| Due to human activities,water pollution problems occur frequently in coastal area damaging natural environment.Prevention and control for marine pollution are essential for sustainable development and ecological civilization construction.As for unexpected pollution incidents,finding the pollutant source definitely is the key point to eliminate the root.In this paper,we try to establish a pollution backward tracking model that can track the pollutant’s source.The model should recover the transport history of pollutant and locate the pollutant’s source basing on the current concentrations data.Identifying the source’s location needs to reversely solve the advection-diffusion equation with minus time step which is an ill-posed inverse problem,or more precisely,the initial condition inverse problem.We select the Gauss filter method to solve it,which means applying filter to the field of concentration flux to eliminate the numerical instability.After that,a fourth order partial derivative term is added to the equation,the same as another inverse problem method-Quasi-reversibility method-does.The new equation is solved by using Galerkin finite element method(FEM).Yet normal Galerkin FEM model only has C0 continuity that is lower than the C1 continuity a fourth order PDE usually requires.The model in this paper will only have C,continuity.To test the model,a series experiments are set,including pure diffusion process test in which velocities are all zeroes and advection-diffusion process test in which velocities are non-zero but steady.In all cases,pollutants are released instantaneously from point-source or line-source.Results show that backward tracking model is able to maintain stable calculation for a limit of time,during which it can recover the transport history and identify the source’s location,but cannot precisely recover concentration value.Numerical instability will become irresistible if simulation keeps going.The time limit of stable calculation has a certain relation to the grid size,diffusion coefficient and filter width of the model.Afterward,backing tracking model is applied to Xiamen Bay to identify the instantaneous pollutant source from the concentration data one tidal period later than the release time.Results show that the model does recover the transport history and give an ideal initial concentration distribution that clearly shows approximate location of the source. |
