPLEC) formulation and the turbulence was modeled with a modified low Reynolds number k-␧ model. When significantly different hill geometries are considered, the agreement between CFD, BLWT, analytical, and NBCC speed-up values expressed by the ratio u共z兲 / uo共z兲 is better for shallow hills than for steep hills as can be seen in Fig. 4. The sizable discrepancy among values near the steep hilltop as shown in Fig. 4(b) is attributed to the presence of flow separation and recirculation behind steep hills for which the isotropic turbulence models used in most of the studies may not be suitable. Similarly, significant difference in roughness of the ground surface affects the wind-flow pattern over hills considerably. This was illustrated by the studies of Kobayashi et al. (1994) regarding airflow above forested and nonforested two-dimensional hills and the research of Lun et al. (2003) for flow around smooth and rough two-dimensional hills. Kobayashi et al. (1994) takes the effect of vegetation cover on airflow and turbulence into account by considering additional drag forces in the RANS equations and the k-␧ model respectively. In the study of Lun et al. (2003) the surface roughness was incorporated through the application of a wall function that contains zo at the ground boundary; three turbulence models were used: the standard, revised k-␧ model by Durbin (1996), and Reynolds stress algebraic equation model by Shih et al. (1995). Comparisons between numerical simulations and BLWT measurements for the mean flow characteristics of flow are shown in Fig. 5 for two cases, without trees and with trees 共tree height= 50 mm兲, on the steep hill (H / L = 1 and H = 200 mm). Numerical simulations agree with the experimental measurements satisfactorily, as shown in Figs. 5(a and b). The agreement between velocity profiles obtained by CFD and BLWT experiments is better for the hill with no trees than the hill with trees, as shown in Fig. 5(c). This possibly indicates the requirements of fine-tuning the roughness parameter application in the numerical models. The separated flow on the leeward side of the

hill for the nonforested case has a profile much thinner than for the forested case, leaving more momentum available to overcome the adverse pressure gradient. Conseqently, separation occurs farther as shown in Figs. 6(a and b). Lun et al. (2003) have obtained similar results as shown in Figs. 6(c and d). By using the nonlinear turbulence model by Shih et al. (1995), numerical results agree better with the experimental data, even in the problematic leeward part. Overall numerical simulations based on the k-␧ model appear very good when the differences between wind tunnel and field data are taken into account. It is worth noting that the speed-up ratios derived from the NBCC (1995) compare well with the computational results. The guidelines (Weng et al. 2000) used in the comparison shown in Figs. 2 and 4 were derived from the multispectral finite-difference (MSFD) model of Belijaars et al. (1987) and its nonlinear extension NLMSFD by Xu et al. (1994). These are theoretical formulations similar to that of Jackson and Hunt (1975), in which the equations of motion are linearized by expressing solution variables as being equal to an undisturbed part and a small perturbation. Fourier transform techniques are used on the resulting equations and allow a solution to be obtained by numerical means. Provision of simple guidelines that can reflect a complex numerical simulation result is an attractive approach.

Two-Dimensional Multiple Hills Carpenter and Locke (1999) investigated the variation of wind speeds over steep and shallow multiple two-dimensional sinusoidal hills. The hills have uniform geometry as shown in Fig. 7. Computational results were obtained by using the finite-element approach with the standard high Reynolds number k-␧ turbulence model. Speed-up ratios for hill geometries used by Carpenter and Locke (1999) were calculated based on guidelines by Weng et al. (2000) and NBCC provisions (NBCC 1995) for the present study. A typical comparison of speed-up ratios u共z兲 / uo共z兲 between CFD,

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Fig. 4. Comparison between BLWT, CFD, analytical, and NBCC speed-up ratios at crest of (a) shallow, and (b) steep sinusoidal hill [Reynolds number R共H兲 = 1.3⫻ 105, roughness length zo = 0.02 m]

