Adaptive numerical homogenization of non-linear diffusion problems
Abstract
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization theory and uses a locally mass-conservative formulation. In addition, we discuss some properties of the standard non-linear solvers and use an error estimator to perform a local mesh refinement. The main idea is to compute the effective parameters in such a way that the computational complexity is reduced without affecting the accuracy. We perform some numerical examples to illustrate the behaviour of the adaptive scheme and of the non-linear solvers. Finally, we discuss the advantages of the implementation of the numerical homogenization in a periodic media and the applicability of the same scheme in non-periodic test cases such as SPE10th project.
Cite
@article{arxiv.1904.10665,
title = {Adaptive numerical homogenization of non-linear diffusion problems},
author = {Manuela Bastidas and Carina Bringedal and Sorin Pop and Florin Radu},
journal= {arXiv preprint arXiv:1904.10665},
year = {2020}
}