AN ADAPTIVE MONTE CARLO MARKOV CHAIN METHOD APPLIED TO THE FLOW INVOLVING SELF-SIMILAR PROCESSES IN POROUS MEDIA

摘要

This article compares adaptive Markov Chain Monte Carlo methods, known as delayed rejection adaptive metropolis (DRAM), with a widely recommended method called Metropolis Hasting (MH), in self-similar media represented by power-law covariance. To carry out this study, we have considered a parameterization of the permeability field by Karhunen-Loeve expansion on porous media. As the numerical solution is approximated on a finite-dimensional space, this article analyzes the convergence of mean and variance obtained from DRAM and MH, refining the finite dimension of the Karhunen-Loeve expansion. It has been noted that the conditioning of data based on the union of the Karhunen-Loeve expansion of DRAM method performs better than the combination of this expansion with MH. Numerical examples related to transient and steady flow on porous media are given to illustrate the efficiency of the proposed method.