BLWT, calculated values using the Weng et al. (2000) guidelines, and NBCC provisions, is shown in Figs. 8 and 9. The agreement between CFD and BLWT results is better for shallow hills than for steep hills. In the case of steep hills, the agreement between CFD and BLWT results is somewhat better for downstream hills than upstream hills. It is interesting to observe the patterns of speed-up ratios indicated by BLWT experiments captured by the CFD simulations as shown in Figs. 8 and 9. NBCC values for the isolated hill cases agree with both BLWT and CFD predictions as discussed in the previous section; however, NBCC speed-up ratios are found to be conservative for use in the case of multiple hills. In particular NBCC overpredicted the speed-up ratios by 57 and 45% for hills 2 and 3 respectively at 40 m above the crest (Fig. 9). The relative size of neighboring hills also plays significant effect on speed-up ratio values. For example, Kim et al. (1997) studied this effect on the mean velocity profile at the top of a small hill caused by a neighboring higher hill located either upwind or downwind of the small hill. Using the Kim et al. (1997) velocity profile, speed-up ratio values were calculated at the crest of small (H / L = 0.6, H = 40 mm) and large (H / L = 0.6, H = 70 mm) hills for four different cases: single small hill, single large hill, upstream small hill and downstream large hill multiple arrangement (small–large) and upstream large hill and downstream small hill multiple arrangement (large–small). Fig. 10 shows speed-up ratios that have been calculated based on the Kim et al. results for mean velocity distributions at the hilltop of the small hill and of the large hill. Clearly the hilltop speed-up ratio profiles of the large hill are not much influenced by the neighbor-

ing small hill as shown in Fig. 10(a), whereas the lower hill is significantly influenced by the neighboring higher hill as shown in Fig. 10(b). It is interesting to note that the speed-up ratio on the small hill increases by about 5 to 10% in the presence of the large hill compared with that of an isolated case. The significant influence of a neighboring hill has also been observed in related experimental studies by Carpenter and Locke (1999), Ferreira et al. (1991), and Miller and Davenport (1998). Kim et al. (1997) solved the RANS equations using body-fitted coordinates and the standard k-␧ turbulence model closure. Lee et al. (2003) studied the effect of distance between two hills on flow characteristics by solving RANS equations and standard k-␧ turbulence closure with uniform upstream flow conditions and orthogonal body-fitted coordinates. From their study, it can be concluded that a neighboring hill can have a significant effect on the velocity pattern even for a distance between hills as large as 6L as can be seen in Fig. 11. Their studies fall short in reporting at what distance the effect of a neighboring hill ceases to be felt.

Two-Dimensional Valleys Maurizi (2000) presented useful computational results dealing with two-dimensional valleys of various slopes and compared them with the wind tunnel experimental data from Busuoli et al. (1993). Out of the three different k-␧ models utilized, the standard

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Fig. 5. Numerical and experimental velocity profiles at different horizontal positions for hill with (a) no tree (Kobayashi et al. 1994); (b) with tree (Kobayashi et al. 1994); and (c) with tree and with no tree at Sections A-A and B-B respectively (H / L = 1, H = 200 mm)

k-␧ model, the one described by Chen and Kim (1987), and the RNG version (Yakhot et al. 1992), RNG was reported to give the best result, hence this is used to calculate speed-up ratio values in the present comparisons. Speed-up ratio values were calculated from computational and experimental velocity profile data taken from Maurizi (2000) and Busuoli et al. (1993) respectively. Fur-

Fig. 6. Numerically obtained streamlines (a) without trees; and (b) with trees (Kobayashi et al. 1994)—velocity field over (c) smooth hill; and (d) rough hill (Lun et al. 2003)

ther speed-up ratio values were calculated for valley geometries used by Maurizi (2000) applying the guidelines of Weng et al. (2000) and the NBCC provisions (NBCC 1995). Comparisons of speed-up values were made for both shallow 共H / L = 0.25兲 and deep 共H / L = 0.66兲 valleys at four different longitudinal locations. Fig. 12 shows good speed-up ratio agreement between all numerical results and the BLWT data at four longitudinal locations in the case of a gently sloping shallow valley. The NBCC provisions for the case of two-dimensional valley seem to agree well with other values for the shallow valley except at the downstream edge of the valley (Section d) as shown in Fig. 12(d). The comparisons of NBCC values with numerical and experimental data become less satisfactory for the deeper valley, and flow recirculation occurs as shown in Figs. 13(b and d). Particularly poor agreement with the NBCC is observed at the downstream edge of the deep valley (Section d) as shown in Fig. 13(d). Values obtained using the guidelines of Weng et al. (2000) are also compared at the center of the valley (Section b), where the model is only applicable. Although the guideline values of Weng et al. (2000) are in good agreement with CFD, BLWT, and NBCC for shallow valley as shown in Fig. 12(b), they overestimate speed-up ratio values for deeper valley as shown in Fig. 13(b).

