Equivalent initial conditions for compatibility between analytical and computational solutions of convection in porous media

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20 Citations (Scopus)

Abstract

The derivation of a set of compatibility conditions for the equivalence between a weak non-linear analytical solution and any computational or numerical solution is presented. Both direct and inverse transformations are derived and shown to apply well for arbitrary initial conditions, provided that a validity condition of the asymptotic expansion associated with the weak non-linear solution is not violated. The results presented by using these compatibility conditions for a comparison between computational and analytical transitional values of a scaled Rayleigh number, that represents the point of transition from steady-to-chaotic solutions, show very good agreement within the validity domain of the asymptotic expansion.

Original languageEnglish (US)
Pages (from-to)197-208
Number of pages12
JournalInternational Journal of Non-Linear Mechanics
Volume36
Issue number2
DOIs
StatePublished - Mar 2001
Externally publishedYes

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Compatibility Conditions
Compatibility
compatibility
Porous Media
Convection
Asymptotic Expansion
Porous materials
Initial conditions
convection
Rayleigh number
Analytical Solution
Equivalence
Numerical Solution
expansion
Arbitrary
equivalence
derivation

ASJC Scopus subject areas

  • Mechanical Engineering
  • Statistical and Nonlinear Physics

Cite this

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abstract = "The derivation of a set of compatibility conditions for the equivalence between a weak non-linear analytical solution and any computational or numerical solution is presented. Both direct and inverse transformations are derived and shown to apply well for arbitrary initial conditions, provided that a validity condition of the asymptotic expansion associated with the weak non-linear solution is not violated. The results presented by using these compatibility conditions for a comparison between computational and analytical transitional values of a scaled Rayleigh number, that represents the point of transition from steady-to-chaotic solutions, show very good agreement within the validity domain of the asymptotic expansion.",
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AB - The derivation of a set of compatibility conditions for the equivalence between a weak non-linear analytical solution and any computational or numerical solution is presented. Both direct and inverse transformations are derived and shown to apply well for arbitrary initial conditions, provided that a validity condition of the asymptotic expansion associated with the weak non-linear solution is not violated. The results presented by using these compatibility conditions for a comparison between computational and analytical transitional values of a scaled Rayleigh number, that represents the point of transition from steady-to-chaotic solutions, show very good agreement within the validity domain of the asymptotic expansion.

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