Journal of Scientific Computing

, Volume 74, Issue 2, pp 1115–1145 | Cite as

Block-Centered Finite Difference Method for Simulating Compressible Wormhole Propagation



In this paper, the block-centered finite difference method is introduced and analyzed to solve the compressible wormhole propagation. The coupled analysis approach to deal with the fully coupling relation of multivariables is employed. By this, stability analysis and error estimates for the pressure, velocity, porosity, concentration and its flux in different discrete norms are established rigorously and carefully on non-uniform grids. Finally, some numerical experiments are presented to verify the theoretical analysis and effectiveness of the given scheme.


Block-centered finite difference Compressible wormhole propagation Non-uniform grids Error estimates Numerical experiments 

Mathematics Subject Classification

65M06 65M12 65M15 



The authors would like to thank the editor and referees for their valuable comments and suggestions which helped us to improve the results of this paper. This work is supported by the National Natural Science Foundation of China Grant No. 11671233, the Science Challenge Project No. JCKY2016212A502.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanChina

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