Identification of space-dependent permeability in nonlinear diffusion equation from interior measurements using wavelet multiscale method

Abstract

Numerical identification of the space-dependent permeability function in a nonlinear diffusion equation is considered. This problem plays an important role in promoting the permeability estimation within multiphase porous media flow. The forward problem is discretized using finite-difference methods and the identification is formulated as a minimization problem with regularization terms. To overcome disturbance of local minimum, a wavelet multiscale method is applied to solve this inverse problem. This method works by decomposing the inverse problem into multiple scales using wavelet transform so that the original inverse problem is reformulated to be a sequence of subinverse problems relying on scale variables, and successively solving these subinverse problems according to the size of scale from the longest to the shortest. The stable and fast regularized Gauss–Newton method is applied to each scale. Numerical simulations show the wide convergence, computational efficiency, anti-noise and de-noising abilities of the proposed algorithm.