【正文】 erence method with a new representation of Neumann’s problem on boundary points, and it gives positive results. The results are in agreement with those obtained by way of experiments. Unami et al. (1999) developed a numerical model using the finite element and finitevolume methods for the resolution of two dimensional free surface flow equations including air entrainment and applied it to the calculation of the flow in a spillway. The results prove that the model is valid as a primary analysis tool for the hydraulic design of 8 spillways. Song and Zhou (1999) developed a numerical model that may beapplied to analyze the 3D flow pattern of the tunnel or chute spillways, particularly the inlet geometry effect on flow condition. Olsen and Kjellesvig (1988) included viscous effects by numerically solving the Reynoldsaveraged NavierStokes (RANS) equations, using the standardequations to model turbulence. They showed excellent agreement for water surfaces and discharge coefficients. Recently, investigations of flow over ogeespillways were carried out using a mercially available putational fluid dynamics program, FLOW3D, which solves the RANS equations (Ho et al., 2020。 fi represents the Reynolds stresses for which a turbulence model is required for closure. To numerically solve the rapidly varying flow over an ogee crest, it is important that the free surface is accurately tracked. In FLOW3D, free surface is defined in terms of the volume of fluid (VOF) function which represents the volume of fraction occupied by the fluid. A twoequation renormalized group theory models (RNG model) was used for turbulence closure. The RNG model is known to describe more accurately low intensity turbulence flows and flow having strong shear regions (Yakhot et al., 1992). The flow region is subdivided into a mesh of fixed rectangular cells. With each cell there are associated local average values of all dependent variables. All variables are located at the centers of the cells except for velocities, which are located at cell faces (staggered grid arrangement). Curved obstacles, wall boundaries, or other geometric features are embedded in 11 the mesh by defining the fractional face areas and fractional volumes of the cells that are open to flow. 4. Conclusions In this study, flow characteristics such as flowrate, water surfaces, crest pressures on the ogeespillway, and vertical distributions of velocity and pressure in consideration of model scale and surface roughness effects are investigated in detail by using mercial CFD model, FLOW3D which is widely verified and used in the field of spillway flow analysis. To investigate the scaling and roughness effects, six cases are adopted. Namely, numerical modeling on the hydraulically smooth (PR00), k = mm (PR05), and k = mm (PR30) for the investigation of roughness effects and prototype (PR05), 1/ 50 model (M50), 1/00 model (M100), 1/200 model (M200) for the investigation of scale effects are carried out. In the modeling of the scaled model, grid resolution, surface roughness,and upstream boundary conditions were adjusted as the geometric similarity to exclude a generation of different numerical error. The important simulation results prise the following: 1) The discharge flowrate decreases slightly as surface roughness height and the length scale of the model to the prototype increase. The water surface fluctuation is negligible and some crest pressure variation occurs with a change of surface roughness and model scale. Numerical errors due to the surface roughness are insignificant if we just use a general roughness height of construction materials and the scale effects of the model are appeared in within an acceptabl