Simulation System For Two-Dimensional Pollutant Transport Problems

With the development of economy and society,people’s demand for oil and its products continues to rise.Oil spills at sea caused by tanker traffic,offshore drilling and oil transportation are becoming more and more frequent,and the leakage of oil pollutants will cause major pollution to the marine environment and serious harm to human health.Therefore,it is urgent to predict the spread process of oil pollutants and reduce the impact of pollutants.This depends on accurately solving the convectiondiffusion-reaction equation.In this thesis,firstly,the mathematical models of oil spill are sorted out,and the shallow water equations and Saint-Venant equations are derived from the continuity equation and momentum equation of Navier-Stokes equations.Secondly,the convection-diffusion-reaction equation describing the transport process of pollutants is introduced,and the Euler form of the mathematical model is transformed into Lagrangian form.Then,the grid-based methods and semi-Lagrangian methods are detailed,including various forms of finite volume method and finite difference method,the idea and implementation steps of semi-Lagrangian method,and the concrete implementation of two interpolation schemes in semi-Lagrangian method.Finally,a series of numerical experiments,such as the two-dimensional Gaussian model transport problem and the two-dimensional autocatalytic reaction flow problem,are carried out to analyze and discuss the numerical simulation results of the two methods for solving the convection diffusion reaction equation.It is shown that the MUSCL scheme with Superbee limiter is the optimal scheme in the Eulerian methods,because it can well eliminate the numerical dissipation and oscillation caused in the low-precision schemes.Compared with the Eulerian method,the Hermite Cubic interpolation in Space Line(HCSL)scheme in the semi-Lagrangian method generally gives more accurate solutions without numerical dissipation and oscillation.The Cubic Spline interpolation in Space Line(CSSL)scheme can give more accurate solutions than HCSL for problems with continuous concentration distribution,but it consumes more simulation time 100 times more than HCSL scheme.In addition,non-physical oscillation will be generated in the region of large concentration gradient.