Non-monotonic Travelling Wave Fronts in a System of Fractional Flow Equations from Porous Media

Motivated by observations of saturation overshoot, this article investigates generic classes of smooth travelling wave solutions of a system of two coupled nonlinear parabolic partial differential equations resulting from a flux function of high symmetry. All boundary resp. limit value problems of t...

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Bibliographic Details
Published in:Transport in porous media 2016-09, Vol.114 (2), p.309-340
Main Authors: Hönig, O., Zegeling, P. A., Doster, F., Hilfer, R.
Format: Article
Language:English
Subjects:
Adaptive systems
Boundary value problems
Civil Engineering
Classical and Continuum Physics
Dynamic systems theory
Dynamical systems
Earth and Environmental Science
Earth Sciences
Flow equations
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Hydrology/Water Resources
Industrial Chemistry/Chemical Engineering
Nonlinear equations
Parabolic differential equations
Partial differential equations
Porous media
System theory
Traveling waves
Wave fronts
Wave velocity
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Summary:Motivated by observations of saturation overshoot, this article investigates generic classes of smooth travelling wave solutions of a system of two coupled nonlinear parabolic partial differential equations resulting from a flux function of high symmetry. All boundary resp. limit value problems of the travelling wave ansatz, which lead to smooth travelling wave solutions, are systematically explored. A complete, visually and computationally useful representation of the five-dimensional manifold connecting wave velocities and boundary resp. limit data is found by using methods from dynamical systems theory. The travelling waves exhibit monotonic, non-monotonic or plateau-shaped behaviour. Special attention is given to the non-monotonic profiles. The stability of the travelling waves is studied by numerically solving the full system of the partial differential equations with an efficient and accurate adaptive moving grid solver.
ISSN:0169-3913
1573-1634
DOI:10.1007/s11242-015-0618-2