Abstract
In this paper we extend the Method of Transport to adaptivity in space and time. The algorithm is described in detail for the linear advection equation in conservation form. A numerical example is presented for two-dimensional Euler equations.
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References
M. Fey, Ein echt mehrdimensionales Verfahren zur Lösung der Eulergleichungen, PhD thesis, ETH Zürich, (1993).
M. Fey, Decomposition of the multidimensional Euler equations into advection equations, Seminar for Applied Mathematics, ETH Zürich, Research Report No. 95–14.
M. Fey, Das Transportverfahren von hoher Ordnung für skalare Erhaltungsgleichungen, Manuscript, (1995).
M. Fey, R. Jeltsch, A.-T. Morel, Multidimensional Schemes for Non-Linear Systems of Hyperbolic Conservation Laws, Numerical Analysis 1995, Edited by D. Griffiths and G.A. Watson, Longman, 1996.
M. Fey, R. Jeltsch, J. Maurer and A.-T. Morel, The method of transport for nonlinear systems of hyperbolic conservation laws in several space dimensions, Seminar for Applied Mathematics, ETH Zürich, Research Report No. 97–12.
M. Fey and H.J. Schroll, Monotone Split-and Unsplit Methods for a Single Conservation Law in Two Space Dimensions, Institut für Geometrie und praktische Mathematik, RWTH Aachen, Research Report, No. 57, (1989).
T. Gutzmer, AMCIT-A New Method for Mesh Adaptation when Solving Time-Dependent Conservation Laws, PhD thesis, ETH Zürich, (1998).
T. Gutzmer, Dynamic Load Balancing for Adaptive Mesh Coarsening in CFD, Parallel Computational Fluid Dynamics’ 97, Proceedings of the Parállel CFD’ 97 Conference, Edited by A. Ecer, D. Emerson, J. Periaux and N. Satofuka, Elsevier Science B.V., to appear.
A. Harten, Adaptive Multiresolution Schemes for Shock Computations, J. Comp. Phys., 115 (1994), 319–338.
R. LeVeque, Simplified Multi-Dimensional Flux Limiter Methods, Proceedings of the ICFD Conference on Numerical Methods for Fluid Dynamics, Reading, 1992.
J. Maurer, The Method of Transport for mixed hyperbolic-parabolic equations, Seminar for Applied Mathematics, ETH Zürich, Research Report No. 97–13.
A.-T. Morel, A Genuinely Multidimensional High-Resolution Scheme for the Shallow-Water Equations, PhD thesis, ETH Zürich, (1997).
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© 1999 Springer Basel AG
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Gutzmer, T. (1999). Adaptive Mesh Coarsening in CFD. In: Fey, M., Jeltsch, R. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 129. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8720-5_47
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DOI: https://doi.org/10.1007/978-3-0348-8720-5_47
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9742-6
Online ISBN: 978-3-0348-8720-5
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