Author(s): M. Kolahdoozan; S. Faraji Gargary
Linked Author(s):
Keywords: PDES; Meshfree methods; DLSM method; Oil spill
Abstract: Meshfree methods were remarkably developed to solve the Partial Differential Equations (PDEs) in the recent years. In these methods, a set of nodal points is used to discretize the computational domain. High flexibility and excellent accuracy of meshfree methods are two major advantages in compare with numerical methods such as Finite Volume and Finite Element methods. In the current study, Discrete Least Squares meshfree (DLSM) method is used to solve the oil spill problems. The DLSM method is based on the minimization of the least squares functional which computed at nodal points. The least square functional is defined as the weighted summation of the squared residuals of the governing differential equations and its boundary conditions. Moving Least Squares (MLS) approximation is used to construct the shape functions. In this study, the DLSM method is applied to solve the oil spill problems which include slick spreading on the water surface and advection-diffusion processes of oil phase in the water column. A set of numerical simulations is carried out to evaluate the performance of DLSM method encountering oil spill problems.
Year: 2016