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Fig. 7. Geometry of shallow and steep sinusoidal hills used in Carpenter and Locke (1999) Scale 1 : 1 , 000

Kim and Patel (2000) simulated wind flow over Askervein Hill by solving the Reynolds-averaged Navier-Stokes equations using body-fitted coordinates. Standard and RNG-based k-␧ models are used together with wall functions to account for surface roughness. Fig. 14(a) shows a contour map of the Askervein Hill. The field measurements were made along lines A-A and B-B at a height of 10 m above the hill surface. Following this work, speed-up ratio values were generated for Askervein Hill using NBCC provisions for the same positions. Note that NBCC provisions are meant for either two-dimensional hills or axisymmetric three-dimensional hills and not for a complex three-dimensional terrain. Section A-A is approximately symmetrical and aligned along the wind direction; hence speed-up values were calculated using NBCC provisions for two-dimensional hills. In the case of Section B-B however, this type of approximation cannot be used

since the section is not aligned in the wind direction; instead a number of two-dimensional sections along the wind direction and perpendicular to Section B-B were considered systematically. Speed-up ratio values using NBCC were then calculated at the points where these two-dimensional cross sections intersect Section B-B and used in the following comparisons. Figs. 14(b and c) show comparisons made among the wind-tunnel experiments, full-scale measurements, two- and three-dimensional numerical computations, and NBCC provisions. There is substantial agreement among all of the results on the windward slope of the hill, but significant differences are found on the leeward side along Line A-A where the full-scale measurements show rapid decrease of speed-up ratio down to 0.3. Only the three-dimensional numerical simulation predicts this behavior although there is some deterioration of agreement with data at the peak. It is conjectured that this trend arises from the three-dimensional flow separation on the leeward slope due to the influence of neighboring hills.

Fig. 8. Comparison between speed-up ratio values obtained from BLWT, CFD, NBCC, and analytical model at 5 m above crest of multiple shallow and steep hills—values from a single hill are also given

Fig. 9. Comparison between speed-up ratio values obtained from BLWT, CFD, NBCC, and analytical model at 40 m above crest of multiple shallow and steep hills—values from a single hill are also given

Three-Dimensional Complex Terrain

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Fig. 10. Comparison of speed-up ratios obtained from computational fluid dynamics models at hilltops of (a) small hill: H / L = 0.6, and H = 40 mm; and (b) large hill: H / L = 0.6, and H = 70 mm

Fig. 11. Vertical profiles of mean streamline velocity over doublehills (Lee et al. 2003) JOURNAL OF AEROSPACE ENGINEERING © ASCE / OCTOBER 2004 / 141

Fig. 12. Vertical profiles of horizontal mean velocity for valley with H / L = 0.25 at four longitudinal locations

Kim and Patel (2000) also reported that flow separation on the leeward side of Askervein Hill was not predicted by the threedimensional computation when the neighboring hills were excluded. In that case, the speed-up ratio distributions were quite similar to those predicted by the two-dimensional computation. The wind-tunnel experiment, which employed a smooth-surface model, failed to depict the decrease of speed-up ratios on the leeward slope. For Section A-A, the agreement between NBCC provisions, field measurement, and three-dimensional CFD values is relatively better for the windward rather than the leeward part of the site. For the case of Section B-B, NBCC predictions represent the experimental data well, as shown in Fig. 14(c). Differences between field- and wind-tunnel measurements should also be considered to put these comparisons into the right perspective.

Overall there is a need for developing guidelines working for a wide spectrum of geometries and roughness conditions of a terrain. Generating data using numerical or experimental simulations and then representing them by simple semiempirical formulas is one way of addressing this issue (Lemelin et al. 1988; Weng et al. 2000). The alternative method the writers have suggested is a combination of CFD and neural network approach. Through CFD simulations, data can be generated and subsequently used to train the neural network. The trained neural network will produce the speed-up ratios when presented with simple geometric parameters (Bitsuamlak et al. 2002). Use of such a neural network will provide flexibility and capability of simple modeling of highly nonlinear relationships for a wide spectrum of geometries.

