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A Shock Indicator for Adaptive Schemes for Conservation Laws

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Abstract

In this paper we discuss an adaptive method for the compulation of discontinuous solutions of hyperbolic conservation laws. In each time level we use very simple sensors for detecting discontinuities of the solution. The adaptive scheme use first order upwind flux computation in the immediate neighborhood of these irregularities. Since the differential equation holds in the smoothness domain, we follow the characteristics in the lime marching procedure at grid points in that domain.

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REFERENCES

  • Bacry, E., Mallat, S., and Papanicolau, G. (1992). A wavelet based space-time adaptive numerical method for partial differential equations. Math. Mod. Num. Anal. 26, 793-834.

    Google Scholar 

  • Bihari, B. L., and Harten, A. (1995). Application of generalized wavelets: an adaptive multi-resolution numerical scheme. J. Comp. App. Math. 61, 275-321.

    Google Scholar 

  • Courant, R., Isaacson, E., and Rees, M. (1952). On the solution of nonlinear hyperbolic differential equations by finite differences. Comm. Pure Appl. Math. 5, 243.

    Google Scholar 

  • Cunha, C., and Gomes, S. M. (1994). A high resolution numerical method for conservation law using biorthogonal wavelets. in Proc. XV Congr. Ibero Latino Americano sobre Métodos Computacionais para Engenharias, Belo Horizonte, pp. 234-244.

  • Glowinski, R., Lawton, W. M., Ravachol, M., and Tenenbaum, E. (1989). Wavelet solution of linear and nonlinear eliptic, parabolic, and hyperbolic problems in one space dimension. AWARE INC. Technical Report.

  • Harten, A. (1993). Discrete multiresolution analysis and generalized wavelets. Appl. Num. Math. 12, 153-192.

    Google Scholar 

  • Lake, L. W. (1989). Enhanced Oil Recovery, Prentice Hall.

  • Le Veque, R. (1990). Numerical Methods for Conservation Laws, Birkhauser Verlag.

  • Liandrat, J., and Tchamitchian, Ph. (1990). Resolution of the ID regularized Burgers equation using a spatial wavelet approximation. NASA-ICASE Report No. 90-83.

  • Maday, Y., Perrier, V., and Ravel, J. C. (1991). Adaptativité dynamique sur bases d'ondelettes pour Papproximation d'equations aux derivées partielles. C. R. Acad. Sci. Paris 312I, 405-410.

    Google Scholar 

  • Sever, M. (1984). Order of dissipation near rarefaction centers. Progress and Supercomputing in Computational Fluid Dynamics. Proceedings of US-Israel Workshop. Birkhauser.

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Authors and Affiliations

  1. Instituto de Matematica Estatistica e Ciências de Computacao, Universidade Estadual de Campinas, Campinas SP, Brasil

    Cristina Cunha & Sônia M. Gomes

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  1. Cristina Cunha
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  2. Sônia M. Gomes
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Cunha, C., Gomes, S.M. A Shock Indicator for Adaptive Schemes for Conservation Laws. Journal of Scientific Computing 12, 205–214 (1997). https://doi.org/10.1023/A:1025625900355

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