Simulation Of Contaminant Transport Using Semi-lagrangian Method And Its Improvement

With the improvement of economic development level,people no longer only focus on their own development and harmonious development of man and nature has become the mainstream values of society.Due to the extensive development of industry,environmental pollution has attracted much attention in recent years,such as,haze,waste gas sewage treatment,pipeline leakage,marine oil spill and so on.The propagation process and effective treatment of pollutants are related to economic development,ecological environment and people’s livelihood.It is of great engineering significance to simulate the migration and diffusion of pollutants by calculation and simulation,and to realize pollution prevention and treatment.The transport of pollutants can be modeled by the advection-diffusion-reaction equation for solving which the grid-based methods are mostly used,including Eulerian method and Lagrangian method.In this paper,the main grid methods are analyzed and summarized,and the feasibility and value of the semi-Lagrangian method,which integrates the advantages of the two grid methods,are obtained.Then the corresponding physical model of pollutant transport is constructed and solved by flexible numerical method based on the operator-splitting idea,which decouples the advection,diffusion and reaction process.From the point of view of mathematics and physics,based on the advection equation in Eulerian form,the semi-Lagrangian method is derived,which is also known as the characteristic line method.To solve the problem of non-physical oscillations caused by the discontinuously distributed concentration in the traditional semi-Lagrangian method,an improved semi-Lagrangian scheme is developed,which simplifies the calculation steps and improves the calculation efficiency.The applicability of the new semi-Lagrangian method for solving pollutant transport problems is verified by a series of numerical experiments.The semi-Lagrangian method is also applied to the two-dimensional advection-diffusion equation,and good simulation results are obtained.Through the theoretical analysis and experimental study in this paper,it lays a foundation for the semi-Lagrangian method and the improved scheme to solve pollutant transport problems.