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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
- H :
height of the cavities
- I :
- K :
- 〈p(M i ,M)〉 :
line vector of monomials
- p T :
- M :
- x, y :
- u, v :
- T :
- 〈αM〉 :
vector of estimated derivatives
- α t :
- β :
coefficient of thermal expansion
practical aperture of the weighting function
- ω(M, M i ):
Nayroles, B., Touzot, G. and Villon, P.: Generalizing the finite element method. Diffuse approximation and diffuse elements,Comput. Mech. 10 (1992), 307–318.
Nayroles, B., Touzot, G. and Villon, P.: l'approximation diffuse,C.R. Acad. Sci. Paris, Série II,313 (1991), 293–296.
Baliga, B. R. and Patankar, S. V.: A new finite element formulation for convection diffusion problems,Numerical Heat Transfer 3 (1980), 393–409.
Baliga, B. R. and Patankar, S. V.: A control volume finite-element method for two-dimensional fluid flow and heat transfer,Numerical Heat Transfer 6 (1983), 245–261.
Prakash, C. and Patankar, S. V.: A control volume-based finite-element method for solving the Navier-Stokes equations using equal order velocity-pressure interpolation,Numerical Heat Transfer 8 (1985), 259–280.
Ni, J. and Beckermann, C.: Natural convection in a vertical enclosure filled with anisotropic porous media,J. Heat Transfer 113 (1991), 1033.
Shiralkar, G. S., Haajizadeh, M. and Tien, C. L.: Numerical study of high Rayleigh number convection in a porous enclosure,Numerical Heat Transfer 6 (1983), 223–234.
Kim, C. J. and Ro, S. T.: Numerical investigation on bifurcative natural convection in an air-filled horizontal annulus,Proc. Tenth Internat. Heat Transfer Conference, Brighton, U.K., Vol. 7, 1994, pp. 85–90.
Barbosa Mota, J. P. and Saatdjian, E.: Hysteresis en convection naturelle entre deux cylindres concentriques poreux, Société Française des Thermiciens, Colloque annuel, 1993.
About this article
Cite this article
Prax, C., Sadat, H. & Salagnac, P. Diffuse approximation method for solving natural convection in porous media. Transp Porous Med 22, 215–223 (1996). https://doi.org/10.1007/BF01143516
- natural convection
- diffuse approximation
- control volume finite-element method