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Diffuse approximation method for solving natural convection in porous media

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The diffuse approximation is presented and applied to natural convection problems in porous media. A comparison with the control volume-based finite-element method shows that, overall, the diffuse approximation appears to be fairly attractive.

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H :

height of the cavities

I :


K :


〈p(M i ,M)〉 :

line vector of monomials

p T :


M :

current point


Nusselt number


inner radius


outer radius


Rayleigh number

x, y :

cartesian coordinates

u, v :

velocity components

T :


〈αM〉 :

vector of estimated derivatives

α t :

thermal diffusivity

β :

coefficient of thermal expansion


practical aperture of the weighting function


scalar field

ω(M, M i ):

weighting function




kinematic viscosity


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Prax, C., Sadat, H. & Salagnac, P. Diffuse approximation method for solving natural convection in porous media. Transp Porous Med 22, 215–223 (1996).

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Key words

  • natural convection
  • diffuse approximation
  • control volume finite-element method