A multidimensional Markov chain model for simulating stochastic permeability conditioned by pressure measures

In this paper, we are interested in simulating a stochastic permeability distribution constrained by some pressure measures coming from a steady flow (Poisson problem) over a two-dimensional domain. The permeability is discretized over a regular rectangular gird and considered to be constant by cell but it can take randomly a finite number of values. When such permeability is modeled using a multidimensional Markov chain, it can be constrained by some permeability measures. The purpose of this work is to propose an algorithm that simulates stochastic permeability constrained not only by some permeability measures but also by pressure measures at some points of the domain. The simulation algorithm couples the MCMC sampling technique with the multidimensional Markov chain model in a Bayesian framework.