University of Science and Technology, Norway
Several important problems can be modeled using nonlinear partial differential equations of convection-diffusion type, the simplest being the Burgers equation. However, in many cases the diffusion may be degenerate. Furthermore, the equation can include a source term. The idea of the operator splitting method is to break the equation into simpler parts, apply fast methods for each of them, and finally combine the individual computations into an approximate solution of the full set of equations. We discuss a general mathematical framework for this. Among the fast methods, we will discuss front tracking in detail.
Applications include two-phase flow in porous media, sedimentation, and gas dynamics.