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Fig. 13. Vertical profiles of horizontal mean velocity for valley with H / L = 0.66 at four longitudinal locations

Concluding Remarks For single two-dimensional hills, general agreement between different numerical speed-up ratio predictions and experimental data including the commentaries of NBCC has been observed. For steep multiple hills the use of speed-up ratios based on studies for single hill from codes and standards is clearly a conservative approach with generally overpredicted speed-up ratios. In general, numerical results agree with field data better on the upstream as opposed to the downstream areas of complex terrain. At present, utilization of numerical simulations to predict wind speed-ups in

practical applications is rather limited and designers still have to rely on physical simulations for complex terrain situations. However, the agreement between different numerical simulations and wind-tunnel tests shown in this paper indicates a promising future for the computational approach. In parallel, simple ways of conveying to the engineering profession the results produced by complex CFD simulations must be devised. To this effect, the writers are currently working on the development of a neural network model trained with CFD-generated data, which will be capable of producing speed-up ratios following input of simple geometrical parameters describing the topography and roughness of the ground.

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Fig. 14. Speed-up ratios for Askervein Hill at 10 m above the ground level for wind angle ␾ = 30° (Teunissen et al. 1987; Salmon et al. 1988) and topographic map of Askervein hill and surrounding area—all distances in meters

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References Beljaars, A. C., Walmsley, J. L., and Taylor, P. A. (1987). “A mixed spectral finite-difference model for neutrally stratified boundary-layer flow over roughness changes and topography.” Boundary-Layer Meteorol., 38, 273–303. Bergeles, G. C. (1985). “Numerical computation of turbulent flow around two-dimensional hills.” J. Wind. Eng. Ind. Aerodyn., 21(3), 307–321. Bitsuamlak, G. T., Stathopoulos, T., and Bedard, C. (2002). “Neural network predictions of wind flow over complex terrain .” 4th Structural Specialty Conf. of the Canadian Society for Civil Engineering, Montréal, S-13. Bowen, A. J. (1979). “Full scale measurements of the atmospheric turbulence over two escarpments.” Proc., 5th Int. Conf. on Wind Eng. Pergamon, Tarrytown, N.Y. 161–172. Bowen, A. J. and Lindely, D. A. (1977). “Wind tunnel investigation of the wind speed and turbulence characteristics close to the ground over various escarpment shapes.” Boundary-Layer Meteorol., 12, 259– 271. Bradley, E. F. (1980). “An experimental study of the profiles of wind speed, shearing stress and turbulence at the crest of a large hill .” Q. J. R. Meteorol. Soc., 106, 121–124. Busuoli, M., Trombetti, F., and Tamperi, F. (1993). “Data sets for studies of flow and dispersion in complex terrain: (II) The RUSVAL wind tunnel experiment (flow data).” Technical paper No. 3, FISBAT-TP93/1, 129 pages, Bologne, Italy. Carpenter, P., and Locke, N. (1999). “Investigation of wind speed over multiple two-dimensional hills.” J. Wind. Eng. Ind. Aerodyn. 83(1–3), 109–120. Chen, Y. S. and Kim, S. W. (1987). “Computation of turbulent flows using an extended k-␧ turbulence closure model.” CR-179204, National Aeronautics Space Administration, Washington, D.C. Durbin, P. A. (1996). “Technical notes: On k-␧ stagnation point anomaly.” Int. J. Heat Fluid Flow, 17(1), 89–90. Ferreira, A. D., Lopes, A. M. G., Viegas, D. X., and Sousa, A. C. M. (1995). “Experimental and numerical simulation of flow around twodimensional hills.” J. Wind. Eng. Ind. Aerodyn., 54/55, 173–181. Ferreira, A. D., Silva, M. C. G., Viegas, D. X., and Lopes, A. G. (1991). “Wind tunnel simulation of the flow around two-dimensional hills.” J. Wind. Eng. Ind. Aerodyn., 38,(2–3), 109–122. Jackson, P. S. (1979). “The influence of local terrain features on the site selection for wind energy generating systems.” Rep. BLWT-1-1979, Faculty of Engineering Science, Univ. of Western Ontario, Ont., Canada 83. Jackson, P. S., and Hunt, J. C. R. (1975). “Turbulent flow over a low hill.” Q. J. R. Meteorol. Soc., 101, 929–955. Kim, H. G., Lee, C. M., Lim, H. C., and Kyong, N. H. (1997). “An experimental and numerical study on the flow over two-dimensional hills.” J. Wind. Eng. Ind. Aerodyn., 66(1), 17–33. Kim, H. G., Patel, V. C., and Lee C. M. (2000). “Numerical evaluation of wind flow over hilly terrain.” J. Wind. Eng. Ind. Aerodyn., 87(1),

