Abstract
A multiresolution method for a one-dimensional strongly degenerate parabolic equation modeling sedimentation-consolidation processes is introduced. The method is based on the switch between central interpolation or exact evaluation of the numerical flux combined with a thresholded wavelet transform applied to point values of the solution to control the switch. A numerical example is presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berres, S., Bürger, R., Karlsen, K.H., Tory, E.M.: Strongly degenerate parabolichyperbolic systems modeling polydisperse sedimentation with compression. SIAM J. Appl. Math. 64, 41–80 (2003)
Bihari, B.L., Harten, A.: Application of generalized wavelets: a multiresolution scheme. J. Comp. Appl. Math. 61, 275–321 (1995)
Bihari, B.L., Harten A.: Multiresolution schemes for the numerical solution of 2-D conservation laws I, SIAM J. Sci. Comput. 18, 315–354 (1997)
Bürger, R., Coronel, A., Sepúlveda, M.: A semi-implicit monotone difference scheme for an initial- boundary value problem of a strongly degenerate parabolic equation modelling sedimentation-consolidation processes. Math. Comp., to appear.
Bürger, R., Kozakevicius, A., Sepúlveda, M.: Multiresolution schemes for strongly degenerate parabolic equations, Preprint 2005-14, Departamento de Ingenierýa Matemática, Universidad de Concepción, Concepción, Chile.
Chiavassa, G., Donat, R.: Point value multiscale algorithms for 2D compressive flows. SIAM J. Sci. Comput. 23, 805–823 (2001)
Gottlieb, S., Shu, C.-W.: Total variation diminishing Runge-Kutta schemes. Math. Comp. 67, 73–85 (1998)
Harten, A.: Multiresolution algorithms for the numerical solution of hyperbolic conservation laws. Comm. Pure Appl. Math. 48, 1305–1342 (1995)
Holmström, M.: Solving hyperbolic PDEs using interpolating wavelets. SIAM J. Sci. Comp. 21, 405–420 (1999)
Mascia, C., Porretta, A., Terracina, A.: Nonhomogeneous Dirichlet problems for degenerate parabolic-hyperbolic equations. Arch. Rat. Mech. Anal. 163, 87–124 (2002)
Michel, A., Vovelle, J.: Entropy formulation for parabolic degenerate equations with general Dirichlet boundary conditions and application to the convergence of FV methods. SIAM J. Numer. Anal. 41, 2262–2293 (2003)
Roussel, O., Schneider, K., Tsigulin, A., Bockhorn, H.: A conservative fully adaptive multiresolution algorithm for parabolic PDEs. J. Comp. Phys. 188, 493–523 (2003)
Shu, C.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In: Cockburn, B., Johnson, C., Shu, C.-W. and Tadmor, E., Advanced Numerical Approximation of Nonlinear Hyperbolic Equations (Quarteroni, A. (ed)), Lecture Notes in Mathematics vol. 1697, Springer-Verlag, Berlin, 325–432 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Bürger, R., Kozakevicius, A. (2006). A Multiresolution Method for the Simulation of Sedimentation-Consolidation Processes. In: de Castro, A.B., Gómez, D., Quintela, P., Salgado, P. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34288-5_33
Download citation
DOI: https://doi.org/10.1007/978-3-540-34288-5_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34287-8
Online ISBN: 978-3-540-34288-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)