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2021 | OriginalPaper | Chapter

8. Performances of the Mixed Virtual Element Method on Complex Grids for Underground Flow

Authors : Alessio Fumagalli, Anna Scotti, Luca Formaggia

Published in: Polyhedral Methods in Geosciences

Publisher: Springer International Publishing

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Abstract

The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults, while the latter are connected to the properties of the rock matrix which might vary abruptly in space. The development of approximation schemes has recently focused on the overcoming of such difficulties with the objective of obtaining numerical schemes with good approximation properties. In this work we carry out a numerical study on the performance of the Mixed Virtual Element Method (MVEM) for the solution of a single-phase flow model in fractured porous media. This method is able to handle grid cells of polytopal type and treat hybrid dimensional problems. It has been proven to be robust with respect to the variation of the permeability field and of the shape of the elements. Our numerical experiments focus on two test cases that cover several of the aforementioned critical aspects.

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previous chapter The Mixed Virtual Element Method for the Richards Equation

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Title: Performances of the Mixed Virtual Element Method on Complex Grids for Underground Flow
Authors: Alessio Fumagalli
Anna Scotti
Luca Formaggia
Publisher: Springer International Publishing
Book: Polyhedral Methods in Geosciences
Print ISBN: 978-3-030-69362-6

Electronic ISBN: 978-3-030-69363-3

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-69363-3_8

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