45–60. Kobayashi, M. H., Pereira, J. C. F., and Siquiera, M. B. B. (1994). “Numerical study of the turbulent flow over and in a model forest on a 2D hill.” J. Wind. Eng. Ind. Aerodyn., 53(3), 357–375. Lee, S. J., Lim, H. C., and Park, K. C. (2003). “Wind flow over sinusoidal hilly obstacle located in a uniform flow.” Wind Struct., 5(6), 515–526. Lemelin, D. R., Surry, D., and Davenport, A. G. (1988). “Simple approximations for wind speed-up over hills.” J. Wind. Eng. Ind. Aerodyn., 28(1–3), 117–127. Lun, Y. F., Mochida, A., Murakami, S., Yoshino, H., and Shirasawa, T. (2003). “Numerical simulation of flow over topographic features by revised k-␧ models.” J. Wind. Eng. Ind. Aerodyn., 91(1–2), 231–245. Maurizi, A. (2000). “Numerical simulation of turbulent flows over 2D valleys using three versions of the k-␧ closure model.” J. Wind. Eng. Ind. Aerodyn., 85(1), 59–73. Miller, C. A., and Davenport, A. G. (1998). “Guidelines for the calculation of wind speed-ups in complex terrain .” J. Wind. Eng. Ind. Aerodyn., 74–76(1), 189–197. National Building Code of Canada (NBCC). (1995). National building code user’s guide—Structural commentaries (Part 4), Canadian Commission on Building and Fire Codes, National Research Council of Canada, Ottawa. Paterson, D. A., and Holmes, J. D. (1993). “Computation of wind flow over topography.” J. Wind. Eng. Ind. Aerodyn., 46/47, 471–478. Pearse, J. R., Lindely, D., and Stevenson, D. C. (1981). “Wind flow over ridges in simulated atmospheric boundary layers.” Boundary-Layer Meteorol., 21(1), 77–92. Quinn, A. D., Robertson, A. P., Hoxey, R. P., and Burgess, L. R. (1998). “The effect of small embankments on wind speeds.” Wind Struct., 1(4), 303–316. Salmon, J. R., Bowen, A. J., Hoff, A. M., Johnson, R., Mickle, R. E., and Taylor, P. A. (1988). “The Askervein Hill experiment: Mean wind variations at fixed heights above the ground.” Boundary-Layer Meteorol., 43, 247–271. Shih, T. H., Zhu, J., and Lumely, J. L. (1995). “A new Reynolds stress algebraic equation model.” Comput. Methods Appl. Mech. Eng., 125, 187–302. Teunissen, H. W., Shokr, M. E., Bowen, A. J., Wood, C. J., and Green, D. W. R. (1987). “Askervein Hill project: Wind-tunnel simulations at three length scales.” Boundary-Layer Meteorol., 38, 1–29. Weng, W., Taylor, P. A., and Walmsley, J. L. (2000). “Guidelines for airflow over complex terrain: Model developments.” J. Wind. Eng. Ind. Aerodyn. 86, 169–186. Xu, D., Ayotte, K. W., and Taylor, P. A. (1994). “Development of a non-linear mixed spectral finite difference model for turbulent boundary-layer flow over topography .” Boundary-Layer Meteorol., 70, 341–367. Yakhot, V., Orzag, S. A., Thamgams, S., Gatski, T. B., and Speziale, C. G. (1992). “Development of turbulence models for shear flows by a double expansion technique.” Fluid Dyn., 4(7), 1510–1520.

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