Identification of diffusion parameters in a non-linear convection–diffusion equation using adaptive homotopy perturbation method

Abstract

This paper is concerned with the numerical identification of diffusion parameters in a non-linear convection–diffusion equation, which arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations. In order to overcome the defect of the local convergence of traditional methods, an adaptive homotopy perturbation method is applied to solve this parameter identification inverse problem. The adaptive homotopy perturbation method provides a simple way to adapt computational refinement to the choice of the homotopy parameter. Numerical simulations illustrate that the proposed algorithm is globally convergent and computationallyefficient.