The corrected operator splitting approach applied to a nonlinear advection-diffusion problem

So-called corrected operator splitting methods are applied to a 1-D scalar advection-diffusion equation of Buckley-Leverett type with general initial data. Front tracking and a 2nd order Godunov method are used to advance the solution in time. Diffusion is modelled by piecewise linear finite element s at each new time level. To obtain correct structure of shock fronts indep endently of the size of the time step, a dynamically defined residual flux term is grouped with diffusion. Different test problems are considered, and the methods are compared with respect to accuracy and runtime. Finally, we extend the corrected operator splitting to 2-D equations by means of dimen sional splitting, and we apply it to a Buckley-Leverett type problem includ ing gravitational effects. (C) 1998 Elsevier Science S.A. All rights reserv ed.