Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/73910
Title: A two-grid block-centered finite difference algorithm for nonlinear compressible darcy–Forchheimer model in porous media
Authors: Liu, W 
Cui, J 
Keywords: Darcy–Forchheimer model
Error estimates
Finite difference method
Numerical experiment
Two-grid method
Issue Date: 2018
Publisher: Springer
Source: Journal of scientific computing, 2018, v. 74, no. 3, p. 1786-1815 How to cite?
Journal: Journal of scientific computing 
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 (Formula presented.) to construct a linear block-centered finite difference scheme. Optimal order error estimates for pressure and velocity are obtained in discrete (Formula presented.) and (Formula presented.) 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.
URI: http://hdl.handle.net/10397/73910
ISSN: 0885-7474
DOI: 10.1007/s10915-017-0516-6
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