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arXiv · 1904.10665

Adaptive numerical homogenization of non-linear diffusion problems

Manuela Bastidas·Carina Bringedal·Sorin Pop·Florin Radu
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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.

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Manuela Bastidas, Carina Bringedal, Sorin Pop, Florin Radu. 2019-04-24. Adaptive numerical homogenization of non-linear diffusion problems. https://arxiv.org/abs/1904.10665

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