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A CFL-Free Explicit Scheme with Compression for Linear Hyperbolic Equations

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Numerical Treatment of Multiphase Flows in Porous Media

Part of the book series: Lecture Notes in Physics ((LNP,volume 552))

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Abstract

We develop an unconditionally stable, explicit numerical scheme for linear hyperbolic equations, which arises as an advection-reaction equation in porous medium flows. The derived scheme generates accurate numerical solutions even if large time steps are used, and conserves mass. Furthermore, this scheme has the capability of performing adaptive compression while maintaining the accuracy of the compressed solution and mass conservation. Numerical results show the strong potential of the method.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, South Carolina, 29208, USA

    Ronald A. DeVore, Hong Wang & Jiang-Guo Liu

  2. INRS-Telecommunications, 16 Place du Commerce le-des-Soeurs (Verdun), Quebec, Canada, H3E 1H6

    Hong Xu

Authors
  1. Ronald A. DeVore
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  2. Hong Wang
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  3. Jiang-Guo Liu
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  4. Hong Xu
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Southern Methodist University, Box 750156, 75275-0156, Dallas, TX, USA

    Zhangxin Chen

  2. Institute for Scientific Computation, Texas A&M University, 77843-3404, College Station, TX, USA

    Richard E. Ewing

  3. Institute of ComputaTional Mathematics, Chinese Academy of Sciences, P.O.Box 2719, 100080, Beijing, P.R.China

    Zhong-Ci Shi

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© 2000 Springer-Verlag Berlin Heidelberg

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DeVore, R.A., Wang, H., Liu, JG., Xu, H. (2000). A CFL-Free Explicit Scheme with Compression for Linear Hyperbolic Equations. In: Chen, Z., Ewing, R.E., Shi, ZC. (eds) Numerical Treatment of Multiphase Flows in Porous Media. Lecture Notes in Physics, vol 552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45467-5_9

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  • DOI: https://doi.org/10.1007/3-540-45467-5_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67566-2

  • Online ISBN: 978-3-540-45467-0

  • eBook Packages: Springer Book Archive

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