Simulation Study Of Pollutant Diffusion Based On The Meshfree Method

Due to the development of unsustainable economic,the natural environment has been destroyed,and the discharge of sewage and haze spread seriously affect people's daily life and health.In addition,the frequent oil spill accidents at sea also seriously pollute the marine environment and bring disaster to the marine life.However,the transport of pollutants mainly involves the solution of the convection diffusion equations,and how to solve the convection diffusion equations accurately is the content of this paper.The numerical methods for solving convection diffusion equations can be divided into mesh method and meshless method.In the based on the grid methods,this paper uses the finite volume method which based on the flux to calculating,the calculation format includes first order and second order and third order accuracy schemes and adding flux limiter TVD(Total Variation Diminishing),MUSCL(Monotonic Upstream Schemes format for Conservation format and Laws)and the improvement of MTVDLF based on TVD(Modified TVD Lax-Friedrichs)format,these methods must divide mesh of problem domain.In addition,according to Lagrange dynamics method,this paper uses the smoothed particle hydrodynamics method based on meshless(Smoothed Particle Hydrodynamics,SPH)to overcome numerical problems in grid,for example excessive mesh distortion and grid motion.For the grid method,the autocatalytic reaction flow model is calculated,and ten common flux schemes based on the finite volume method are derived,and their numerical characteristics are compared by numerical experiments.The results show that the low order accuracy schemes cause serious numerical dissipation and numerical oscillations,which greatly reduce the numerical accuracy.The MTVDLF scheme with flux limiter can effectively eliminate the numerical dissipation and numerical oscillation,and the MTVDLF with Superbee limiter is most suitable for simulating the autocatalytic reaction flow problem.Secondly,for the meshless method,the pollutant diffusion problem is simulated.The SPH method and the first order precision Euler forward method are used to discretize the spatial derivatives and time derivatives of the governing equations respectively,and the corresponding numerical computation schemes are constructed.In addition,the method adds virtual particles,overcoming the boundary effect problem which caused by the boundary kernel function is cut off.In order to verify the accuracy of the Lagrange particle model,the simulation of one-dimensional convection diffusion equation in the open channel flow and the two-dimensional convection diffusion equation of Cosine Hill problem.The experimental results show the reliability and accuracy of the SPH method in solving pollutant transport problems.Finally,in order to find a precise time integration method,five time-stepping integration methods are used to simulate oil spill trajectory.According to the experimental results,Velocity Verlet is the most accurate time integration method.