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ABSTRACT:Oil spills is one of the most important hazards in the estuarine and coastal water. In recent decades, engineers try to predict the status of oil slick to manage the pollution spreading. The prediction of oil slick transport is carried out mainly by means of numerical models. In the current study, the development and application of a two-phase fluid flow model to simulate oil transport in the marine environment are presented. Different transport and fate processes are included in the developed model. The model consists of the Lagrangian method for the advection process, the Random Walk technique for horizontal diffusion process and the empirical equations for the fate processes. The major forces for driving oil particles are fluid current, wind speed and turbulent flow. Therefore, the multi-component hydrocarbon method has been included to the developed model in order to predict fate processes. As prediction of particle velocity components is of major importance for oil slick advection, therefore the binomial interpolation procedure has been chosen for the particle velocity components computations. In addition, shoreline boundary condition is included in the developed model to simulate shore response to oil slick transport near the beaches. The results of the model applications are compared with the analytical solutions, experimental measurements and other numerical models cited in literature. Comparisons of different sets of results represent the capability of developed model to predict the oil slick transport. In addition, the developed model is tested for two oil spill cases in the Persian Gulf.

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In this paper, a collocated Mixed Discrete Least Squares Meshless (MDLSM) method is proposed and used to attain an e cient solution to engineering problems. Background mesh is not required in the MDLSM method; hence, the method is a truly meshless method. Nodal points are used in the MDLSM methods to construct the shape functions, while collocated points are used to form the least squares functional. In the original MDLSM method, the locations of the nodal points and collocated points are the same. In the proposed Collocated Mixed Discrete Least Squares Meshless (CMDLSM) method, a set of additional collocated points is introduced. It is expected that the accuracy of results may improve by using the additional collocated points. It is noted that the size of coe cient matrix is not increased in the proposed CMDLSM method compared with the MDLSM method. Therefore, the required computational e ort for solving the linear algebraic system of equations is same as that in MDLSM method. A set of benchmark numerical examples, cited in the literature, is used to evaluate the performance of the proposed method. The results indicate that the accuracy of solutions is improved by using additional collocated points in the proposed CMDLSM method.

Abstract. A Mixed formulation of Discrete Least Squares Meshless (MDLSM) as atruly mesh-free method is presented in this paper for solving both linear and non-linear propagation problems. In DLSM method, the irreducible formulation is deployed, which needs to calculate the costly second derivatives of the MLS shape functions. In the proposed MDLSM method, the complex and costly second derivatives of shape functions are not required. Furthermore, using the mixed formulation, both unknown parameters and their gradients are simultaneously obtained circumventing the need for post-processing procedure performed in irreducible formulation to calculate the gradients. Therefore, the accuracy of gradients of unknown parameters is increased. In MDLSM method, the set of simultaneous algebraic equations is built by minimizing a least squares functional with respect to the nodal parameters. The least squares functional is de ned as the sum of squared residuals of the di erential equation and its boundary condition. The proposed method automatically leads to symmetric and positive-de nite system of equations and, therefore, is not subject to the Ladyzenskaja-Babuska-Brezzi (LBB) condition. The proposed MDLSM method is validated and veri ed by a set of benchmark problems. The results indicate the ability of the proposed method to e ciently and e ectively solve the linear and non-linear propagation problems.