A Study of the Modelling Error in Two Operator Splitting Algorithms for Porous Media Flow

Operator splitting methods are often used to solve convection-diiusion problems of convection dominated nature. However, it is well known that such methods can produce signiicant (splitting) errors in regions containing self sharpening fronts. To amend this shortcoming, corrected operator splitting methods have been developed. These approaches use the wave structure from the convection step to identify the splitting error. This error is then compensated for in the diiusion step. The main purpose of the present work is to illustrate the importance of the correction step in the context of an inverse problem. The inverse problem will consist of estimating the fractional ow function in a one-dimensional saturation equation.