# A Two-Grid Block-Centered Finite Difference Algorithm for Nonlinear Compressible Darcy–Forchheimer Model in Porous Media

A Two-Grid Block-Centered Finite Difference Algorithm for Nonlinear Compressible... In this paper, a block-centered finite difference method is proposed to discretize the compressible Darcy–Forchheimer model which describes the high speed non-Darcy flow in porous media. The discretized nonlinear problem on the fine grid is solved by a two-grid algorithm in two steps: first solving a small nonlinear system on the coarse grid, and then solving a nonlinear problem on the fine grid. On the coarse grid, the coupled term of pressure and velocity is approximated by using the fewest number of node values to construct a nonlinear block-centered finite difference scheme. On the fine grid, the original nonlinear term is modified with a small parameter $$\varepsilon$$ ε to construct a linear block-centered finite difference scheme. Optimal order error estimates for pressure and velocity are obtained in discrete $$l^\infty (L^2)$$ l ∞ ( L 2 ) and $$l^2(L^2)$$ l 2 ( L 2 ) norms, respectively. The two-grid block-centered finite difference scheme is proved to be unconditionally convergent without any time step restriction. Some numerical examples are given to testify the accuracy of the proposed method. The numbers of iterations are reported to illustrate the efficiency of the two-grid algorithm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

# A Two-Grid Block-Centered Finite Difference Algorithm for Nonlinear Compressible Darcy–Forchheimer Model in Porous Media

, Volume 74 (3) – Aug 1, 2017
30 pages

/lp/springer_journal/a-two-grid-block-centered-finite-difference-algorithm-for-nonlinear-oXAquwNWvO
Publisher
Springer US
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
10.1007/s10915-017-0516-6
Publisher site
See Article on Publisher Site

### Abstract

In this paper, a block-centered finite difference method is proposed to discretize the compressible Darcy–Forchheimer model which describes the high speed non-Darcy flow in porous media. The discretized nonlinear problem on the fine grid is solved by a two-grid algorithm in two steps: first solving a small nonlinear system on the coarse grid, and then solving a nonlinear problem on the fine grid. On the coarse grid, the coupled term of pressure and velocity is approximated by using the fewest number of node values to construct a nonlinear block-centered finite difference scheme. On the fine grid, the original nonlinear term is modified with a small parameter $$\varepsilon$$ ε to construct a linear block-centered finite difference scheme. Optimal order error estimates for pressure and velocity are obtained in discrete $$l^\infty (L^2)$$ l ∞ ( L 2 ) and $$l^2(L^2)$$ l 2 ( L 2 ) norms, respectively. The two-grid block-centered finite difference scheme is proved to be unconditionally convergent without any time step restriction. Some numerical examples are given to testify the accuracy of the proposed method. The numbers of iterations are reported to illustrate the efficiency of the two-grid algorithm.

### Journal

Journal of Scientific ComputingSpringer Journals

Published: Aug 1, 2017

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations