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Analytical solutions of the magma equations for molten rocks in a granular matrix

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  • Abourabia, Aly M.
  • Hassan, Kawsar M.
  • Morad, Adel M.

Abstract

In this paper, we present a theoretical study of the two phase system of flow, using a set of partial differential equations in a three-dimensional model in order to focus on the basic physical processes that control magma migration in porous media. It is found that under certain conditions (physically justifiable simplifications) a nonlinear dispersive wave equation which describes the flow of an incompressible fluid through a viscous matrix composed of incompressible solid grains may be derived to give the evolution of the porosity and the analytical solutions of the modeled equation, which exhibit a porosity shock and solitary waves. The types of solutions are defined and discussed over a reasonable range of geophysical parameters stemmed from Galeras volcano data in south-western Colombia. The dispersion properties and the relation between group and phase velocities of the model equation are discussed in the one-dimensional case. The diagrams are drawn to illustrate the physical properties of the solutions.

Suggested Citation

  • Abourabia, Aly M. & Hassan, Kawsar M. & Morad, Adel M., 2009. "Analytical solutions of the magma equations for molten rocks in a granular matrix," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1170-1180.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:1170-1180
    DOI: 10.1016/j.chaos.2009.03.078
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    References listed on IDEAS

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    1. Abourabia, A.M. & El-Danaf, T.S. & Morad, A.M., 2009. "Exact solutions of the hierarchical Korteweg–de Vries equation of microstructured granular materials," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 716-726.
    2. El-Danaf, Talaat S. & Ramadan, Mohamed A. & Abd Alaal, Faysal E.I., 2005. "The use of adomian decomposition method for solving the regularized long-wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 747-757.
    3. Zayed, E.M.E. & Abourabia, A.M. & Gepreel, Khaled A. & El Horbaty, M.M., 2007. "Travelling solitary wave solutions for the nonlinear coupled Korteweg–de Vries system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 292-306.
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    1. Abourabia, A.M. & Morad, A.M., 2015. "Exact traveling wave solutions of the van der Waals normal form for fluidized granular matter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 333-350.

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