###### Abstract  
This paper presents a three-dimensional numerical simulation model of an oil spill for application in emergency treatment methods under icy water conditions. The combined effects of wind, wave, current and ice implemented in our model correspond to Arctic Ocean conditions. A discrete element method combined with an overset grid was adopted to track the trajectory movements of oil film with medium-density ice floes and simulate the flow field of moving ice of large displacement in six degrees of freedom (6 DOF). The probability of oil spill area extensions were estimated by a response surface method (RSM). Results showed reduced risk of pollution in icy water conditions and greater drift action of oil film. Accordingly, the spraying location and quantity of oil-dispersant could be rapidly specified.  
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spills [5]. Additionally, the \"particle flow\" method was used to calculate the transport positions of oil particles at each time step to simulate the transport process of the oil film and associated oil-spill trajectory [6]. The trajectory of oil-spill diffusion on the sea surface was presented visually using a discrete phase model (DPM) in FLUENT software [7]. The Sea Track Web system was applied for oil drift forecasting [8].  
The forecasting of oil spills in water is complex, and the presence of ice in cold waters increases further the difficulty of this research. This is because of the fundamental interaction among different ice blocks that possess different equilibrium thickness in cold and warm open waters [9]. Depending on the natural geographic condition of the Bohai Sea, a dynamic sea ice model has been developed to understand the effects of various forces on sea ice movement [10]. Based on continuum theory, the viscous-plastic constitutive relationship of sea ice was analyzed to forecast the movement of an oil spill with different ice densities [11]. The morphology of \"oil particles\" was used to establish the drift-diffusion model of the oil spill [12]. Afterwards, the evaporation and emulsification processes were added to the forecasting of oil spills in the pack ice area to correct the drift equation [13]. A surface current model and a sea ice model were combined to simulate the oil slick movement process, including drifting, spreading, evaporation and emulsification [14]. However, in its current model, the waves on the sea surface were neglected, and only the oil spill on the ice surface could be forecasted. The movement of an oil spill under ice was observed with the help of 3-D under-ice imagery from an autonomous underwater vehicle [15]. Nevertheless, the spread of an oil spill under the ice was difficult to predict precisely.  
The objective of this work has been to consider synthetically the real environmental elements of wind, current as well as waves in the Icelandic Sea of the Arctic Ocean with the aim to simulate an authentic environment flow field for the prediction of oil-spill trajectory. To achieve this, the multi-phase volume of fluid method (VOF) [16] and discrete element methods (DEM) [17] were adopted to track the non-linear free surface and establish a three-dimensional icy waters model. The Eulerian-Lagrangian method was applied to simulate the movement of the oil spill in ice-infested and ice-free waters. To shorten the forecasting time, the response surface method (RSM) [18] was used to fit the functional relationship between the oil-spill variables and various responses.