Application of reverse simulation to the pollution problem in a bay

Reverse simulation is one of the useful tools to specify pollutant source. This is the solution of an advection and diffusion equation in negative time advancing. However, numerical instability arises with solving the negative diffusion term. The present study examines the cause of numerical instability and introduces the method to secure numerical stability in reverse simulation. A Gaussian filter is applied to the flux of pollutant. Reverse simulation was carried out for a simple rectangular bay using MEC Ocean Model. As a result, in the reverse simulation of the advection term, the numerical diffusion arises in the same way as the forward simulation. In the reverse simulation of the diffusion term, the numerical vibration arises, while its magnitude depends on the simulation area and period. The rate of the amplification of numerical vibration was larger with smaller mesh size and with longer period of numerical simulation. The numerical stability was secured by applying the Gaussian filter to the flux of the concentration of pollutant, resulting in the addition of 4
^th
order derivative term to the governing equation. The numerical instability is also caused by the fixed boundary condition. This depends not on filter width but on the mesh size and the time step. As future study, the filter width, the mesh size, and the time step should be determined to obtain the stable solution of reverse simulation, and to keep the accuracy of the reverse simulation as much as possible.