Mathematical and Computational Oil Spills Modelling

The model of oil spill evolution on the water surface based on quasi-linear convection-diffusion equation is considered. To solve the latter the method of finite differences is used. Two-dimensional problem is reduced to one-dimensional by alternating direction method. For one-dimensional case traditional difference approximations are briefly discussed. And also difference schemes obtained by computer algebra based method of automatic generation of difference schemes are considered. For generated schemes the order of approximation and linear numerical dissipation are estimated. For explicit schemes stability conditions are briefly discussed. In the absence of convection a numerical comparison of traditional implicit difference scheme and one implicit scheme generated automatically with similarity solution of quasi-linear diffusion equation is carried out. This comparison shows that generated implicit scheme allows to obtain the relative error less than for traditional scheme. Using obtained implicit scheme evaluation of oil slick thickness changes in the presence of oil evaporation is done. Two different models were used to estimate oil evaporation rate. The first one is based on hypothesis that oil evaporation is regulated by air boundary layer. The second assumes that oil evaporation is regulated by oil diffusion. Calculations show that the choice of model essentially influences on oil slick thickness and oil total volume changes in time.

quasilinear advection-diffusion equation, finite difference method, Grorbner basis, difference schemes generation, oil spills, oil evaporation